Analysis of the effectiveness of investment projects in terms of inflation and risk.

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If two projects independent, then the NPV and IRR criteria give the same result regarding the acceptance or rejection of the project: a project accepted according to the NPV criterion will be accepted according to the IRR criterion, and vice versa. To understand this, let's go back to Fig. 7.1 and note that: 1) the project is accepted if the cost of capital is less than IRR, and 2) the NPV of the project is always positive if the price of capital is less than IRR. Thus, for all values ​​of the price of capital less than 11.8%, the project L will be accepted under both criteria, while both criteria recognize the project as unsuitable if the cost of capital is above 11.8%. Project S, like all other independent projects, can be analyzed in a similar way, while the condition will always be observed: if IRR > k, then NPV > 0.

Alternative projects

Now suppose that the projects S and Lalternative, i.e., they are not independent. This means that you can choose either project S or project L, or both projects are rejected, but both projects cannot be accepted at the same time. From fig. 7.1 it can be seen that when k > 7.2%, NPV S > NPV L and IRR S > IRRL-Thus, with k > 7.2% both criteria give the same result when choosing a project from two alternative ones. At k< 7.2% критерии дают уже различные результаты: по критерию NPV предпочтителен проект L, according to the IRR criterion - project S. What would be the correct answer? Logic dictates that the NPV criterion is better, since it selects the project that increases the wealth of shareholders to a greater extent.

Reasons for conflict. Two main reasons cause the intersection of NPV graphs and thus lead to a contradiction between the NPV and IRR criteria: 1) project scale, i.e. the amount of investment in one project is greater than in another; 2) intensity of cash inflow, i.e. most of the inflow of funds for one project is carried out in the first years, for the second - in the last, which was the case with projects L and S.

If such differences appear in the analysis of projects, the firm will have unequal amounts of free resources to invest in different years, depending on which project it has chosen. For example, if one project requires more investment than the second, then, having chosen the second project, the firm at the moment t = 0 will have free financial resources available for investment in some additional project. Similarly, if the projects require the same investment, but one of them is cashing in faster, the firm will have additional opportunities to refinance them. In such a situation, the price of capital at which incremental cash flows can be reinvested is very important. This position is illustrated below.

1. Project scale. Alternative projects very often vary in size. Suppose a firm has the opportunity to buy a copper mine for $5 million. If the purchase goes through, the company will be able to transport the ore for smelting in two ways. Plan 5 ( small project) provides for the purchase of a fleet of trucks for $ 1 million, as a result, the cost of the project will be $ 6 million. Plan L (large project) provides for costs of 15 million dollars. for the installation of a conveyor for moving ore, which will increase the cost of the project to 20 million dollars. If trucks are used, then the cost of their operation will be higher than when using a conveyor. For simplicity, let's assume that the project will run for 5 years, after which the ore reserves will run out. Assume also that the expected post-tax cash flow occurs at the end of each year and is $2 million. according to Alan 5 and in million dollars. according to plan L.

Considering the cost of capital equal to 10%, you can find for each project NPV (in million dollars) and IRR:

NPVL = $2.74 million IRRL = 15.2%.

NPVS = $1.58 million IRRS = 19.9%.

NPV∆ = $1.16 million IRR∆ = 13.2%.

Thus, the criteria lead to different results: NPVL > NPVS, but IRR S > IRRL. What project should be accepted? If we assume that the price of capital is constant, i.e., the company can raise funds in the required volumes on terms of 10%, then one should choose a project with a large NPV, i.e. L . One more project ∆ can be considered as an independent one, composed of incremental values ​​of the initial projects and requiring investments of 14 million dollars. Therefore, the project L can be divided into two components: one is equivalent to a project S, and the other is the "residual project" equal to the hypothetical project ∆. Project ∆ requires an investment of $14 million, annual revenues of $4 million, and NPV equals the difference between NPVS and NPVL, i.e. e.$1.16 million Thus, the hypothetical project ∆ has NPV∆ > 0, so it should be accepted. Therefore, project L must be accepted.

Other considerations can be made. Project L can be conditionally divided into two projects, the first with an investment of 6 million dollars. and NPV = $1.58 million in the second with an investment of 14 million dollars. and NPV = $1.16 million Since both components have NPV > 0, they should be accepted. If the project S will be adopted, the second component of the draft L, i.e. the hypothetical project ∆ will be automatically rejected. Thus, the NPV criterion is preferable, since it is he who does not reject project L.

