Ambiguity of results contradicting each other when considering several alternative investment projects, depending on the chosen method of its economic assessment

Projects are called alternative if the implementation of one of them makes it impossible or inappropriate to implement the others.

Most often, alternative projects are projects that serve to achieve the same goal, but only one of the alternative projects can be implemented.

The most difficult problem in investment analysis is making a decision on choosing the best of alternative projects. In this situation, the analyst should:

choose the best of several projects aimed at achieving the same investor goal;

choose the best one from several independent projects if investment capital is not enough to implement all of them;

choose different options for one project.

Choosing the best investment option from a number of alternatives is done in steps:

the compliance of each option with all existing technical, environmental, social and other restrictions is checked;

an analysis of the financial viability of each project is carried out. Projects that do not meet the first two conditions are excluded from further consideration. Sometimes their parameters, financing conditions and (or) the organizational and economic mechanism for implementation can be adjusted in such a way as to satisfy the conditions of feasibility and financial solvency;

the absolute effectiveness of each project is assessed using a system of international indicators, such as: payback period, accounting return on investment;

the comparative effectiveness of projects is assessed.

It is also impossible not to dwell on the problem of inconsistency in performance indicators.

When choosing between mutually exclusive projects, a situation may arise where one of them has a higher net present value, another has a higher return on investment index, and the third has a higher internal rate of return.

This situation is called a criteria conflict.

Efficiency is a deeper characteristic of the functioning of the system as a whole (both from the cost and effectiveness side). That is why the assessment and selection of alternative investment projects should be based on efficiency indicators, and indicators of various types of effects can and should be used as additional ones when making investment decisions.

Based on the above arguments, and also taking into account the basic concept of financial analysis - the concept of limited resources, it is believed that the return on investment index (PI) should be the main criterion for choosing the best of competing investment projects.

The PI index as an indicator of efficiency has a number of undeniable advantages, namely:

takes into account the time distribution of real money flows;

considers the sum of the effects obtained over the entire life of the project;

allows you to correctly compare projects that differ in their scale (“physical” volumes of investment, production, sales, etc.).

As for the internal rate of return indicator, many researchers do not recommend taking it as the main criterion for choosing the best of alternative projects.

The main claims made against this indicator can be reduced to several points:

the inability to choose among projects with different lifespans;

the impossibility of correctly comparing projects with different investment volumes;

unrealistic assumptions about the conditions for reinvesting cash proceeds from projects;

multiple values ​​of the internal profitability ratio for projects with an unconventional cash flow structure.

Unfortunately, the current regulatory documents are aimed at effect indicators when choosing alternative projects.

In accordance with the Methodological recommendations for assessing the effectiveness of investment projects, approved by the Ministry of Economy of the Russian Federation, the Ministry of Finance of the Russian Federation, the State Committee of the Russian Federation for Construction, Architectural and Housing Policy on June 21, 1999 N VK 477, when comparing alternative investment projects, preference should be given project with the greatest effect value Para. 5 of section 2.2 of the Methodological recommendations for assessing the effectiveness of investment projects approved by the Ministry of Economy of the Russian Federation, the Ministry of Finance of the Russian Federation, the State Committee of the Russian Federation for Construction, Architectural and Housing Policy on June 21, 1999 N VK 477. At the same time, the main indicator characterizing the absolute and the comparative effectiveness of investment projects is the value of the expected net cash income.

Investment projects financed in whole or in part from the relevant budget are subject to verification before their approval for the effectiveness of the use of funds allocated for capital investments. The purpose of such verification, in addition to the effectiveness of the capital investments made, is to prevent the creation of facilities, the use of which violates the rights of individuals and legal entities and the interests of the state, does not meet established requirements, etc. At the same time, it is stipulated that the cases and procedure for carrying out inspections are established accordingly by regulatory legal acts of the Government of the Russian Federation, regulatory legal acts of constituent entities of the Russian Federation, and municipal legal acts.

In particular, the verification mechanism for federal budget funds is established by Decree of the Government of the Russian Federation of August 12, 2008 No. 590. The predominant methods for assessing the effectiveness of modernization as a form of current investment are foreign methods based on discounted cash flows. It is these methods that are enshrined in the already mentioned Methodological Recommendations for assessing the effectiveness of investment projects.

