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Introduction
Market economy in Russian Federation is gaining more and more power. Along with it, competition is gaining strength as the main mechanism for regulating the economic process. The competitiveness of an enterprise, a joint-stock company, or any other economic entity can only be ensured by the correct 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 include 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. Financial management of an enterprise involves the development of methods that an enterprise sets for itself in order to achieve certain goals, the final of which is to ensure a strong and stable 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 financial condition, which has actually developed. It provides an opportunity to answer questions about how effective was the management of financial resources and property, whether the structure of the latter is rational; how borrowed and own sources of financing are combined, what is the return on production potential, asset turnover, return on sales, etc.
Financial decisions are made specifically for this enterprise; for another enterprise, they may be completely different. Moreover, financial decisions in the same enterprise can be completely different in different periods his activities. It is worth changing 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 in one way or another are connected with investment activity. Making investment decisions becomes more difficult various factors: type of investment; the cost of the investment project; plurality of available projects; limited financial resources available for investment; the risk associated with the adoption of a particular decision, etc.
The purpose of this work is to conduct a comparative analysis of investment projects of different duration.
1. Options and methods for evaluating investment projects
1.1 Development of options for investment projects
All enterprises in one way or another are connected with investment activity. Making investment decisions is complicated by various factors: type of investment; the cost of the investment project; plurality of available projects; limited financial resources available for investment; the risk associated with the adoption of 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 production activities, development of new activities. The degree of responsibility for the adoption of an investment project within a particular direction is different. So, if we are talking about replacing existing production capacities, the decision can be made quite painlessly, since the company's management clearly understands the 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 the main activity, 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 question of the size of the proposed investment is important. Thus, the level of responsibility associated with the adoption of projects worth 1 million rubles. and 100 million rubles, different. Therefore, the depth of the analytical study of the economic side of the project, which precedes the decision, should also be different; In addition, in many firms, it is becoming common practice to differentiate the right to make decisions of an investment nature, i.e. the maximum amount of investment is limited, within which one or another manager can make independent decisions.
Often decisions must be made in an environment 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. It is obvious that 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, much 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.
A very significant risk factor. Investment activity is always carried out in conditions of uncertainty, the degree of which can vary significantly. Thus, at the time of the acquisition of 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 management activities, is based on the use of various formalized and non-formalized methods. The degree of their combination is determined by various circumstances, including those of them, as far as the manager is familiar with the available apparatus applicable in a particular case. In domestic and foreign practice, there are a number of formalized methods, calculations, which 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 to a certain extent conditional, it is easier to make final decisions.
1.2 Methods for evaluating investment projects
At the heart of the adoption process management decisions of an investment nature are 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 problem here is the problem of their comparability. It can be perceived differently depending on the existing objective and subjective conditions: the rate of inflation, the size of investments and generated revenues, the forecasting horizon, the skill level of an analyst, etc.
The methods used in the analysis of investment activity can be divided into two groups: a) based on discounted estimates; b) based on accounting estimates. Let's take a look at the key ideas behind these methods.
The method of calculating the net present effect is based on comparing the value of the original investment (1C) with the total amount of discounted net cash flows generated by it over the forecast period. Since cash inflows are spread over time, they are discounted by a factor r set by the analyst (investor) on their own based on the annual percentage return that they want or can have on their capital invested.
Suppose a forecast is made that an investment (1C) will generate annual income in the amount of P 1, P 2, ... P n over n years. The total accumulated value of discounted income (PV) and the net present effect (NPV) are respectively calculated by 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 years, it is necessary to take into account, if possible, all types of income, both industrial and non-productive, that may be associated with this project. So, if at the end of the project implementation period it is planned to receive funds in the form of the salvage 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 involves not a one-time investment, but a consistent 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.
Manual calculation using the above formulas is quite time-consuming, therefore, for the convenience of using this and other methods based on discounted estimates, special statistical tables have been developed in which the values of compound interest, discount factors, discounted value of the 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 the predictive assessment of the change in the economic potential of the enterprise in the event that the project under consideration is accepted. This indicator is additive in terms of time, i.e. NPV of different projects can be summarized. This is a very important property that distinguishes this criterion from all the others and allows it to be used as the main one when analyzing the optimality of an investment portfolio.
The method of calculating the return on investment index is, in fact, a consequence of the previous one. Profitability Index (PI) is calculated using the formula
Obviously, if: PI > 1, then the project should be accepted;
PI< 1, то проект следует отвергнуть;
PI = 1, then the project is neither profitable nor unprofitable.
Unlike the net present effect, the profitability index is a relative indicator. Due to this, it is very convenient when choosing one project from a number of alternative ones with approximately the same NPV values, or when completing an investment portfolio with the maximum total NPV value.
Method for calculating the rate of return on investment.
Under rate of return , or internal rate of return, investments (IRR) understand the value of the discount factor at which the NPV of the project is zero: IRR = r, at which NPV = f (r) = 0.