Meaning k, at which the NPVs of the projects are the same, is the IRR of the project ∆ and is equal to 13.2%. At k > 13.2% there is no conflict between NPV and IRR criteria. In our example, ∆ ~ 10%, which led to the emergence of conflict.

2. Intensity of cash inflowfunds. The conflict between NPV and IRR can also arise from differences in the distribution of the total amount of cash inflows over time, even if the two projects have exactly the same amount of initial investment. The possibility of such a contradiction was discussed above when discussing the evaluation criteria. Let's consider one more example. Assume that a $10 million acquisition project is being analyzed. rights to logging and lumber production. If we start clearing timber immediately in accordance with short-term plan S, our expected cash receipts will be $4 million in the first two years, $3 million in the next two years, and $2 million in the last two years. There is another plan - a long-term plan L, according to which the start of deforestation is delayed for a year, which will allow the trees to grow. Due to this, the cash inflow will be $2 million in the second year, $3 million in the third, $5 million in the fourth, and $9 million in the fifth.

Assuming that the cost of capital in each case is 10%, we find NPV (in million dollars) and IRR for each project:

NPVL = 2.91 billion dollars IRR L = 17.3%.

NPV S = $2.49 million IRR S = 20.5%.

NPV ∆ = $0.42 million IRR∆ = 12.5%.

Again, the two criteria give different results: due to the difference in the intensity of cash inflows, NPVL > NPVs, but IRRs > IRRL.

We already know that a high discount rate has had a greater impact on cash flow elements in recent years. Therefore, the NPV schedule of long-term projects such as the project L, has a greater steepness of inclination to the abscissa axis compared to short-term projects of the project type S. If the value of the price of capital lies to the left of the abscissa of the intersection point of the two graphs, a contradiction arises. This is precisely the situation that takes place in our example: the price of capital k= 10%, and the abscissa of the point of intersection of the graphs is 12.5%.

In the previous example, when two projects differed in size but had no difference in cash inflow intensity, we selected a hypothetical project ∆ that had a positive NPV to show why a project with a large NPV should be accepted. You can make similar calculations for the last example. Project L consists of two parts: analogue of the project S and a hypothetical project ∆ with positive NPV = $0.42 mln. Taking on a project S, we automatically reject the project ∆, that is, we lose the opportunity to increase the value of the firm. Thus, it is advisable to reject the project S and accept the project L.

The key issue of the conflict. It can be seen that in both examples considered there are incremental cash flows. Therefore, the key point in the analysis of alternative projects is to decide what is the value of accelerating cash flow. The value of the cash flow depends on the allowable rate of return at which the incremental cash flows from earlier years can be reinvested. Using a CriterionNPVimplicitly assumes that the available interest rate at which incoming cash can be reinvested is the price of capital, while applying the criterionIRRmeans that the firm has some investment opportunity with a rate equal toIRR. These assumptions are tacitly assumed in the discounting process. Thus, according to the NPV criterion, discounting is performed according to the price of capital, while according to the IRR criterion - according to the IRR of the project. Naturally, the incoming cash can be paid out to shareholders in the form of dividends in the amount they spend on beer and pizza, however, the premise of the possibility of reinvestment is integral part calculation of IRR and NPV criteria.

Conflict resolution. Which of the prerequisites is more reasonable: reinvestment of the funds generated by the project at the price of capital or reinvestment at the project's IRR rate? Our point of view is this.

Assume that the firm's cost of capital is 10%. Management can raise financial resources in the required amounts at this rate. This condition is assumed unchanged for some foreseeable future. Further assume that all potential projects have the same degree of risk as the firm's current projects.

The capital budgeting process suggests that potential projects should be valued at the rate k= 10%. All projects with NPV > 0 are accepted. The capital needed to finance them is available both now and in the future.

What to do with the incoming funds generated by existing projects? These funds can be: a) paid to the owners of the sources of funds, i.e. shareholders and creditors, providing them with a return on average of 10%, or b) used as an alternative to external sources of funds, the price of which is 10%. Thus, the firm will receive a savings of 10%, and this 10% is precisely the allowable and possible rate of reinvestment of incoming cash.

4. The IRR criterion unconditionally assumes reinvestment at the IRR rate itself. It also assumes: a) the availability of sources in the capital market and b) the expected price of capital does not change, i.e. the available reinvestment rate is 10%. Even if the firm accepts projects with a higher average IRR, say 30%, this is beside the point, since new projects can always be financed from external sources with a cost of capital of 10%, so the affordable rate of reinvestment of cash generated by existing projects , again equal to the price of the firm's capital.