The rules for conducting inspections of investment projects involving the construction, reconstruction of capital construction projects and (or) other investments in fixed capital, financed in whole or in part from the budget of a constituent entity of the Russian Federation or a municipal entity, are approved accordingly by the regulatory legal acts of the constituent entity of the Russian Federation or municipal legal acts ( for example, Decree of the Government of the Moscow Region dated 08/09/2010 No. 643/32 “On approval of the Procedure for checking investment projects for the effectiveness of using budget funds of the Moscow Region allocated for capital investments” URL: http://www.referent.ru/3/ 75541; Resolution of the administration of the Voskresensky municipal district of the Moscow region dated October 22, 2010 No. 2023 “On approval of the Procedure for checking investment projects for the effectiveness of using budget funds of the Voskresensky municipal district allocated for capital investments” URL: http://www.regionz.ru/ index.php?ds=978171, etc.)

Based on the above analysis, it can be argued that focusing on indicators of the effect created by the project does not stimulate increasing the efficiency of social production and the optimal use of limited resources.

In this regard, it seems that the main criteria when choosing alternative projects should be the return on investment index and the internal rate of return of the project.

However, it cannot be said that when assessing the effectiveness of investments, it is necessary to remember the possibility of errors and not rely on one criterion, especially since each of them emphasizes a particular aspect of the project’s state.

Only the various criteria taken together provide the most complete picture of the effectiveness of making an investment decision.

Method for calculating the net present effect

This method is based on comparing the value of the original investment (IC) with the total discounted net cash flows it generates over the forecast period.

The NPV indicator represents the difference between all cash inflows and outflows brought to the current point in time (the moment of evaluation of the investment project). It shows the amount of cash an investor expects to receive from a project after cash inflows have paid off its initial investment costs and the periodic cash outflows associated with the project. Since cash payments are valued based on their time value and risk, NPV can be interpreted as the value added by the project. It can also be interpreted as the investor's total return.

In other words, for a payment flow CF (Cash Flow), where -- payment in years () and an initial investment IC (Invested Capital) in the amount of net present value is calculated using the formula:

where is the discount rate.

In a generalized version, investments should also be discounted, since in real projects they are not carried out simultaneously (in the zero period), but are extended over several periods. Calculation of NPV is a standard method for assessing the effectiveness of an investment project and shows an assessment of the effect of an investment given to the present moment in time, taking into account the different time value of money. If the NPV is greater than 0, then the investment is economically efficient, and if the NPV is less than 0, then the investment is economically unprofitable (that is, an alternative project, the profitability of which is accepted as the discount rate, requires less investment to obtain a similar income stream).

Using the NPV, you can also evaluate the comparative effectiveness of alternative investments (with the same initial investments, the project with the highest NPV is more profitable). But still, for comparative analysis, relative indicators are more applicable. In relation to the analysis of investment projects, such an indicator is the internal rate of return.

Internal rate of return(English internal rate of return, generally abbreviated as IRR) is the interest rate at which the net present value (net present value - NPV) is equal to 0. NPV is calculated based on the stream of payments discounted to today.

Thus, for a flow of payments CF, where is payment in years () and an initial investment of the internal rate of return is calculated from the equation:

When making investment decisions, IRR is used to calculate the rate of alternative investments. When choosing from several projects with different IRR, the project with the maximum IRR value is selected. This criterion is not used if cash flows change sign several times during the period under review.

As for the IRR indicator, it has a number of serious shortcomings. Let us briefly describe them:

• 1. In a comparative analysis of alternative projects, the IRR criterion can be used rather conditionally.
• 2. The IRR criterion shows only the maximum level of costs that can be associated with the project being evaluated.
• 3. One of the significant disadvantages of the IRR criterion is that, unlike the NPV criterion, it does not have the property of additivity, i.e. for two investment projects A and B, which can be implemented simultaneously:

NPV(A + B) = NPV(A) + NPV(B),

but IRR(A + B) is not equal to IRR(A) + IRR(B).

According to the requirements of the Central Bank of the Russian Federation, banks are required to indicate the EIR - the effective interest rate. This rate can be independently calculated by the borrower using a spreadsheet editor and the IRR formula (in Microsoft Excel IRR).

Index Current version return on investment (PI from Profitability Index) is calculated as the ratio of the sum of discounted cash flows to the initial investment:

NCF (net cash flow) -- net cash flows (discounted),

Investments

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.

If PI > 1 -- the project should be accepted, PI< 1 -- отвергнуть. В случае, когда PI = 1 предполагается отсутствие как прибыли, так и убытков.

Method for determining the payback period of investments

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 uniform distribution of projected income from the investment. If income is distributed evenly over the years, then the payback period is calculated by dividing one-time costs by the amount of annual income due to them. When a fraction is obtained, it is rounded up to the nearest whole number. If the profit is distributed unevenly, then the payback period is calculated by directly calculating the number of years during which the investment will be repaid by cumulative income. The general formula for calculating the PP indicator is:

A very common situation is when a manager needs to make a choice from several possible investment projects for implementation. The reasons may be different, including the limited availability of financial resources.

