Analysis of alternative projects. Analysis of investment projects

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 return to Fig. 7.1 and note that: 1) the project is accepted if the price of capital is less than the IRR, and 2) the NPV of the project is always positive when the price of capital is less than the IRR. Thus, for all values of the cost of capital less than 11.8%, the project L will be accepted under both criteria, while both criteria will 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, and the condition will always be met: if IRR > k,

then NPV > 0.

Alternative projects will be accepted under both criteria, while both criteria will recognize the project as unsuitable if the cost of capital is above 11.8%. Project Now let's assume that the projects Thus, for all values of the cost of capital less than 11.8%, the projectAnd alternative, Thus, for all values of the cost of capital less than 11.8%, the project, that is, they are not independent. This means that you can choose either project S or project or both projects are rejected, but both projects cannot be accepted at the same time. From Fig. 7.1 it is clear that when k> 7.2%, NPV S > NPV L and IRR S > IRRL-Thus, when This means that you can choose either project S or project< 7.2% критерии дают уже различные результаты: по критерию NPV предпочтителен проект Thus, for all values of the cost of capital less than 11.8%, the project, k > will be accepted under both criteria, while both criteria will recognize the project as unsuitable if the cost of capital is above 11.8%. Project. 7.2% both criteria give the same result when choosing a project from two alternative ones.

At according to IRR criterion - project Which answer will be correct? Logic dictates that the NPV criterion is better, since it selects the project that increases shareholder wealth to a greater extent. Reasons leading to contradiction. Two main reasons determine the intersection of NPV graphs and thereby lead to a contradiction between the NPV and IRR criteria: 1) project scale, Thus, for all values of the cost of capital less than 11.8%, the project Now let's assume that the projects will be accepted under both criteria, while both criteria will recognize the project as unsuitable if the cost of capital is above 11.8%. Project.

that is, the amount of investment for one project is greater than for another; 2) intensity of cash flow, = 0 will have free financial resources available for investment in some additional project. Similarly, if projects require the same investments, but one of them has a faster cash inflow, 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 point is illustrated below.

1. Project scale. Alternative projects very often vary in size. Thus, for all values of the cost of capital less than 11.8%, the project Suppose a company has the opportunity to buy a copper mine for $5 million. If the purchase goes through, the company will be able to transport ore for smelting in two ways. Thus, for all values of the cost of capital less than 11.8%, the project.

Plan 5 (small project) involves purchasing a fleet of trucks for $1 million, resulting in a project cost of $6 million. Plan

(major project) involves costs of 15 million dollars. to install a conveyor for moving ore, which will increase the cost of the project to $20 million. If you use trucks, then their operating costs will be higher than when using a conveyor. For simplicity, we will assume that the project will operate for 5 years, after which the ore reserves will dry up. Let us also assume that the expected after-tax cash receipts occur at the end of each year and amount to $2 million. according to Alan 5 and in million dollars. according to plan

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

NPVL = 2.74 million dollars. IRRL = 15.2%.

NPVS = 1.58 million dollars. IRRS = 19.9%. . NPV∆ = 1.16 million dollars. Thus, for all values of the cost of capital less than 11.8%, the project IRR∆ = 13.2%. will be accepted under both criteria, while both criteria will recognize the project as unsuitable if the cost of capital is above 11.8%. Project, Thus, the criteria lead to different results: NPVL > NPVS, but IRR S > IRRL. Which project should be adopted?$1.16 million

Thus, the hypothetical project ∆ has NPV∆ > 0 and should be accepted. Therefore, Project L must be accepted. Other arguments 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 dollars. will be accepted under both criteria, while both criteria will recognize the project as unsuitable if the cost of capital is above 11.8%. Project V Thus, for all values of the cost of capital less than 11.8%, the project, the second with an investment of $14 million. and NPV = 1.16 million dollars. Since both components have NPV > 0, they should be accepted. If the project

will be accepted, the second component of the project like all other independent projects, can be analyzed in a similar way, and the condition will always be met: if IRR > i.e., the hypothetical project ∆ will be automatically rejected. Thus, the NPV criterion is preferable because it does not reject project L. k Meaning ~ at which the NPV of projects are the same, represents the IRR of the project ∆ and is equal to 13.2%. At

2. 13.2% there is no contradiction between the NPV and IRR criteria. In our example ∆10%, which led to the conflict. Intensity of cash inflow Thus, for all values of the cost of capital less than 11.8%, the project, funds

Inconsistency between NPV and IRR can also arise due to differences in the distribution of total cash inflows over time, even if 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 look at another example.