Thus, we have come to the conclusion that the affordable and possible reinvestment rate is the price of capital, which is implied in the criterionNPV. This justifies the preference for the NPV criterion, at least for firms that have the desire and ability to raise capital at a reasonable price, close in value and to the price of capital prevailing in the firm. In Chapter 10, when discussing the problem of optimizing the capital budget, we will see that under certain conditions the application of the NPV criterion is doubtful, but in most cases this criterion is undoubtedly better than IRR.

Once again, for independent projects, both criteria give the same results. However, when evaluated alternative projects, especially differing in scale and/or temporal intensity of cash inflows, the criterion should be appliedNPV.

Topic 7. Alternative investment projects.

Alternative investment projects are compared in terms of commercial and budgetary efficiency. The most important characteristic of the commercial efficiency of investment projects is the payback period (period) of costs, and budget and efficiency - the ratio of budget revenues to the volume of budget allocations.

During the preliminary examination, the financial condition of the applicant is analyzed, the reliability of the data is verified, and a preliminary financial assessment of investment projects is given. The results of the preliminary study are the basis for a comprehensive examination, which implies a financial and economic assessment of the project itself. At this stage, an analysis of project risks, the reasons for their occurrence is also carried out, measures of insurance against risks are developed. At the same time, project financing schemes, alternative options are developed, the initial data on the project are adjusted. If necessary, independent experts and specialized firms can be involved at each stage of the examination. Examination of particularly significant projects is carried out with the involvement of the Scientific and Expert Council of Aviabank, whose activities are regulated by the Regulations on the Scientific and Expert Council. The Council makes recommendations on determining the scientific and technical level and commercial viability of the projects it considers.

Ranking of considered real investment projects by risk level. A generalized comparative assessment of alternative investment projects in terms of risk level is carried out in two ways

The equipment can also be used in alternative investment project B, and during the same period, i.e. until completely worn out. The main indicators of project B, calculated on the condition that the equipment is provided free of charge, are

Alternative investment projects, in accordance

Alternative investment projects are compared in terms of commercial and budgetary efficiency.

Example. Enterprise experts evaluate the profitability of two alternative investment projects that can be implemented over the next year, using the indicators given in Table. 6.1. Let's estimate the expected profitability of projects. Using (3.1), we find for the first project

The principle of positivity and maximum effect focuses on the implementation of those projects that provide a positive effect, and when comparing alternative investment projects, preference should be given to a project with highest value effect.

The method based on finding T. b. allows the designer (designer, etc.) to calculate several such points, taking into account alternative investment proposals that develop as a result of the presence of various design capacities or technological processes, machine designs, equipment. Changes in technological processes can have a significant impact on variable costs, since, for example, more advanced and therefore more expensive technology usually leads to lower unit variable costs, especially regarding labor costs. In turn, significant changes in production volumes can cause an increase (decrease) in fixed costs. Finding T. is possible and evident. graphically by finding functional relationships according to the above equations. The point of intersection of two lines (for example, y \u003d ax + buy \u003d px) will be the desired T. b. Break-even analysis is also a useful tool for financing investment projects (financial planning). So, for example, in order to ensure the annual repayment of a loan (loan, credit), you can calculate an additional T. b., but taking into account interest rates.

The means of solving the problems facing the enterprise and achieving investment goals are alternative investment projects. In this case, it is necessary to make a selection of one or more projects based on certain criteria. Usually, alternative projects are compared with each other in turn and the best one is selected in terms of profitability, low cost and safety for investors. For this, various formalized and non-formalized methods are used. Decision making is complicated by such factors as limited financial resources, the presence of investment risks, etc. The evaluation of long-term projects is especially laborious, for which the probability of achieving the forecast is low.

At the stage of official presentation of alternative investment projects, a detailed selection of information is carried out, more thorough than that used in the initial selection. This information should be more objective and reliable. Many enterprises have developed a standard procedure for submitting investment projects. As a rule, the project initiator, when drawing up a formal proposal, fills out a set of documents in a certain form and highlights there the possible options for his project, which seem to him the most preferable after the initial assessment. Usually, the deadlines are set within which proposals at enterprises are accepted for consideration.

One of the important components of the efficiency of the economic system is the efficiency of capital investments. It is expressed as the ratio of the effect obtained to the capital investments that caused this effect. The efficiency of capital investments is measured by a set of indicators, which includes the overall effect of capital investments, their rate of return, payback period, comparative efficiency, etc. Indicators of the economic efficiency of capital investments are used to compare alternative investment projects and select the optimal project.