Of all the criteria considered, the most acceptable ones for making investment decisions are the NPV, IRR and PI criteria. Despite the noted relationship between these indicators, when assessing alternative investment projects, the problem of choosing a criterion still remains. The main reason lies in the fact that NPV is an absolute indicator, while PI and IRR are relative.

When making a decision, you can be guided by the following considerations:

• a) it is recommended to choose an option with a large NPV, since this indicator characterizes the possible increase in the economic potential of the enterprise (increasing the economic power of the enterprise is one of the highest priority targets);
• b) it is also possible to calculate the IRR coefficient for incremental indicators of capital investments and income; Moreover, if IRR > CC, then the incremental costs are justified and it is advisable to accept a project with large capital investments.

The most preferred criterion is the NPV criterion. There are two main arguments in favor of this criterion:

It gives a probable estimate of the capital gain of the enterprise if the project is accepted; It has the property of additivity, which allows you to add the values ​​of the NPV indicator for various projects and use the aggregated value to optimize the investment portfolio.

When considering several alternative investment projects, depending on the chosen method of its economic assessment, one can obtain far from unambiguous results, often contradicting each other, and this despite the fact that there are obvious relationships between the NPV, PI, IRR and CC indicators:

if NPV > 0, then simultaneously IRR > CC and PI > 1;

if NPV = 0, then simultaneously IRR = CC and PI = 1;

There is an opinion among financial analysts that net present value (NPV) is not the most effective criterion for assessing the choice of a financial decision.

The NPV indicator is very informative for various participants in an investment project. A positive value characterizes the increase in net cash flow for the project, and therefore increases the market value of the company and, accordingly, the welfare of its owners. A high positive NPV value is a kind of project shield in case of negative changes in the external environment. However, you should pay attention to two significant factors - the planning horizon (duration of the investment project) and the choice of discount rate.

If we focus solely on the NPV indicator, then among alternative investment projects, most often the optimal one will be a project that requires significant investments and takes longer to implement. Let's consider a hypothetical example where the discount rate is 10% (Table 1).

Table 1. Comparative analysis of alternative investment projects

The absolute value of the NPV indicator of project A is six times higher than the NPV value of project B. Obviously, it is not entirely correct to compare alternative investment projects that are not comparable in terms of the time factor. To level out temporary incomparability, you can:

• - predict additional investments and net cash flow for a shorter project for a period equal to the duration of an alternative project (repetition of a shorter investment project);
• - use methods such as the chain repetition method within the overall duration of projects; method of endless chain repetition of compared projects; equivalent annuity method.

It should be noted that these methods can be used in conditions of certainty and risk. In conditions of high risk and uncertainty, these methods should be abandoned and alternative projects of different durations should be ranked based on calculated NPV values ​​and other criteria. Project implementation time is a weak side of the NPV indicator and largely depends on the accuracy of the forecast made, since the external environment is characterized by a high degree of unpredictability. The second important factor when calculating NPV is the choice of discount rate. It depends on a number of factors. An arbitrary choice of discount rate should not be allowed, from the lowest interest rate on government securities (guaranteed return) to unreasonably high interest rates, taking into account all possible interests and risks of investors.

Based on the above judgments, we will highlight the main positive and negative aspects of the NPV indicator, which are shown in Table 2:

Table 2. Strengths and weaknesses of the NPV indicator

Thus, it is not possible to unequivocally state that the NPV indicator is absolutely objective when making investment decisions. This requires more than one formalized argument, otherwise single-criteria decision-making can lead to serious negative consequences. It is advisable to calculate several both absolute and relative indicators, taking into account from which position the project is assessed, and, accordingly, make an informed decision.

However, after calculating all the coefficients, certain contradictions may arise between them. Therefore, it is necessary, depending on the specifics of the alternative investment project, taking into account from whose side the project is being assessed, to weigh the significance of certain coefficients (that is, determine priority), and use the rest as auxiliary ones.

alternative project payback given

Evaluation of investments in conditions of shortage of financial resources

One of the incentives that forces a company to choose one or more from several promising and profitable investment projects is the limited availability of financial resources.

Financial limit for investment represents a fixed limit on the annual amount of capital investment that a company can afford based on its financial situation. If there are financial restrictions on investment, a firm can accept some investment projects that make up a combination that will provide the greatest effect.

Suppose a firm has the following investment proposals, ranked in descending order by profitability index (the ratio of the present value of future net cash flows to initial costs):

Based on its financial situation, the company plans to allocate 2.0 million rubles for investments. In this case, the company will select those of the proposed projects that promise the greatest profitability, and the amount of all initial costs will not exceed 2.0 million rubles.