Let's assume that a $10 million acquisition project is being analyzed. rights to logging and lumber production.

If we immediately begin cutting down the forest in accordance with the 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

According to which the start of deforestation is delayed for a year, which will allow the trees to grow. > Thanks 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 equal to 10%, we find the NPV (in millions of dollars) and IRR for each project: Thus, for all values of the cost of capital less than 11.8%, the project, has a greater slope to the x-axis compared to short-term projects such as a project will be accepted under both criteria, while both criteria will recognize the project as unsuitable if the cost of capital is above 11.8%. Project. If the value of the price of capital lies to the left of the abscissa of the point of intersection of the two graphs, a contradiction arises. This is precisely the situation that occurs in our example: the price of capital This means that you can choose either project S or project= 10%, and the abscissa of the intersection point of the graphs is 12.5%.

In the previous example, when two projects differed in size but did not differ in cash flow intensity, we selected a hypothetical project ∆ that had a positive NPV to show why the project with a large NPV should be accepted. You can make similar calculations for the last example. Project Thus, for all values of the cost of capital less than 11.8%, the project consists of two parts: an analogue of the project will be accepted under both criteria, while both criteria will recognize the project as unsuitable if the cost of capital is above 11.8%. Project and a hypothetical project ∆ with positive NPV = 0.42 million dollars. Taking on a project will be accepted under both criteria, while both criteria will recognize the project as unsuitable if the cost of capital is above 11.8%. Project, we automatically reject the project ∆, i.e. we lose the opportunity to increase the value of the company. will be accepted under both criteria, while both criteria will recognize the project as unsuitable if the cost of capital is above 11.8%. Project Therefore, it is advisable to reject the project Thus, for all values of the cost of capital less than 11.8%, the project.

and accept the project Key issue of the conflict . It can be noted that in both examples considered there are incremental cash flows.Therefore, a key point in analyzing alternative projects is to decide what is the value of accelerating cash flow.The value of cash flow depends on the acceptable rate of return at which incremental cash flows from early years can be reinvested.Using the criterionNPVUsing the criterion. implicitly assumes that the available interest rate at which incoming funds can be reinvested is the price of capital, whereas the application of the criterion

IRR means that the company has some investment opportunities with a rate equal to

Suppose the firm's cost of capital is 10%. Management can attract financial resources in the required amounts at this rate.

This condition is assumed to remain unchanged for some foreseeable future. Let us further assume that all potential projects have the same degree of risk as the firm's current projects. This means that you can choose either project S or project The capital budgeting process requires that potential projects be priced at

= 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 an average return of 10%, or b) used as an alternative to external sources of funds, the price of which is equal to 10%. Thus, the company will receive savings of 10%, and these 10% precisely represent the acceptable and possible rate of reinvestment of incoming funds. 4. The IRR criterion unconditionally assumes reinvestment at the IRR rate itself.Therefore, a key point in analyzing alternative projects is to decide what is the value of accelerating cash flow.. It is also assumed: a) availability of capital market sources and b) constant expected price of capital, i.e., the available reinvestment rate is 10%. Even if a firm accepts projects with a higher average IRR, say 30%, this is not relevant since new projects can always be financed externally at a cost of capital of 10%, so an affordable reinvestment rate for cash generated by existing projects , again equal to the firm's cost of capital.

Thus, we came to the conclusion that However, when alternative projects are being evaluated, especially ones that differ in scale and/or timing of cash flows, the criterion should be appliedTherefore, a key point in analyzing alternative projects is to decide what is the value of accelerating cash flow..

36. Analysis of alternative projects

When considering several alternative projects simultaneously, it is important to consider the relationships between them.

Projects are said to be mutually independent if the acceptance or rejection of one of them does not affect the possibility or effectiveness of the adoption of the other.