The meaning of calculating this ratio when analyzing the effectiveness of planned investments is as follows: IRR shows the maximum allowable relative level of expenses that can be associated with a given project. For example, if the project is fully financed by a loan from a commercial bank, then the IRR value shows the upper limit of the acceptable level of the bank interest rate, the excess of which makes the project unprofitable.
In practice, any enterprise finances its activities, including investment, from various sources. As a payment for the use of financial resources advanced into the activities of the enterprise, it pays interest, dividends, remuneration, etc., i.e. incurs some reasonable costs to maintain its economic potential. An indicator that characterizes the relative level of these costs can be called the price of advanced capital (CA). This indicator reflects the minimum return on the capital invested in its activities, its profitability, which has developed at the enterprise, and is calculated using the average, arithmetic weighted formula.
The economic meaning of this indicator is as follows: an enterprise can make any investment decisions, the level of profitability of which is not lower than the current value of the CC indicator (or the price of the source of funds, for this project, if it has a target source). It is with him that the IRR indicator calculated for a specific project is compared, while the relationship between them is as follows.
If: IRR > СС, then the project should be accepted;
IRR< СС, то проект следует отвергнуть;
IRR = CC, 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 applied using tabulated values of discount factors. To do this, using tables, two values of the discount factor r 1< 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 calculation accuracy 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 - the nearest to each other values of the discount coefficient that satisfy the conditions (in case of changing the sign of the function from "+" to "-"):
r 1 - the value of the tabulated discount factor, minimizing 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, maximizing the negative value of the NPV indicator, i.e. f(r 2)=max (f(r)< 0}.
By mutual replacement of 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 most 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:
PP = min n, at which
Some experts still recommend taking into account the time aspect when calculating the PP indicator. In this case, the cash flows discounted by the price of the advanced capital are taken into account. Obviously, the payback period is increasing.
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 income from recent periods. As an example, let's consider two projects with the same capital costs (10 million rubles), but different projected annual income: project A - 42 million rubles. within three years; for project B - 3.8 million rubles. within ten years. Both of these projects during the first three years provide a return on capital investments, therefore, from the standpoint of this criterion, they are equal. However, it is clear that project B is much more profitable.
Second, because this method is based on undiscounted estimates, it does not distinguish between projects with the same amount of cumulative returns but different distributions over the years. So, from the standpoint 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 it may be appropriate to apply the payback method. In particular, this is a situation where the company's management 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 a situation where investments are associated with 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 of 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 deductions 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 is found by dividing the initial amount of capital investments by two, if it is assumed that after the expiration of the analyzed project, all capital costs will be written off; if residual or salvage value (RV) is allowed, then its estimate should be taken into account.
This indicator is compared with the ratio of return on capital advanced, 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 return on capital advanced, 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 drawbacks, 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 during different 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 criterion adopted, the choice will be different. Despite the fact that there are obvious relationships between NPV, PI, IRR, CC indicators:
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 an unambiguous conclusion. What criterion should be used in this case? To illustrate, consider a simple example.
Some arguments in favor of one criterion or another have been given above. First of all, it is necessary to emphasize once again that methods based on discounted estimates are more justified from a theoretical point of view, since they take into account the time component of cash flows. However, they are relatively more computationally intensive.
Thus, we can draw the main conclusion that 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.
Analysis of alternative projects
If projects A and B are considered in isolation, then each of them must be approved, since they meet 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 (the last line of the table); at the same time, if IRR > СС, then the incremental costs are justified and it is advisable to accept a project with large capital investments.
Studies conducted by leading experts in the field of financial analysis have shown that 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; the criterion fully meets the main goal of the activities of managerial 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 up 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's briefly characterize them.
1. In a comparative analysis of alternative projects, the IRR criterion can be used rather conditionally. So, 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 more flexibility in varying sources of financing investments, the price of which can vary significantly. However, this preference is highly arbitrary. Since IRR is a relative indicator, it is impossible to draw correct conclusions about alternative projects from the standpoint of their possible contribution to increasing the capital of the enterprise; this shortcoming is especially pronounced if the projects differ significantly in terms of cash flows.
Analyze two alternative projects if the company's cost of capital is 10%.
discounted investment cash flow
Analysis of projects with different cash flows (thousand rubles)
At first glance, the first project is more preferable, since its IRR is much higher than the IRR of the second project. However, if the enterprise has the opportunity to finance project B, it should certainly be preferred, since the contribution of this project to increasing the capital of the company 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 evaluated project. 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 distinguishing between situations when the price of capital changes. Let's consider a corresponding example.
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) ? 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 condition of the example, it is necessary to analyze several scenarios:
a) the feasibility of accepting each of the projects separately (A, B or C);
b) the feasibility of accepting a combination of projects (A+B) and (A+C).
Analysis of a combination of investment projects (million rubles)
From the above calculations, it can be seen 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 the analysis of non-ordinary investment flows (the name is conditional). In the previous paragraphs, the standard, most simple and typical situations were considered when the cash flow develops according to a well-defined pattern: investment or capital outflow (with the "-" sign in the calculations) and capital inflow or inflow (with the "+" sign in the calculations). However, other, extraordinary situations are also possible, when the outflow and inflow of capital alternate. In particular, the situation when the project ends with an outflow of capital is quite real. This may be due to the need to dismantle the equipment, the cost of restoring the environment, 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 from them may not always be correct.