In our case, these are proposals (3, 6, 4, 2 and 5), since they have the highest profitability, and the amount of starting capital is equal to 2.0 million rubles. (800,000 + 200,000 + 350,000 + 250,000 + 400,000).

The company will not accept proposal No. 1, although the initial costs are significantly lower than other projects, and its profitability exceeds one, which in other conditions would be quite acceptable.

When considering several alternative investment projects, Depending on the chosen method of its economic assessment, you can get far from unambiguous results, often contradicting each other. At the same time, between the considered indicators of investment efficiency ( NPV PP, IRR) there is a certain relationship.

So, if NPV> 0, then simultaneously IRR > SSi P.I.> 1; at NPV= 0, simultaneously IRR> SSi PI = 1.

To decide which criterion is best to use in this case, let’s look at an example.

Example 4.13

The company is considering four options for investment projects that require equal starting capital investments (2,400 thousand rubles). It is necessary to make an economic assessment of each project and select the optimal one. Projects are financed through a bank loan at an annual interest rate of 18%.

The dynamics of cash flows and calculated efficiency indicators are given in table. 4.9.

Table 4.9

Dynamics of cash flows and calculated performance indicators,

Projected Cash Flows
	project 1	project 2	project 3	project 4
Fourth
Indicators
PP, years

Analysis of the data presented in the table allows us to draw the following conclusions:

• 1. Best indicator NPV= 809.6 thousand rubles. belongs to the first project. Consequently, the adoption of this project promises the greatest capital gain.
• 2. In this first investment project, the greatest value of all the indicators under consideration is PI == 1.337, i.e. the reduced sum of cash flow terms is 33.7% higher than the starting capital.
• 3. The highest value of the indicator IRR= 27.8% has a fourth investment project. However, given that the bank provided the loan at 18.0% per annum, this advantage is not significant.
• 4. Shortest payback period PP= 1.79 has the fourth project, but given that the difference in payback time between the largest value (2.33 years) and the smallest value is a little more than six months, this advantage can be neglected.

Thus, having considered four investment projects according to four indicators, we can give preference to the first project.

In works devoted to methods of economic assessment of investments, preference is given to the indicator NPV

This is explained by the following factors:

• 1. This indicator characterizes the projected amount of capital growth of the enterprise in the event of the implementation of the proposed investment project.
• 2. When designing the use of several investment projects, you can summarize the indicators NPV each of them, which gives in aggregate form the value of capital gains.

When analyzing alternative investment projects, the use of the internal rate of return indicator - IRR due to a number of inherent disadvantages, it should be limited. Let's look at some of them.

1. Because IRR is a relative indicator, then based on its value, it is impossible to draw a conclusion about the size of the increase in the enterprise’s capital when considering alternative projects.

Suppose there are two alternative projects (Table 4.10). If we judge the project only by the indicator IRR then project A is more preferable. However, it provides less capital growth than Project B.

If an enterprise has the opportunity to implement project B without borrowing funds, then it becomes more attractive.

Data from two projects, thousand rubles.

Project	Size investment	Cash flow by year				NPV with a yield of 15%
		first	second	third year 3

If we judge projects only by the indicator IRR then project A is more preferable. At the same time, it provides a capital gain in a smaller amount than Project B.

If an enterprise has the opportunity to implement project B without borrowing money, then it becomes more attractive.

• 2. From the definition of the essence of the indicator IRR it follows that it shows the maximum relative level of costs associated with the implementation of the investment project. Consequently, if this indicator is the same for two investment projects and exceeds the price of investment (for example, bank interest on borrowed capital intended for the implementation of projects), then other criteria must be used to select between projects.
• 3. Indicator IRR unsuitable for analyzing projects in which cash flow alternates with inflows and outflows of capital. In this case, the conclusions drawn based on the indicator IRR may be incorrect.

Comparative analysis of projects of various durations

When comparing projects of different durations, it is advisable to use the following procedure:

1. Determine the common multiple of the number of years of implementation of each project. For example, Project A has a duration of 2 years and Project B has a duration of 3 years, therefore the common multiple for these projects will be 6 years. Where can we make the assumption that within 6 years, project A can be repeated three times (three cycles), and project B - twice (two cycles).

Consequently, project A will have three streams of annual payments: the first-second year, the third-fourth year and the fifth-sixth year, and project B will have two streams: the first-third year and the third-sixth year.

• 2. Assuming that each project will be repeated several cycles, calculate the total value of the indicator NPV for recurring projects.
• 3. Select the project from the original ones whose total value NPV repeating flow will be greatest.