The joint effect from the implementation of several independent projects is equal to the sum of the effects from the implementation of each of them.

Complementary projects are those that, for whatever reason, can only be accepted or rejected at the same time.

If only some of these projects are implemented, the overall goals may not be achieved.

Projects are called mutually influencing if, during their joint implementation, positive or negative effects arise that do not appear during the implementation of each of the projects separately.

Each of the projects significantly affects the other, and the refusal of one of them makes the implementation of the other impossible or impractical.

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:

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

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

3) choose different options for one project.

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

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

2) 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;

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

4) the comparative effectiveness of projects is assessed.

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From the book Budget System of the Russian Federation author Burkhanova Natalya

5.1. Types of projects There are many types of projects depending on various characteristics.1. By implementation environment:? projects in a newly created environment (company);? projects within an existing company.2. By project start point:? creation projects are necessary for

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From the book Financial Analysis author Bocharov Vladimir Vladimirovich

46. Ranking of projects To rank projects, the following methods are used: 1) payback period method; 2) “accounting return on investment” method; 3) net present (discounted) value NVP method; 4) internal rate of return method IRR. Payback period.

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Chapter 8 Financial analysis of the effectiveness of investment projects 8.1. Investment rules The most common factors for achieving investment goals are: 1) collecting the necessary information to develop a business plan for an investment project; 2) studying and

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Topic 5. Evaluation of investment projects. Cost Analysis

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54. Uncertainty of investment projects Uncertainty of investment projects is caused by incomplete or inaccurate information about the conditions for the implementation of individual planned decisions, causing certain losses (in some cases, additional benefits).

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From the book Marketing for Government and Public Organizations author Kotler Philip

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From the book Fundamentals of Management by Meskon Michael

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Project Management “A project is a set of tasks or activities related to achieving a planned goal, usually unique and non-repeating.” Almost all managers are involved in project management. If operations are project oriented

Development of alternative project options. The process of forming a plan for an investment project involves the development of alternative options for achieving the stated goals of the project, the subsequent analysis of each option from the point of view of its feasibility, as well as the development of criteria for selecting the most preferable alternatives.
Alternative options should, first of all, take into account production expansion strategies, which may involve both significant capital expenditures aimed at rapid capital growth, and the use of limited enterprise resources (and correspondingly slow capital growth). If growth is slow, expansion strategies should also include modest capital expenditures in the future as additional opportunities arise. These options are extreme, between which there may be additional ones, differing in a certain (specific) level of capital investment, conditions for project implementation and investment in terms of timing, technology and other characteristics.
The main criteria that determine the differences between project options when formulating alternatives and their comparative analysis are their cost, deadlines, and capital growth from the implementation of the project.
Additional and special development and analysis should be carried out on various provisions of the project that distinguish the options under consideration, as well as the general conditions for the implementation of the project, which will be developed in more detail in the future (adopted legislative provisions and government actions, infrastructure and sources of supply of raw materials, available reserves of natural resources, location project, technologies used, etc.).
Current legislative acts and the position of the government, on which the success of the project depends, are the most important and general issues in the formation of alternative options for its development. They must be analyzed along with the main determinants of the alternatives being considered. Investors generally insist that all regulations, tariffs and other agreements that are critical to the success of the project be as binding as possible. To do this, project participants must take specific responsibility for the fact that during its implementation they will comply with all the requirements and provisions set for obtaining a particular permit to implement the project under certain conditions. It is also necessary to provide for insurance of the main types of risk for possible environmental damage in connection with the operation of the project (for example, leakage of oil and petroleum products, release of hazardous waste, air pollution with harmful emissions and other impacts associated with the implementation of the project).
For international projects, in each individual case the principles of distribution between participants, third parties and investors of risks associated with the protection of property (expropriation, the right of the government to participate in a profitable enterprise or inconvertibility of the currency, etc.) must be agreed upon. In some cases, where there is significant concern about the political climate in which a project is being developed, the host government and government agencies may provide assurances against political risk. To make a preliminary assessment of the feasibility of the developed options for achieving the project’s goals, it is necessary to formulate as complete a list of problems as possible that may prevent the achievement of the desired result.
The main problems affecting the implementation of the project are formulated based on the results of an analysis of the external environment, identifying the strengths and weaknesses of the project and the organization implementing the project (if the project is being implemented at an existing enterprise).
Problems are determined by the insufficiency or unreliability of the necessary information about the project and its external environment, as well as the related inability to clearly formulate the desired result and assess the objective possibilities of achieving it.
Among the main problems that influence the fate of the project, problems associated with the definition and implementation of both general and immediate goals and specific functional goals and objectives should be taken into account. At the same time, all possible problems whose resolution causes difficulties should be identified. First, it is necessary to analyze in detail all the difficulties that may be caused by the complexity of the project and its individual components during their development and as the project is implemented. Such problems may be associated with ensuring competitive advantages of goods or services during its implementation that are sufficient for the success of the project, with the novelty and undeveloped technology of their production, ensuring low production and sales costs, etc. Secondly, it is necessary to evaluate the available sources of information about the project and its external environment for their reliability and sufficiency for making decisions to correctly formulate the goals of the project and determine ways to achieve them. Thirdly, it is necessary to take into account the problems associated with the risks of failure to achieve the desired result of the project when market conditions and other conditions for its implementation change.