If we recall that IRR is the root of the equation NPV \u003d O, and the function NPV \u003d f (r) is an algebraic equation k-th degree, where k is the number of years of project implementation, then, based on the Descartes rule, the equation NPV=0 has as many solutions as the number of times the sign of the cash flow changes. In other words, if the values of the cash flow 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), one can notice its different representation depending on the values of the discount factor and signs of cash flows ("+" or "-"). There are two most realistic typical situations.
Possible representations of the NPV change graph
The given types of the 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 the growth of r and has a single value of IRR. In the second situation, the type of graph may be different. In table. 5 shows options for investment projects that correspond 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 IRRs
Streams with multiple IRRs(thousand roubles.)
2.2 Comparative analysis of projects of different duration
AT 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 duration of projects z = HOK (i, j);
considering each of the projects as repetitive, analyze the NPV of projects A and B, implemented the required number of times during the period z;
select the project from the source for which the total NPV of the recurring flow has the highest greater value.
The total NPV of the recurring flow is found by the formula
Where NPV (i) is the net present value of the original (recurring) project;
i is the duration of this project;
r - discount factor in fractions of a unit;
n - the number of repetitions of the original project (it characterizes the number of terms in brackets).
In each of the two situations below, it is required to choose the most preferred project if the cost of capital is 10%:
a) project A: -100; fifty; 70;
project B: -100; thirty; 40; 60;
b) project C: -100; fifty; 72;
project B: -100; thirty; 40; 60.
If we calculate the NPV for projects A, B and C, then they will amount to 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 reduced flows. In both cases, the least common multiple is 6. During this period, project A can be repeated three times, and project B twice.
NPV calculation scheme for reduced flows
It can be seen from the above diagram that in the case of a three-fold repetition of project A, the total NPV is 8.28 million rubles:
where 3.30 is the reduced income of the first implementation of project A;
2.73 - reduced income of the second implementation of project A;
2.25 - the reduced 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 get 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. So, 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 compared projects, the project with the higher NPV (i, ?) is preferred. So, for this example:
option (a):
project A: i= 2, so
project B: i=3, so
option (b):
project B: NPV (3, ?) = 21.71 million rubles;
project B: NPV (2, ?) = 28.57 million rubles.
Conclusion
The fixed assets of enterprises and economic organizations are a set of means of labor operating for a long period in the sphere of material production and non-production sphere. They have a monetary value. Monetary expression of the value of fixed assets is necessary for their classification, determination of volume, structure, calculation of indicators of the qualitative state and efficiency of their use. Fixed assets are valued at original, residual and replacement cost.
The initial cost of fixed assets is determined by the sum of all monetary costs for their creation. It includes expenses for the construction of buildings and structures, the purchase of equipment, including the cost of its delivery and installation, at the prices in force at that time.
The residual value is the difference between the original cost and the accumulated 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. Evaluation of 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 they were created or acquired, under the influence of depreciation of fixed assets and the reduction in the cost of their production, it could change significantly. To determine the replacement cost, periodic, approximately once every 10 years, revaluation of fixed assets is carried out.
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One of the motives forcing the company to choose one or more of several promising and profitable investment projects is the limited financial resources. An investment cap is a fixed limit on the annual amount of capital investment that a firm can afford based on its financial position. In the presence of financial restrictions on investments, the firm may accept some investment projects that make up such a combination that will provide the greatest effect.
Suppose that the firm has the following investment proposals (see Table 8.1.1), ranked in descending order by profitability index (the ratio of the present value of future net cash flows to initial costs).
Table 8.1.1
Based on its financial position, the company plans to allocate 2 million rubles for investments. In this case, the company will choose from the proposed projects those that promise the greatest profitability, and the sum of all initial costs will not exceed 2 million rubles.
In our case, these are proposals 3, 7, 4, 2 and 6, since they have the highest profitability, and the amount of starting capital is 2 million rubles. (800+200+350+250+400).
The firm will not accept proposal 1, although the initial costs are significantly inferior to other projects, and its profitability, although more than one, is inferior in size to other projects.
When considering several alternative investment projects, depending on the chosen method of its economic evaluation, one can get far from unambiguous results, often contradicting each other. At the same time, between the considered indicators of investment efficiency ( NPV; PI; IRR) there is a certain relationship.
So if NPV>0 , then simultaneously IRR> CC and PI>1 ;
At NPV=0 , simultaneously IRR> CC and PI=1 .
To decide which criterion to use in this case, consider an example.
Example 1. The firm is considering four options for investment projects that require equal initial investment (2400 thousand rubles). It is necessary to make an economic assessment of each project and choose the best one. Financing of projects is carried out at the expense of a bank loan in the amount of 18% per annum.
Dynamics of cash flows and calculated performance indicators are given in Table. 8.1.2.