The total ARC of a repeating flow is found by the formula:

Where NPV^- net present value of the original (repeating) project; j- the duration of this project; P - number of repetitions (cycles) of the original project (number of terms in brackets); i- interest rate in fractions of a unit used for discounting (rate of expected income)

Example 4.14

There are a number of investment projects, the implementation of which requires an equal amount of starting capital - 200 thousand rubles. The price of capital, i.e. the estimated income is 10%. It is necessary to select the most optimal one if the payment flows (inflow) are characterized by the following data, thousand rubles:

• Project A: 100; 140;
• Project B: 60; 80; 120;
• Project B: 100; 144.

Calculation NPV We present each project in the table. 4.11.

Calculations show that if the Lego project cycle is repeated three times, the total APP value will be 16.52 million rubles.

For projects B and C, the APP values ​​are 18.88 and 24.79, respectively. Since the highest APP value belongs to project B, it can be considered the most attractive.

Calculation NPV projects A, B, C, thousand rubles.

Discount coefficient/ =10%

Option A

Option B

Option B

Cycle 1

Cycle 2

Cycle 3

Cycle 1

Cycle 2

Cycle 1

Cycle 2

Cycle 3

Flow

Flow

Flow

Flow

Flow

Flow

Flow

Flow

Fourth

Analysis of alternative investment projects

Assessing the economic efficiency of investments allows the economist to make a choice from several possible investment projects. One of the incentives that forces an enterprise to choose one or more from several promising projects is limited financial resources. Of all the criteria under consideration, the most acceptable for making investment decisions are the criteria NPV, IRR, P.I..

For the projects under consideration, A, B and C can be considered, since all efficiency criteria satisfy the requirements for them: P.I. > 1; PP less than 5 years; NPV > 0; IRR> 0.1. However, the best project will be project B, since it NPV IRR, P.I. more.

When making a decision, you can be guided by the following considerations:

1) it is recommended to choose the option with a larger NPV, since this indicator characterizes the possible increase in the economic potential of the enterprise (increasing the economic power of the enterprise is one of the highest priority targets);

2) it is also possible to calculate the coefficient IRR for incremental indicators of capital investments and income. If IRR > CC, then the incremental costs are justified and it is advisable to accept a project with large capital investments. The most preferred criterion is NPV.

Starting investments of projects:

Project A - 34 million rubles; Project B - 45 million rubles; Project B - 45 million rubles, which are designed for 5 years.

Let's consider the dynamics of cash flows and performance indicators of projects B and C, since these projects have the same starting investments.

Of the projects reviewed, according to all criteria for the effectiveness of the requirements placed on them: PI > 1; RR - less than 5 years; NPV > 0; IRR > 0.1, project B is preferred, and project C is rejected.

Analysis of the effectiveness of investment projects in conditions of inflation and risk

Evaluation of projects in conditions of inflation

When assessing the effectiveness of capital investments, it is necessary to take into account, whenever possible, the influence of inflation, because inflation distorts the results of analysis of the effectiveness of long-term investments. The simplest method is to adjust the discount factor to the inflation index. For practical calculations, the formula will look like

Where R- discount factor taking into account inflation; i- inflation index.

Let's consider the economic feasibility of implementing project B under the following conditions: the amount of investment is 45 million rubles; implementation period - 5 years; income by year (million rubles) - 34; 23; eleven; 9; 0; current rate of return (excluding inflation) - 12%; average annual inflation index - 11%.

We will evaluate the project without and taking into account inflation.

1. Without taking into account inflation:

N 34/1.12+23/1.254+11/1.405+9/1.574 - 45 = 30.357 + 18.341 + 7.829 + 5.718 - 45 = 17.245 million rubles.

Therefore, in the absence of inflation, it is advisable to accept the project ( NPV 0).

2. Taking into account inflation: (23%)

p = 0,12 + 0,11 = 0,23 (23%).

N 34/1.23 + 23/1.513 + 11/1.861 + 9/2.289 - 45 = 27.642 + 15.202 + 5.911 + 3.932 - 45 = 7.687 million rubles;

NPV 0, therefore, the project can be accepted.

Risk assessment of investment projects

The risk of an investment project is expressed in the deviation of funds for a given project from the expected. The greater the deviation, the more risky the project is considered. There are several approaches to assessing the risks of investment projects:

1) simulation model of risk assessment;

2) method of changing cash flow (method of reliable equivalents);

3) risk adjustment method of discount rate.

The implementation of a real investment project is associated with a certain amount of risk. An increase in risk is associated with an increase in probable income. Therefore, the greater the risk on a specific project, the higher the risk premium should be. This can be taken into account by adding a premium to the risk-free discount factor.

The risk-free discount rate is generally in line with government securities. Bonds, stocks, etc. are riskier.