More on the topic DEVELOPMENT OF ALTERNATIVE OPTIONS FOR THE PROJECT AND FORMULATION OF PROBLEMS THAT AFFECT ITS IMPLEMENTATION:

12.4. Alternative solutions to energy problems
Chapter 13. ANALYSIS OF THE INFLUENCE OF UNCERTAINTY AND RISK FACTORS ON THE RESULTS OF IMPLEMENTATION (EFFICIENCY) OF THE PROJECT

In practice, most investment projects are conflicting, or in other words, competing. In this situation, the enterprise is faced with the need to select a project not just based on economic efficiency criteria, but in comparison with other projects, i.e. an assessment of the relative effectiveness of investments is required.

There are two types of competing projects: independent and alternative.

TO independent include projects for different purposes. The issue of their acceptance (or non-acceptance) is decided not only on the basis of the values of the project’s economic efficiency indicators, but also on the availability of investment resources at the enterprise.

Investments are called alternative(or mutually exclusive), when acceptable investment projects cannot be implemented simultaneously, i.e. accepting one of them excludes the possibility of accepting the other.

When evaluating alternative projects, the choice is made based on indicators PP (DPP), NPV, IRR, etc. If the two projects are independent, then the above criteria give the same result regarding the acceptance or rejection of the project. If alternative projects are analyzed, diametrically opposed conclusions can be drawn about the advisability of their inclusion in the plan. For example, according to the NPV, PI and IRR indicators, projects can be rejected as ineffective, but according to the PP and ARR indicators, they can be accepted. In this case, it is usually recommended to use the NPV criterion as a basis. The preference for net present value is due to the fact that the main goal of the company is to maximize its value. However, in practice this goal is not always the dominant one. Internal rate of return (IRR) is often preferred because it is easier to make investment decisions based on relative valuations. In any case, when assessing the attractiveness of an investment, an investor is often guided by subjective assessments of the economic indicators and risk used. And, say, in a situation of acute need for funds, minimizing the payback period may be a priority.

In the context of multi-criteria selection of the most appropriate investment, you can use the following recommendations:

Firstly, one indicator, the most important from the point of view of the enterprise strategy, must be selected and a single project must be selected based on it.

Secondly, it is necessary, based on the attraction of information, to formulate additional criteria that reflect the requirements of the enterprise strategy for investment policy.

Numerous studies of investment decision-making practices indicate that the most common criteria are NPV and IRR. Unfortunately, there are situations when these indicators conflict with each other. The premise of the conflict is that the value of cash flows depends on the interest rate at which the cash flows will be reinvested. In the case of NPV, discounting is carried out at the price of capital, while the use of the IRR criterion means that the enterprise has projects with an IRR return.

The IRR criterion makes sense for projects with one alternation of sign (transition from minus to plus) of the cash flow for the project. The NPV and IRR are consistent if the net present value is positive. If this is not the case, then it is possible to find a discount rate at which both projects have the same NPV. The abscissa of the intersection point, showing the value of the discount rate at which two alternative projects have the same NPV, is called Fisher point . The Fisher point separates situations when making a decision on the economic attractiveness of a project based on the NPV criterion depends on the value of the discount rate.