Table 8.1.2
|
Projected cash flows, thousand rubles |
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|
Indicators |
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Analysis of the data given in the table allows us to draw the following conclusions:
best indicator NPV= 809.6 thousand rubles belongs to the first project. Therefore, the adoption of this project promises the greatest capital gain.
In the first investment project, the indicator PI=1,33 7, i.e. the reduced sum of the members of the cash flow is 33.7% higher than the value of the start-up capital.
The largest value of the indicator IRR=27.8% has a fourth investment project. However, given that the bank provided a loan at 18% per annum, this advantage is not significant.
The shortest payback period PP=1.79 for the fourth project, but given that the difference in payback periods between highest value(2.33 years) and the smallest value is just over half a year, this advantage can be neglected.
Thus, having considered four investment projects according to four indicators, we can give preference to the first project.
In works devoted to methods of economic evaluation of investments, preference is given to the indicator NPV.
This is explained by the following factors:
This indicator characterizes the predicted value of the enterprise's capital growth in the event of the implementation of the proposed investment project.
When designing the use of several investment projects, it is possible to summarize the indicator NPV each of them, which gives the aggregate amount of capital gains.
When analyzing alternative investment projects, the use of the internal rate of return indicator - IRR due to a number of inherent shortcomings should be limited. Let's consider some of them.
1. Since the IRR is a relative indicator, based on its value, it is impossible to draw a conclusion about the size of the increase in the capital of the enterprise when considering alternative projects.
For example, let's take two alternative projects, which are presented in Table. 8.1.3.
Table 8.1.3
|
Investment amount, thousand roubles. |
Cash flow by years |
IRR, % |
NPV at a yield of 15%, thousand rubles. |
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If we judge projects only by the indicator IRR, then Project A is preferable. At the same time, it provides capital gains in a smaller amount than project B.
If the company has the opportunity to implement project B without borrowing, then it becomes more attractive.
2. From the definition of the essence of the indicator IRR it follows that it shows the maximum relative level of costs associated with the implementation of the investment project. Therefore, if this indicator is the same for two investment projects, and it exceeds the price of investments (for example, bank interest on borrowed capital intended for the implementation of projects), then other criteria must be used to select between projects.
3. Indicator IRR unsuitable for the analysis of projects in which cash flow alternates between inflow and outflow of capital. In this case, the conclusions drawn from the indicator IRR, may not be correct.
Initial Key Provisions
From the position of the management personnel of the enterprise, investment projects can be classified in a more differentiated way than was done in Chapter 2 on the following grounds:
Type of expected income - cost reduction, additional income from the expansion of traditional industries and technologies, entering new markets, expansion into new business areas, reducing the risk of production and marketing, social effect; "
Relations of interdependence - mutually concluding (alternative) projects, relations of complementarity, substitution, economic independence;
Type of cash flow - ordinary, extraordinary. Two analyzed projects are called independent if the decision to accept one of them does not affect the decision to accept the other.
Two analyzed projects are called alternative if they cannot be implemented simultaneously, i.e. acceptance of one of them means that the second project should be automatically rejected.
Projects are interconnected by complementary relations if the adoption of a new project contributes to the growth of one or more other projects.
Projects are linked by a substitution relationship if the adoption of a new project leads to some decrease in income for one or more existing projects.
A cash flow is called an ordinary cash flow if it consists of an initial investment made at one time or over several consecutive base periods and subsequent cash inflows. If cash inflows alternate in any sequence with their outflows, the flow is called extraordinary.
Investment projects differ in the degree of risk: the least risky projects carried out under the state order; the most risky projects associated with the creation of new industries and technologies.
Administration of investment activity includes the following stages: planning, promotion, project implementation, control, evaluation, analysis of results.
The critical points in the capital budgeting process are: forecasting sales volumes, taking into account possible demand for products (since most of projects associated with additional product launches); assessment of cash inflows by years; assessment of the acceptable value of the price of capital, used, among other things, as a discount factor.
Analysis of the possible capacity of the product sales market, i.e. forecasting the volume of sales is extremely important, since its underestimation can lead to the loss of a certain share of sales, and overestimation - to inefficient use of the production capacities commissioned under the project, i.e. to the inefficiency of the investments made.
The price of capital raised to finance a project may change (usually upwards) due to different circumstances. This means that a project accepted under one set of conditions may become unprofitable under another. Different projects respond differently to an increase in the price of capital. Thus, a project in which the bulk of the cash flow falls in the first years of implementation, i.e. reimbursement of the investments made is carried out
more intensively, less sensitive to price increases for the use of sources of funds.
Investment projects analyzed in the capital budgeting process have a certain logic:
Most often, the analysis is carried out by year;
It is assumed that the entire investment is made at the end of the year preceding the first year of the project's cash flow;
Cash inflow (outflow) takes place at the end of the next year;
The discount factor used to evaluate projects should correspond to the length of the period underlying the investment project (for example, the annual rate is taken only if the period is one year).
Project evaluation and review methods fall into two categories:
1) based on discounted estimates;
2) based on accounting estimates.