Consider an investment project, the average rate of return is 12%. The expert-determined risk associated with the implementation of project A was 13%, project B - 16%, and with the implementation of project C 17%. Project implementation period is 5 years. Assess the effectiveness of projects taking into account risk

Assessing the effectiveness of projects taking into account risk

Project B with great NPV is considered preferable.

Projects with lower indicators are rejected - these are A and B.

If the implementation of any investment project from a certain set will reduce the profitability of the remaining investments, they are called interchangeable. An extreme case of fungibility occurs when the implementation of one of the investment projects makes it impossible to obtain cash income from the remaining investments. Such investments are called mutually exclusive.

This type of investment is very common in industry and the IRR and NPV methods very often rank the same set of mutually exclusive investments differently.

Table 2.3

If projects A and B are considered in isolation, then each of them should be approved because they satisfy all the criteria. However, if the projects are alternative, then the choice is not obvious, since project A has a higher NPV value, but project B is preferable in terms of IRR.

When making a decision, you can be guided by the following considerations:

a) it is recommended to choose an option with a large NPV, since this indicator characterizes the possible increase in the economic potential of the enterprise (increasing the economic power of the enterprise is one of the highest priority targets);

b) it is necessary to take into account the effect of scale (discussed below).

Research conducted by leading experts in the field of financial analysis has shown that the most preferred criterion is the NPV criterion. There are two main arguments in favor of this criterion:

1) it gives a probable estimate of the capital gain of the enterprise if the project is accepted; the criterion fully meets the main goal of the activities of management personnel, which is to increase the economic potential of the enterprise.

2) it has the property of additiveness, which allows you to add up the values ​​of the NPV indicator for various projects and use the aggregated value to optimize the investment portfolio.

Regarding the IRR , it has a number of serious shortcomings. Let us briefly describe them.

1. In a comparative analysis of alternative projects, the IRR criterion can be used rather conditionally. Thus, if the calculation of the IRR criterion for two projects showed that its value for project A is greater than for project B, then in a certain sense, project A can be considered more preferable, since it allows greater flexibility in varying the sources of financing for investments, the price of which can significantly vary. However, this preference is very conditional. Since IRR is a relative indicator, on its basis it is impossible to draw correct conclusions about alternative projects in terms of their possible contribution to increasing the capital of the enterprise; This disadvantage is especially pronounced if projects differ significantly in the amount of cash flows.

Table 2.4

For example, Project A may seem preferable because its IRR is significantly higher than the IRR of the second project. However, if an enterprise has the opportunity to finance project B, it should certainly be preferred, since the contribution of this project to increasing the company’s capital is an order of magnitude greater than the contribution of project A.

2. The IRR criterion shows only the maximum level of costs that can be associated with the project being evaluated. In particular, if the price of investment in both alternative projects is less than the IRR values. for them, the choice can only be made using additional criteria. Moreover, the IRR criterion does not allow us to distinguish between situations where the price of capital changes. Let's look at a corresponding example.

Let's plot the function NPV=f(r) for some hypothetical projects A and B.

Figure 2.1

The point of intersection of two graphs, showing the value of the discount factor at which both projects have the same NPV, is called the Fisher point. It is notable in that it serves as a boundary point separating situations that are captured by the NPV criterion and not captured by the IRR criterion.

Sometimes the IRR criterion not only fails to prioritize between projects, but also does not distinguish between situations when the discount rate is greater or less than the Fisher point rate. On the contrary, the NPV criterion allows you to set priorities in any situation. If the discount rate is less than the Fisher point, then project B should be preferred and vice versa.

The same thing is demonstrated effect of scale.

The goal is to show that when analyzing mutually exclusive investments, ranking results based on IRR are less reliable than ranking results based on NPV.

Example (discount rate 10%).

Table 2.5

	Cash flows

Based on the IRR criterion, project A is more desirable.

Taking into account the effect of scale, we note that project B requires additional investments of 5,000 and gives a return of 5,700. The internal rate of return on additional cash flows is 14% (5700/5000 = 1.14 and this corresponds to the Fisher point). This is an investment opportunity for the company if it can raise additional funds at 10%. By investing in project A, we will save 5,000, which will bring 5,500 at a yield of 10% per annum. This is less than the 5,700 that could be obtained by investing additional funds in Project B.

Figure 2.2

As can be seen from Figure 2.2, investment project B is more desirable at a discount rate of less than 14%.

Thus, when analyzing investments using the IRR method, one should not lose sight of the size of the investment.

If there are more than two mutually exclusive investments, then you will have to compare investment projects in pairs and repeating the procedure n-1 times, we will get the winning project.

3. One of the significant drawbacks of the IRR criterion. is also that, unlike the NPV criterion, it does not have the property of additivity, i.e. for two investment projects A and B, which can be implemented simultaneously:

IRR (A+B)IRR(A)+IRR(B).