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Introduction

The market economy in the Russian Federation is gaining more and more strength. Along with it, competition is gaining strength as the main mechanism for regulating the economic process. The competitiveness of an enterprise, joint stock company, or any other economic entity can only be ensured by proper management of the movement of capital and financial resources at their disposal.

Finance is a set of monetary relations that arise in the process of production and sale of products (works, services) and includes the formation and use of cash income, ensuring the circulation of funds in the reproduction process, organizing relationships with other enterprises, the budget, banks, insurance organizations, etc.

Financial management is the science of managing all these processes. Enterprise financial management involves the development of methods that the enterprise sets for itself to achieve certain goals, the ultimate of which is to ensure a strong and sustainable financial condition.

Financial management includes the development and selection of criteria for making the right financial decisions, as well as the practical use of these criteria, taking into account the specific conditions of the enterprise.

The initial basis for managing the finances of an enterprise is its actual financial condition. It makes it possible to answer questions about how effective the management of financial resources and property was, whether the structure of the latter is rational; how debt and own sources of financing activities are combined, what is the return on production potential, asset turnover, return on sales, etc.

Financial decisions are made specifically for a given enterprise; for another enterprise they may be completely different. Moreover, financial decisions at the same enterprise can be completely different at different periods of its activity. It is necessary to change any one parameter in internal or external conditions - and this change necessitates reorientation in a number of strategic and tactical areas of influence on the finances of the enterprise. All enterprises are to one degree or another related to investment activities. Making investment decisions is complicated by various 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 purpose of this work is to conduct a comparative analysis of investment projects of different durations.

1. Options and methods for evaluating investment projects

1.1 Development of investment project options

All enterprises are to one degree or another related to investment activities. Making investment decisions is complicated by various 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 of the economic side of the project, which precedes decision-making, must also be different; In addition, in many companies the practice of differentiating the right to make investment decisions is becoming commonplace, i.e. the maximum amount of investment within which one or another 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.

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 and calculations are known, with the help of which they can serve as the basis for making decisions in the field of investment policy. There is no universal method suitable for all occasions. Perhaps management is still more of an art than a science. Nevertheless, having some estimates obtained by formalized methods, even if somewhat conditional, makes it easier to make final decisions.

1.2 Methods for evaluating investment projects

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 perceived differently depending on the existing objective and subjective conditions: the inflation rate, the size of investments and generated revenues, the forecasting horizon, the analyst’s skill level, etc.

Methods used in the analysis of investment activity can be divided into two groups: a) based on discounted valuations; b) based on accounting estimates. Let's look at the key ideas behind these methods.

The method for calculating the net present effect is based on comparing the value of the initial investment (1C) with the total amount of discounted net cash flows generated by it during the forecast period. Since the cash inflow is distributed over time, it is discounted using a factor r, set by the analyst (investor) independently based on the annual percentage return that he wants or can have on the capital he invests.

Let's say a forecast is made that the investment (1C) will generate annual income in the amount of P 1, P 2,... P n for n years. 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. 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.

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 the projected average inflation rate.

Calculation using the above formulas manually is quite labor-intensive, therefore, for the convenience of using this and other methods based on discounted valuations, special statistical tables have been developed in which the values of compound interest, discount factors, discounted value of a monetary unit, etc. are tabulated. depending on the time interval and the value of the discount factor.

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

The method for calculating the return on investment index is, in fact, a consequence of the previous one. The profitability index (PI) is calculated using the formula

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

P.I.< 1, то проект следует отвергнуть;

PI = 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 a portfolio of investments with the maximum total NPV value.

Method for calculating the rate of return on investment.

Under rate of return , or internal rate of return, investment (IRR) understands 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 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's interest rate, above which the project will be 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 some reasonable costs 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 enterprise's current minimum return on capital invested in its activities, its profitability, and is calculated using the arithmetic weighted average formula.