Example It is necessary to assess the level of financial risk for an investment operation according to the following data, two alternative investment projects are submitted for consideration (project. .A "and project B") with the probability of expected income presented in Table. 3.2.

The final selection for the implementation of individual alternative investment projects is carried out taking into account all three criteria based on the priorities determined by the enterprise.

In general, DEA technology is an effective benchmarking tool for independent or weakly dependent projects. However, it should be noted its insufficient sensitivity in the formation of estimates in the context of a comparative analysis of objects of various sizes and the limited possibility of application in the formation of investment programs consisting of strongly related projects. In addition, the representation of generalized inputs (outputs) in efficiency ratios as a linear combination of all inputs (outputs) is a significant simplification from a practical point of view. Building the models themselves and giving them a meaningful meaning (as well as a meaningful assessment of the results) in each specific case is difficult without the involvement of the accumulated practical experience and knowledge of experts in the relevant subject area. The use of DEA technology for selecting projects in investment analysis can be very productive at the final stage of selection, when a financial and economic analysis of each project is carried out, a set of alternative projects that meet the required performance criteria are identified, and it is necessary to select the best of them according to a set of criteria. At the stage of preliminary selection of investment projects for further analysis, it is advisable to use simpler (less labor-intensive) methods.

If the value of the price of capital is outside the Fisher point, then the NPV and 1RR criteria give the same results when evaluating alternative investment projects, if the price of capital is less than the Fisher point, then the NPV and IRR criteria contradict each other.

Rank alternative investment projects A and B

By the type of complementarity in the presence of group relations between projects (independent investment projects, interdependent and interdependent, additional, alternative).

Basic financial criteria. The financial analysis of industrial investments mainly consists in measuring (evaluating) the final financial results of investments - their profitability for the investor. Such a task is faced both at the stage of the initial analysis of the financial "attractiveness" of the project, and when developing a business plan. A negative conclusion usually gives reason to refuse further, more thorough and in-depth study of the project. Without the calculation of this kind of meters, it is impossible to compare alternative investment projects. Of course, when deciding on the choice of an object for investment, other criteria are taken in addition to financial ones. For example, the environmental consequences of the project, the possibility of creating additional jobs, the development of a production base in a given area, etc. In this chapter, the discussion is limited to financial criteria only.

The discount rate must include, regardless of the type of investment, the minimum guaranteed level of return,

The ambiguity of the results that contradict each other when considering several alternative investment projects, depending on the chosen method of its economic evaluation

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 in a number of problems of investment analysis is the decision to choose the best of the alternative projects. In this situation, the analyst should:

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

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

select different options for the same project.

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

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

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 of implementation can be adjusted in such a way as to satisfy the conditions of feasibility and financial solvency;

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

the comparative effectiveness of projects is evaluated.

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

When choosing one of the mutually exclusive projects, a situation may arise when one of them has a higher net present value, the other has a higher ROI, and the third has a higher internal rate of return.

This situation is called a conflict of criteria.

Efficiency is a deeper characteristic of the functioning of the system as a whole (both costly and productively). That is why the evaluation and selection of alternative investment projects should be based on performance indicators, and indicators various kinds effects can and should be used as additional 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 a performance indicator has a number of undeniable advantages, namely:

takes into account the time distribution of real money flows;

considers the sum of the effects received throughout the life of the project;

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

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

The main claims expressed against this indicator can be reduced to several provisions:

the impossibility of choosing among projects that have different life cycles;

the impossibility of a correct comparison of projects with different amounts of investment;

unrealistic assumption about the terms of reinvestment of cash receipts from projects;

the multiplicity of values ​​of the internal profitability ratio for projects with an unconventional structure of cash flows.

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

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

Investment projects financed in whole or in part at the expense of the corresponding budget, before their approval, are subject to verification 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 objects, the use of which violates the rights of individuals and legal entities and the interests of the state, does not meet the established requirements, etc. At the same time, it is provided that the cases and procedure for carrying out inspections are established, respectively, by the regulatory legal acts of the Government of the Russian Federation, the regulatory legal acts of the 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 prevailing methods for evaluating 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 evaluating the effectiveness of investment projects.