The application of methods for evaluating and analyzing projects involves the multiplicity of predictive estimates and calculations used. The longer the project is in time, the more uncertain and risky the cash flow of the last years of its implementation becomes.
Project Evaluation Criteria
The main criteria used in the evaluation of investment projects are:
Net Present Effect (NetPresent Value-NPV);
Return on investment index (ProfitabilityIndex-PI);
Internal rate of return (Internal Rate of Return-IRR);
Modified Internal Rate of Return (ModifiedInternalRate of Return-MIRR);
Payback period (Playback Period - PP). The NPV criterion shows the following:
if NPV if NPV = 0, then if the project is accepted, the welfare of the owners of the enterprise will increase.
The PI criterion characterizes income per unit of costs; it is this criterion that is most preferable when it is necessary to streamline independent projects in order to create an optimal portfolio in the case of a limited amount of investment from above.
The IRR criterion shows the maximum level of costs that can be associated with a given project, i.e. if the price of capital raised to finance the project is greater than the IRR, then the project can only be completed at a loss, therefore, it is unacceptable.
The MIRR criterion is a discount factor that equalizes the present value of cash outflows (investments) and the accumulated value of inflows, and the operations of discounting outflows and increasing inflows are performed using the cost of the project capital.
The PP criterion shows the number of base periods for which the original investment will be fully recovered from the cash inflows generated by the project. If the base period is a year, most often the calculation is by years, however, a fractional part of the year can also be distinguished, if we abstract from the initial assumption that cash inflows are carried out at the end of the year.
The NPV criterion reflects the predictive assessment of changes in the economic potential of the enterprise in the event of the adoption of the project under consideration and is additive in the spatio-temporal aspect, i.e. The NPVs of different projects can be summed to find the overall effect.
The IRR criterion shows only the maximum level of costs that can be associated with the estimated project, in particular, if the IRR of two alternative projects is greater than the price of the sources of funds attracted for their implementation, then the choice of the best of them according to the IRR criterion is impossible. This criterion does not have the property of additivity. For non-ordinary cash flows, IRR can have multiple values.
The NPV criterion involves discounting the cash flow at the price of the project capital, and the IRR criterion - at a rate numerically equal to IRR.
When calculating NPV, as a rule, a constant discount rate is used, however, in some circumstances, it is possible to use discount factors individualized by years.
Unlike the IRR criterion, the MIRR criterion allows you to analyze extraordinary cash flows.
The PP criterion does not take into account the impact of income of recent periods that go beyond the payback period. It does not allow distinguishing between projects with the same amount of cumulative income, but different distribution of it over the years. This criterion does not have the property of additivity. Unlike other criteria, the critical
b. Popov Y. M., Lyapunov S. I.
RR allows you to give estimates (albeit rough) of the liquidity and riskiness of the project.
Criteria NVP, IRR, PI, CC are connected by obvious relationships:
if NPV > 0, then IRR > CC and PI > 1;
if NPV if NPV = 0, then W? = CCuP1= 1,
where CC is the price of capital raised to implement the project.
When analyzing alternative projects, the NPV, PI, IRR, MIRR criteria may contradict one another, i.e. a project accepted according to one criterion may be rejected according to another criterion.
Two main reasons determine the possible contradictions between the criteria:
1) the scale of the project, i.e. the elements of the cash flows of one project differ significantly (by one or more orders of magnitude) from the elements of another;
2) intensity of cash flow i.e. whether the main share of the total amount of cash receipts falls mainly on the first or last years of the life of the project.
The NPV criterion is the most universal and preferable in the analysis of investment projects, since it characterizes the possible increase in the welfare of the owners of the enterprise.
Its main disadvantage is that this is an absolute indicator, and therefore it cannot provide information about the so-called project safety margin.
This means the following: if a mistake is made in the cash flow forecast, how big is the risk of turning the project from profitable to unprofitable?
Information about the safety margin of the project is provided by the IRR and PI criteria. Thus, all other things being equal, the larger the IRR compared to the price of capital for the project, the greater the margin of safety.
There are also possible projects that are only costly in nature, i.e. do not affect cash flow. In this case, the same criteria apply, only in relation to the flow characterizing the current costs by years.
To analyze projects, the MRU schedule is often used as a function of the cost of capital. This chart:
Represents a non-linear relationship;
Crosses the y-axis at a point equal to the sum of all elements of the undiscounted cash flow, including the value of the original investment;
Crosses the x-axis at a point corresponding to the IRR of the project;
May have multiple intersection points for non-ordinary streams.
The Fisher point is a boundary point on the abscissa of the NPV graph that separates situations that are captured by the NPV criterion and those that are not captured by the IRR criterion.
If the value of the price of capital is beyond the Fisher point, then the NPV and IRR criteria give the same results when evaluating alternative investment projects. If the price of capital is less than the value at the Fisher point, then the NPVn IRR criteria contradict each other.
The value at the Fisher point is numerically equal to the incremental flow IRR, i.e. a flow composed of the differences of the corresponding elements of the flow flows. To find it, it is necessary to draw up a hypothetical project (incremental flow) and determine the IRR of this project.