The economic meaning of this indicator is as follows: an enterprise can make any investment decisions, the level of profitability of which is not lower than the current value of the CC indicator (or the price of the source of funds for a given 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< СС, то проект следует отвергнуть;

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

The practical application of this method is complicated if the analyst does not have a specialized financial calculator at his disposal. In this case, the method of successive iterations is used using tabulated values of discount factors. To do this, using tables, two values of the discount factor r 1 are selected< r 2 таким образом, чтобы в интервале (r 1 , r 2) функция NPV=f(r) меняла свое значение с «+» на «-» или с «-» на «+». Далее применяют формулу:

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)< 0 (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 (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 (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 “+”.

The method of determining the payback period of investments 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:

PP = min n, at which

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

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

First, it does not take into account the impact of recent earnings. As an example, consider two projects with identical capital costs (10 million rubles), but different projected annual incomes: for project A - 42 million rubles. within three years; for project B - 3.8 million rubles. within ten years. Both of these projects provide a return on capital investments within the first three years, so from the standpoint of this criterion they are equal. However, it is obvious that Project B is much more profitable.

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

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, and 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. This situation is typical for industries or activities that are characterized by a high probability of fairly rapid technological change.

The method for calculating the investment efficiency ratio has two characteristic features: firstly, it does not involve discounting income indicators; secondly, income is characterized by the net profit indicator PN (balance sheet 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 the presence of residual or salvage value (RV) is allowed, then its assessment must be taken into account.

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).

This indicator is compared with the rate of return on advanced capital, 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 the average annual profit, but the varying amount of profit over the years, as well as between projects that have the same average annual profit, but generated over different periods of time. number of years, etc.

2. Analysis of investment projects

2.1 Analysis of alternative projects

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.

It was noted above that depending on the adopted criterion, the choice will be different. Despite the fact that there are obvious relationships between the indicators NPV, PI, IRR, CC:

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

if NPV< 0, то одновременно IRR < CC и PI < 1;

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

It is not always possible to draw a clear conclusion. What criterion should be used in this case? To illustrate, consider a simple example.

Some arguments in favor of one or another criterion were given above. First of all, it is necessary to emphasize once again that methods based on discounted valuations are more justified from a theoretical point of view, since they take into account the time component of cash flows. At the same time, they are relatively more computationally intensive.

Thus, the main conclusion can be drawn that 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 is that NPV is an absolute indicator, while PI and IRR are relative.

Analysis of alternative projects

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 and PI.

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 (last line of the table); Moreover, if IRR > CC, then the incremental costs are justified and it is advisable to accept a project with large capital investments.

Research conducted by leading experts in the field of financial analysis has shown that the most preferable 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; the criterion fully meets the main goal of the activities of management personnel, which, as noted earlier, is to increase the economic potential of the enterprise;

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.

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. 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 from the perspective of their possible contribution to increasing the capital of the enterprise; This drawback is especially pronounced if projects differ significantly in the amount of cash flows.

Analyze two alternative projects if the company's cost of capital is 10%.

investment cash flow discounted

Analysis of projects with different cash flows (thousand rubles)

At first glance, the first project is 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 cost 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.

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) ? IRR(A) +IRR(B).

Analyze the feasibility of investing in projects A, B, C, provided that projects B and C are mutually exclusive, and project A is independent. The price of the investment source is 10%.

Based on the example conditions, it is necessary to analyze several scenarios:

a) the feasibility of adopting each of the projects separately (A, B or C);

b) the feasibility of adopting a combination of projects (A+B) and (A+C).

Analysis of a combination of investment projects (million rubles)

From the above calculations it is clear that all three initial projects are acceptable, so it is necessary to analyze their possible combinations. According to the IRR criterion, the combination of projects A and B is relatively better, but this conclusion is erroneous, since the other combination gives a greater increase in the company’s capital. In addition, it is clear that only the NPV criterion has the additivity property.

4. The IRR criterion is 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.

If we recall that IRR is the root of the equation NPV = O, and the function NPV = f (r) is an algebraic equation of the kth degree, where k is the number of years of project implementation, then, based on Descartes’ rule, the equation NPV = 0 has so many decisions on how many times the sign of the cash flow changes. In other words, if cash flow values alternate in sign, several values of the IRR criterion are possible.