NPV has this property.

4. IRR criterion. completely unsuitable for analyzing extraordinary investment flows (the name is conditional). The previous paragraphs examined the standard, simplest and most typical situations when cash flow develops according to a very specific pattern: investment or capital outflow (with a “-” sign in calculations) and capital receipts or inflows (with a “+” sign in calculations). However, other, extraordinary situations are also possible when the outflow and inflow of capital alternate. In particular, the situation is quite real when the project ends with an outflow of capital. This may be due to the need to dismantle equipment, the cost of environmental restoration, etc. It turns out that in this case, some of the considered analytical indicators with a change in the initial parameters may change in an unexpected direction, i.e., conclusions drawn on their basis may not always be correct.

Summarizing all of the above, it can be noted that for ranking mutually exclusive projects, NPV can serve as a criterion when the discount rate is equal to the corresponding opportunity cost of capital.

IRR is preferably used to know the difference between the predicted IRR and the required return. This difference is a margin of safety that allows you to compare investment returns and risk.

If the NPV method is used, then the rules for making investment decisions are as follows:

If it is necessary to make a decision on whether to approve an investment project or not, then the criterion is: NPV>0.

If there is a set of mutually exclusive investments, but only one can be implemented, then you need to take the project with the maximum NPV.

The IRR method can also be used to choose between several investment projects if the value of money in all future time periods is the same. If the method is used correctly, it will lead to the same decision as the NPV method. But the rules for using IRR are more complicated:

The same project can have multiple IRRs.

Finding the best project from mutually exclusive ones using the pairwise method is a labor-intensive task.

When analyzing the IRR of a project, it is necessary to determine whether the cash flows correspond to the usual traditional project: for cash flows of the borrowed type (when positive cash flows are followed by negative ones), the NPV curve has a positive slope and NPV increases with increasing discount rate.

If the cost of capital changes over time, it is better to use the NPV method.

Traditionally, capital investment objects are usually associated with investment projects. According to the Law "On Investment Activities..." investment project - this is a justification of the economic feasibility, volume and timing of capital investments, including the necessary design and estimate documentation developed in accordance with the legislation of the Russian Federation and duly approved standards (norms and rules), as well as a description of practical actions for making investments (business plan).

This definition makes it difficult to use important terms and characteristics of an investment project. Indeed, as follows from the above text of the Law, an investment project is, first of all, a comprehensive plan of activities aimed at creating a new or modernizing existing production of goods (works, services) in order to obtain economic benefits. Based on this, it is difficult, for example, to introduce such fundamental concepts as “the effectiveness of an investment project”, “individual entrepreneur cash flows”, “individual entrepreneur payback”, etc.

The term "project" is understood in two senses:

• as a set of documents containing the formulation of the purpose of the upcoming activity and the definition of a set of actions aimed at achieving the goal;
• as the complex of actions itself (works, services, acquisitions, management operations and decisions) aimed at achieving the formulated goal.

In investment theory and practice, the term “project” is usually used in the second sense.

An investment project (IP) in the “Methodological Recommendations...” is defined in the same way as in the Law “On Investment Activities...”.

According to the “Methodological Recommendations...” at the heart of any investment project there is always a certain project as a set of works and services aimed at achieving investment goals, and the investment project gives a description of this project from the point of view of the economic feasibility of its implementation. Consequently, an investment project is always generated by some project (in the sense of the second definition), the rationale for the feasibility and characteristics of which it contains. In this regard, one or another properties, characteristics, parameters of the IP (duration, implementation, cash flows, etc.) are understood as the corresponding properties, characteristics, parameters of the project generating it. In other words, when assessing the acceptability of an individual project for the construction and operation of, for example, a gas station, it should be assumed that there is a set of works (project) for the construction of a gas station, the description of which is fixed in the investment project. Then the “effectiveness of the investment project” of a gas station means the effectiveness of the project as a set of works.

Classification of investment projects

The most important classification criterion is the degree of mutual influence of investment projects on each other, which is understood as the relationship of decisions and results in one project from decisions made on another project: it is considered that project A affects project B if decisions on project A must be taken into account decisions on project B (and vice versa - if in order to make decisions on project B it is necessary to take into account decisions on project A).

Based on their mutual influence on each other, investment projects can be divided into the following types.

Independent investment projects – when the decision to accept one project does not affect the decision to accept another IP.

In order for investment project A to be independent of project B, at least two conditions are necessary:

• – there must be technical capabilities to implement project A, regardless of whether project B is accepted or not. For example, it is technically possible to organize the production of window frames without implementing a project for the production of window glass. In the same way, from a technical point of view, it is possible to implement a project for the construction of a gas station without taking into account decisions on the construction project of, say, a kindergarten;
• – the income expected from project A should not be affected by decisions made on project B.