For comparative analysis projects of different duration, the methods of the least common multiple, the infinite repetition of the compared projects, the equivalent annuity are applied.
In the context of inflation, either the forecast cash flow or the discount factor is adjusted.
Analysis of investment projects under risk conditions is performed by one of the methods: risk-free equivalent or risk-adjusted discount factor.
Optimization of the capital budget takes place whenever, for some reason, the amount of investment is limited from above.
Investment Opportunity Schedule (IOS) - a graphical representation of the analyzed projects, arranged in order of decreasing internal rate of return IRR.
Graph of the marginal cost of capital (Marginal Cost of Capital - MCC) - a graphical representation of the weighted average cost of capital as a function of the volume of attracted financial resources.
The value of the marginal price of capital of the indicator is used as an estimate of the minimum allowable return on investments in medium-risk projects.
Depending on the type of constraint, the budgeting process can perform spatial or temporal optimization.
Examples of making a decision to invest in a project
Task 1. Compare two business projects according to the NPV, IRR and RR criteria, if the cost of capital is 13%:
A 20,000 7,000 7,000 7,000 7,000
B 25,000 2,500 5,000 10,000 20,000
Task 2. The amount of required investment for a business project is 18,000 dollars. USA, estimated income: in the first year - 1500 dollars. USA, in the next 8 years - 3600 dollars. USA annually. Assess the feasibility of accepting the project if the cost of capital
Task 3. The amount of investment - 1 million rubles; forecast estimate of income generated by years (thousand rubles): 344; 395 - 393; 322.
Calculate the values of the IRR and MIRR indicators if the cost of capital is 10%
Task 4. The company intends to invest up to 65 million rubles. in next year. The divisions presented their proposals for possible investment (in million rubles). Project Amount of investment IRR NPV A 50 15 12 B 35 19 15 C 30 28 42 D 25 26 1 E 15 20 10 F 10 37 11 G 10 25 13 I 1 18 0.1 Select the most appropriate combination of projects if the criterion is :
a) internal rate of return (IRR);
b) net present effect (NPV);
c) return on investment index (PI).
Answers to tasks
1. For the project: AW = 821, IRR = 15%, PP = 2.6 years.
2. The project should be accepted.
3. RR = \1%, MIRR = 14%.
4. a) F + C + D; b) C + B; c) C + G + F + E.
Determining the share of investors in the profits of the project
An effective business idea, when implemented, leads to a sufficient expected profit for both the enterprise and the investor. The general model for determining the shares of the enterprise and the investor in the total rate of return can be as follows: CI + KP = OK; (4.1) PI + PP = OP; (4.2) PI: KI > Ltsh; (4.3) PP: CP > Аchtf, (4.4) where CI is the investor's capital; kp - the capital of the enterprise; OK - the total capital intended for the implementation of business ideas (OK - KI + KP); pi - investor's profit; pp - profit of the enterprise; op - total profit to be distributed among the participants of the business project (OP - PI + PP); Ml and - the rate of return on the investor's capital; is the rate of return on the company's capital. Taking into account (4.1) and (4.2), we can write:
Nou = OP: OK,
where Nou is the general rate of profit sufficient for the enterprise and the investor from the implementation of a business idea. From conditions (4.1)-(4.4), we can derive an equation for determining the shares of the investor and the enterprise in the overall rate of return:
NmxdM + NmxdKnZNQn.
Hence the investor's shares (^uop "(Mim x dm): JV0"; ^nop "(Mw x kn): Won.
where u/ki - share of the investor's capital;
dKU - share of the company's capital. Typically, an enterprise is faced with a situation where there is not one, but many business ideas. Which of them is optimal and capable of bringing the maximum profit? According to the business planning model, this is the idea for which the objective function is valid:
Thus, from the many options for implementing a business idea, one is selected that, with a given total capital and a sufficient rate of return for the investor, is able to bring the maximum total profit. This means that there are effects
of the common capital, which are not subject to distribution between the investor and the enterprise, but are wholly owned by the enterprise. In other words, an enterprise, in the course of implementing a business idea, improves the organization of management, increases the efficiency of supply and marketing, and develops know-how. These additional sources of income usually serve as the basis for rewarding initiators of original business ideas and stimulate innovative business ideas.
Accounting for monetary and financial factors
In many cases, project financing requires both local and foreign currency. Many non-convertible currencies have higher inflation rates than convertible ones. Foreign investors and bankers prefer to read and analyze project financial data expressed in internationally recognized monetary units.
When financial institutions show interest in the financial side of a business project, consideration should be given to agreeing with them on the choice of currency to be used to present financial data. Effectively, this means that all local costs (mostly in non-convertible monetary units) must be converted into agreed international (freely convertible) units.
Usually, when speaking about the opportunity cost of capital, they mean the investment of capital (in case of project abandonment) in financial instruments. However, an approach is possible, in which the number of alternative directions includes capital-forming projects (hereinafter referred to as projects in this section). Consider when this is possible and how the opportunity cost of capital is determined.