When considering the graph of the NPV function = f (r, P k) (Fig. 2), you can notice its different representation depending on the values of the discount factor and the signs of cash flows (“+” or “-”). There are two most realistic typical situations.

Possible representations of the NPV change graph

The given types of graph of the function NPV= f (r, P k ,) 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. In table 5 shows options for investment projects corresponding to the situations described; graphs of the function NPV=f(r) are shown in Fig. 3.

Graph of the function NPV = f(r) for projects with different numbers of IRR

Streams with Multiple IRRs(thousand roubles.)

2.2 Comparative analysis of projects of different durations

In real life, it is quite likely that projects of different durations need to be compared. Let projects A and B be designed for i and j years, respectively. In this case it is recommended:

find the least common multiple of the project duration z = HOK (i, j);

considering each of the projects as recurring, analyze the NPV of projects A and B, implemented the required number of times during period z;

select the project from the original ones for which the total NPV of the repeating flow has the greatest value.

The total NPV of a repeating flow is found by the formula

Where NPV (i) is the net present value effect of the original (repeating) project;

i is the duration of this project;

r is the discount factor in fractions of one;

n is the number of repetitions of the original project (it characterizes the number of terms in brackets).

In each of the two situations below, you need to select the most preferred project if the cost of capital is 10%:

a) project A: -100; 50; 70;

project B: -100; thirty; 40; 60;

b) project B: -100; 50; 72;

project B: -100; thirty; 40; 60.

If we calculate the NPV for projects A, B and C, they will be 3.30 million rubles, 5.4 million rubles, 4.96 million rubles, respectively. These data cannot be directly compared, so it is necessary to calculate the NPV of the given flows. In both cases, the least common multiple is 6. During this period, project A can be repeated three times, and project B twice.

Scheme for calculating NPV based on given flows

From the above diagram it can be seen that in the case of a three-fold repetition of project A, the total NPV is equal to 8.28 million rubles:

where 3.30 is the present income of the first implementation of project A;

2.73 - present income of the second implementation of project A;

2.25 - present income of the third implementation of project A.

Since the total NPV in the case of a double implementation of project B is greater (9.46 million rubles), project B is preferable.

If we make similar calculations for option (b), we find that the total NPV in the case of a three-fold repetition of flow B will be 12.45 million rubles. (4.96+4.10+3.39). Thus, in this option, Project B is preferable.

The considered technique can be simplified in computational terms. Thus, if several projects are analyzed that differ significantly in the duration of implementation, the calculations can be quite tedious. They can be reduced if we assume that each of the analyzed projects has been implemented an unlimited number of times. In this case, the number of terms in the formula for calculating NPV (i, n) will tend to infinity, and the value of NPV (i, ?) can be found using the well-known formula for an infinitely decreasing geometric progression:

Of the two projects being compared, the project with a higher NPV value (i, ?) is preferable. So, for the example considered:

option(s):

project A: i= 2, so

project B: i=3, therefore

option (b):

project B: NPV (3, ?) = 21.71 million rubles;

project B: NPV (2, ?) = 28.57 million rubles.

Conclusion

Fixed assets of enterprises and economic organizations represent a set of means of labor operating over a long period in the sphere of material production and non-production sphere. They have a monetary value. The monetary expression of the value of fixed assets is necessary for their classification, determination of volume, structure, calculation of indicators of quality and efficiency of their use. Fixed assets are valued at initial, residual and replacement cost.

The initial cost of fixed assets is determined by the sum of all monetary costs for their creation. It includes the costs of construction of buildings and structures, purchase of equipment, including the cost of its delivery and installation, in prices prevailing at that time.

The residual value is the difference between the original cost and the amount of accrued depreciation, i.e. that part of the cost of fixed assets that has not yet been transferred to the costs of producing products or providing services in the form of depreciation.

Replacement cost is the cost of creating or acquiring fixed assets, expressed in current prices. An assessment of the fixed assets on the balance sheet of enterprises at replacement cost is necessary to determine their actual value in modern conditions, since from the moment of their creation or acquisition it could have changed significantly under the influence of depreciation of fixed assets and the reduction in the cost of their production. To determine the replacement cost, periodic, approximately once every 10 years, revaluations of fixed assets are carried out.

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