The rules for auditing investment projects that provide for the construction, reconstruction of capital construction facilities 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 formation, are approved, respectively, by regulatory legal acts of a constituent entity of the Russian Federation or municipal legal acts ( for example, Decree of the Government of the Moscow Region dated 09.08.2010 No. 643/32 “On Approval of the Procedure for Checking Investment Projects for the Efficiency of the Use of Budget Funds of the Moscow Region Allocated for Capital Investments” URL: http://www.referent.ru/3/ 75541; Decree of the Administration of the Voskresensky Municipal District of the Moscow Region dated 10.22.2010 No. 2023 “On Approval of the Procedure for Inspecting Investment Projects for the Efficiency of Using Budget Funds of the Voskresensky Municipal District Allocated to Capital ozheniya" URL: http://www.regionz.ru/index.php?ds=978171 etc.)

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

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

However, one cannot fail to say that in the course of evaluating 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 some particular aspect of the state of the project.

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

Net Present Effect Calculation Method

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

The NPV indicator is the difference between all cash inflows and outflows, reduced to the current point in time (the moment the investment project is evaluated). It shows the amount of cash that an investor expects to receive from a project after the cash inflows have recouped its initial investment costs and the periodic cash outflows associated with the implementation of the project. Because cash payments are valued in terms of their time value and risks, NPV can be interpreted as the value added by the project. It can also be interpreted as the total profit of the investor.

In other words, for the flow of payments CF (Cash Flow), where is the payment in years () and the initial investment IC (Invested Capital) in the amount of the net present value is calculated by 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 at once (in the zero period), but are stretched 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, reduced to the present moment of time, taking into account the different time value of money. If the NPV is greater than 0, then the investment is economically viable, and if the NPV is less than 0, then the investment is not economically viable (i.e., an alternative project whose return is taken as the discount rate requires less investment to generate a similar income stream).

With the help of NPV, one can also evaluate the comparative efficiency of alternative investments (with the same initial investment, 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 accepted abbreviation - IRR (INR)) 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 the flow of payments CF, where is the payment in years () and the initial investment in the amount 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 the cash flows change sign several times during the period under review.

As for the IRR indicator, it has a number of serious shortcomings. Let's 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 evaluated project.
• 3. One of the significant drawbacks of the IRR criterion is that, unlike the NPV criterion, it does not have the additivity property, 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 the 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 amount 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 amounts of required investments. In this case, the one that provides greater efficiency of investments 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 the world accounting and analytical practice; it does not imply a temporal ordering of cash receipts. The algorithm for calculating the payback period (PP) depends on the uniformity of the distribution of projected income from the investment. If the income is evenly distributed over the years, then the payback period is calculated by dividing the one-time costs by the amount of annual income due to them. Upon receipt fractional number it is rounded up to the nearest integer. If profits are unevenly distributed, then the payback period is calculated by directly counting the number of years during which the investment will be repaid with cumulative income. The general formula for calculating the PP indicator is as follows:

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 appropriate for making investment decisions are the NPV, IRR and PI criteria. Despite the noted relationship between these indicators, the problem of choosing a criterion still remains when evaluating alternative investment projects. 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 the 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; at the same time, if IRR > СС, then the incremental costs are justified and it is advisable to accept the 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 up 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 evaluation, far from unambiguous results can be obtained, 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 > СС and PI > 1;

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

There is an opinion among financial analysts that the net present value (Net Present Value, NPV) is not the most effective criterion for evaluating the choice of a financial solution.

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 shield for the project in case of negative changes in the external environment. Nevertheless, attention should be paid to two significant factors - the planning horizon (the duration of the investment project) and the choice of the discount rate.

If we focus solely on the NPV indicator, then among alternative investment projects, the most often optimal project will be one that requires significant investments and is longer in terms of implementation time. Consider a hypothetical example where the discount rate is 10% (Table 1).

Table 1. Comparative analysis alternative investment projects

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

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

It should be noted that these methods can be used under conditions of certainty and risk. In conditions of a high degree of risk and uncertainty, these methods should be abandoned and alternative projects of different duration should be ranked based on the calculated NPV values ​​​​and other criteria. The project implementation time is weak side indicator of NPV and to a greater extent depends on the accuracy of the forecast, since for external environment characterized by a high degree of unpredictability. The second important factor in calculating NPV is the choice of discount rate. It depends on a number of factors. It is impossible to allow an arbitrary choice of the discount rate from the lowest interest on government securities (guaranteed yield) to unreasonably high interest, taking into account all kinds of interests and risks of investors.

Based on the above considerations, we single out the main positive and negative sides NPV indicators, which are given in table 2:

Table 2. Strong and weak sides 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-criterion decision-making can lead to serious negative consequences. It is advisable to calculate several both absolute and relative indicators, taking into account from what position the project is being evaluated, and, accordingly, make an informed decision.

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

alternative project payback reduced