Alternative projects should be included in the number of alternative directions if (and only if) these projects alternative capital.
We introduce the following definition.
Projects are called alternative in terms of capital if each of them can be carried out only at the expense of the financial resources necessary for the implementation of other projects.
Therefore, if there is an opportunity to receive money independently (for example, from a bank), no project can be alternative to this project in terms of capital(although it can be alternative to it for other reasons: for example, projects can solve the same problem or use the same limited non-monetary resources - land, for example, etc.). If the projects are not alternative in terms of capital, the opportunity cost of capital in one of them does not depend on the cost of capital in the others.
Now the financial feasibility condition can be formulated as follows: the project is financially feasible if at each calculation step the total balance of its cash flow (the sum of all inflows and outflows) is non-negative.
We often have to deal with projects where the difference between inflows and outflows is negative at some step m , but positive in the previous steps. It is possible to ensure the financial feasibility of such a project by raising additional funds at the step m , either from the outside (for example, in the form of an additional loan), or due to the “withdrawal” of part of the funds in the previous steps. In the latter case, it is assumed that in the previous steps monetary part positive balance is deposited. Where the balance of flows is negative, the necessary amounts are withdrawn from the deposit (including tax deductions), and if there is enough money on the deposit, the project becomes financially feasible.
This procedure: an additional outflow of funds to the deposit at some steps and an additional inflow from the deposit at others - must be taken into account when calculating performance indicators.
In the literature, projects are often referred to as financially feasible, starting from the moment when their cash flows can be converted into flows without negative balance values without attracting external funds (due to the transfer - for example, “through a deposit” - of excess funds from earlier steps). We prefer to call such flows potentially financially feasible.
An approximate condition for the potential financial feasibility of the project is non-negativity at each calculation step accumulated total cash flow balance.
It should be emphasized that before evaluating the effectiveness of the project, it should be turned from potentially financially feasible into financially feasible, i.e. provide for those financial transactions that will make the total balance of all inflows and outflows non-negative at each calculation step.
Let us now consider the possibility of using the introduced indicators to compare projects that are alternative in terms of capital. Naturally, it is assumed that the compared projects are effective, i.e. each of them RNFV i >0 : an inefficient project simply should not be pursued, and therefore the opportunity cost of abandoning it is not determined by its effect. In order not to clutter up the record, when comparing projects that are alternative in terms of capital, we will omit the index indicating the direction of investment. Assume for simplicity that the compared projects P1 and P2 start and end at the same time (if, for example, the second project ends later, the cash flow of the first can be supplemented with the required number of zeros), require the same initial investment To and their cash flows
are the simplest. In this case, there are two possibilities for comparing projects P1 and P2:
determine independently of each other and compare with each other RNFV both projects and select the one with RNFV more (with certain areas of use (reinvestment) of funds);
define RNFV of the P1 project, taking into account the lost profit due to the abandonment of the P2 project, and recognize it as effective if this value turns out to be non-negative.
Let's consider the second way. In this case, the benefit lost when the P2 project was abandoned “in favor” of the P1 project is FV 2 (M ) , and the comparison result is determined by the sign of the quantity FV 1 (M ) - FV 2 (M ) . The same result can be obtained from the “usual” formula for RNFV , unless the costs K compound according to opportunity cost of capital, which evaluates the lost profit in terms of the cost of capital in project 2 and is equal to
Indeed, in this case
In terms of the opportunity cost of capital, it is profitable to carry out project P1 at the expense of project P2 if
Where is determined by (1.30).
Let now the volumes of initial investments for projects P1 and P2 ( K 1 and K 2 ) various. The outlined scheme is preserved here, however, when calculating the lost profit, it must be taken into account that the abandonment of the P2 project leads to the release of additional funds K 2 - K 1 (at K 1 < K 2 ) or linking the sum K 1 - K 2 (at K 1 >K 2 ). Consider first the first case ( K 1 < K 2 ). Since the method RNFV assumes that free funds are used in the direction with the highest available yield, the released difference K 2 -K 1 invested on a deposit at a rate equal to the opportunity cost of capital reduces the lost profit in case of abandoning the P2 project. Thus, the amount of lost profit should be taken equal to
Due to the effectiveness of the P2 project, this value is positive. The opportunity cost of capital for project P1 will be determined by the formula
And the condition for the profitability of the implementation of the P1 project at the expense of the P2 project will again be written in the form
Which, of course, is equivalent to the condition
Finally, consider the case when K 1 > K 2 . In this case, for the implementation of the P1 project, it will be necessary to abandon the P2 project, as well as, possibly, some other projects. Denote by n (n? 2 ) numbers of projects that have to be abandoned for the implementation of the P1 project. In addition, part of the funds is either taken “from the deposit” or put “on the deposit”, depending on the sign of the difference. The opportunity cost in this case is
the opportunity cost of capital is determined by the formula
and the condition for the profitability of the implementation of the P1 project at the expense of the P2 project will be written in the form
In the absence of alternative projects (
) this condition goes over into (1.31), which is natural.
We also note that in the case when there are many projects alternative to this one, the amount of lost profits should be determined as the largest of the similar values.