If we consider the above pairs of investment projects, it is obvious that, according to this condition, the construction projects of a gas station and a kindergarten are not interconnected - it is difficult to imagine that the income of the owners of a gas station is determined by the results of the functioning of the kindergarten. As for the first pair of projects - the production of window frames and window glass, the conclusion that there is no relationship between their income seems incorrect.

The assumption that these two projects need to be implemented simultaneously is justified.

Sometimes a company, due to lack of financial resources, cannot implement two projects at the same time. In such a situation, the acceptance of one project will entail the rejection of the second. However, it would be incorrect to call projects dependent only on the grounds that the investor does not have enough funds for their joint implementation. Indeed, if a company does not have the financial capacity to simultaneously build a gas station and a kindergarten, then because of this these projects will not become interdependent.

Dependent investment projects – these include projects for which the decision to implement one project affects another project, i.e. The cash flows for project A change depending on whether project B is accepted or rejected.

Dependent projects can be divided into several types.

• 1. Alternative (mutually exclusive) projects – when two or more analyzed projects cannot be implemented simultaneously, and the acceptance of one of them automatically means that the remaining projects cannot be implemented. For example, on an allocated plot of land either a workshop, a canteen, or a parking lot can be built - the adoption of one of these projects automatically makes it impossible to implement the others.
• 2. Complementary projects when the implementation of several projects can only take place jointly. Two types of complementary projects are of significant interest:
  • A) complimentary projects – in this case, the adoption of one investment project leads to an increase in income from other projects. An example of complementary projects can be the projects discussed above for the production of window frames and window glass;
  • b) projects connected by substitution relationships, when the adoption of a new project leads to a slight decrease in income from one or more existing projects. Substitution relationships are connected, for example, between a project for the production of durable goods (power tools) and a complementary production project for the repair of these tools. Indeed, the manufacturer of power tools understands that it will face difficulties in marketing its products if repair shops are not opened. But for the manufacturer, the ideal situation would be when there was no possibility of repair and in case of any malfunction of the power tool, it would be replaced with a new copy.

The second criterion for classifying investment projects is the period of their implementation (creation and operation). According to this criterion, investment projects are divided into three types:

• 1) short-term investment projects – implementation period up to three years;
• 2) medium-term investment projects – implementation period is three to five years;
• 3) long-term investment projects – implementation period is over five years.

The third criterion for classifying projects is their scale. It should be taken into account that scale of the investment project characterizes its social significance, which is determined by the impact of the project implementation results on at least one of the internal or external markets (financial, goods and services, resources), as well as on the environmental and social situation. In terms of scale, it is recommended to divide projects into the following types.

• 1. Global investment projects, the implementation of which significantly affects the economic, social or environmental situation throughout the world or in a large group of countries. An example of such projects is the construction of continental oil and gas pipelines, the creation of a global information exchange network system, the formation of direct East-West rail transit, etc.
• 2. National economic investment projects , affecting the entire country as a whole or its large regions (Ural, Volga region), and when assessing them, we can limit ourselves to taking into account only this influence. Projects of this scale include federal highways and railway lines, large power plants, etc.
• 3. Large-scale investment projects, covering individual industries or large territorial entities (subject of the Federation, cities, districts), and when assessing them, one cannot take into account the impact of these projects on the situation in other regions or industries - the construction of large enterprises, bridges, regional information systems, etc.
• 4. Local investment projects , the action of which is limited to the framework of the given enterprise implementing the IP. Their implementation does not have a significant impact on the economic, social and environmental situation in the region and does not change the level and structure of prices on commodity markets.

It should be borne in mind that global, national economic and large-scale projects are socially significant projects, the results of which are important for society as a whole. Local projects are not considered socially significant.

The fourth criterion for classifying investment projects is their main focus. Direction of the investment project depends on his goals. From the point of view of this criterion, investment projects can be divided into the following types:

• commercial investment projects , whose main goal is to make a profit;
• social investment projects oriented towards solving, for example, problems of unemployment in the region or social adaptation of former military personnel, etc.;
• environmental investment projects, whose main focus is improving the living environment of people, as well as flora and fauna, for example, establishing a park, constructing wastewater treatment plants, land reclamation, etc.

The appropriate classification of projects allows firms to purposefully pursue an investment policy, rationally use financial and other resources, and achieve an optimal ratio of project costs and results obtained from it.

• "Methodological recommendations for assessing the effectiveness of investment projects." Official publication. M.: Economics, 2000. P. 104.