In real life, any enterprise is faced with limited resources at its disposal. This problem makes it necessary to choose from the whole variety of forms of business activity those that most accurately meet the objectives of the enterprise and allow the most efficient use of available resources.
A resource is any factor consumed in the process of production. It is customary to divide the resources of enterprises into financial, material and labor resources.
If the resources of the enterprise allow it to implement only one of the available investment opportunities, then the projects corresponding to these opportunities are alternative, in other words, none of them can be implemented without abandoning the implementation of all other projects. The most frequent limitation leading to the need to choose among alternative projects is the limited financial capabilities of the enterprise.
If an enterprise has the ability to implement several projects, and the decision to implement any of them does not entail a refusal to implement or, on the contrary, the need to implement any other of the existing projects, then such projects are called independent. When evaluating such projects, limited resources are not decisive in deciding on implementation.
In practice, an enterprise usually deals with a set of projects, some of which are alternative (mutually exclusive in relation to each other), and some are independent. The choice of evaluation criteria in the formation of the set will be discussed further.
The fundamental difference in the evaluation of alternative and independent projects is as follows. When considering a set of mutually exclusive projects, the task of evaluation is reduced to finding among them the most efficient one in terms of the use of available scarce resources. In this case, the criterion that takes into account the rarity of a particular resource will be preferable as the main one for making an investment decision.
An interesting option is to compare two projects, in which the simplest formulation of the concept of project profitability, calculated through the ratio of income and expenses, is used as a classification feature.
In accordance with this approach, two projects are called mutually exclusive if the profitability of the first decreases to zero if the other is accepted, and vice versa. Another name for such projects is alternative: these are two projects designed to achieve the same goals, and it is impossible to accept them and implement them profitably at the same time. An example of such projects is the construction of a nuclear power plant and a coal-fired power plant (considered simultaneously and in the same area). Two projects are called conditional if the profitability of each without accepting the other is zero. Let's assume that the project involves the installation of new filters to remove pollutants (instead of traditional technology) on the pipes of coal fired water heaters. It is obvious that accepting this project and purchasing new filters, unless a decision is made to build a coal-fired power plant and preference is given to building a nuclear power plant, does not make sense, since the nuclear power plant does not produce hydrocarbon emissions. Note that the conditional relationship is not always symmetrical: you can build a coal-fired power plant, but not install new filters on it.
Two projects are called independent if the acceptance or rejection of one of them does not affect the profitability of the other. Let's consider two projects: the construction of a coal-fired power plant and the construction of a sports and recreation complex for the workers of the power plant. Since the sports and recreation complex can be used by both coal-fired power plant workers and nuclear power plant workers, these two projects are independent of each other. Even if none of the new power plants is built, the complex will be useful to the workers of the one that already exists.
Substitute projects are called if the profitability of one of them decreases (but does not completely disappear) when the other is accepted. This relationship can be either symmetrical or asymmetrical, and substitution can take place on both the cost and benefit sides.
Two projects are called synergistic if the adoption of one of them increases the profitability of the other. This relationship can be either symmetrical or asymmetrical. In addition, the increase in profitability can take place both on the cost side and on the benefit side. Consider a project? - construction of a dam and project K - construction of a road bridge across the same river. Suppose that a decision is made to implement the project?, then a road can be laid on top of the dam, and this will take much less money than building a road bridge. The two projects show synergy on the cost side, but there is no cost synergy on the other side. Let us give an example of synergy on the side of benefits. Assume that Project E is a program to expand a seaport in order to make better use of port facilities and the harbour, by large ships. Project M is a program for the modernization and extension of the airport's runway. In the case of Project E implementation, the main result of the improvement of the port facilities will be the more intensive operation of equipment for servicing container cargo. If, along with this, the airport is modernized (project M), then heavier aircraft will be able to land in it. The modernization of the airport without the transformation of the seaport will facilitate the influx of tourists, but the city will not be attractive for the organizers of sea cruises.
In the case of a set of independent projects, the task investment analysis consists in establishing the compliance of each of the projects with the requirements imposed on it (for example, the riskiness of implementation, the prospects for a particular area of business activity, etc.). It is possible that all projects to some extent meet the requirements for them. In this case, it becomes necessary to rank the significance of a particular parameter or introduce additional evaluation criteria.
If an enterprise faces a set of projects in its activities, some of which are mutually exclusive with respect to each other, and some are independent, then the task of evaluating projects, from the point of view of optimal financial management of the enterprise, is reduced to the formation of a portfolio within the available financial resources that provides the most their effective use.
More on the topic Alternative and independent projects:
- 8. You have about 10 years until retirement. You have decided to invest in an attractive, from your point of view, real estate construction project (about 1 million rubles), but after counting your savings, you understand that you will have to borrow another 500,000 rubles, since the minimum entry into the project is 1 .5 million rubles You will most likely be given a loan, the project is designed for 5 years. The loan rate is 16% per annum, the expected profitability of the project is 25% per annum. Probability of project success, according to independent experts, approx.