The adoption of any decision of an investment nature is necessarily associated with an assessment economic efficiency projects. At the same time, the question often arises of which performance parameters, which criteria to give preference to. For example, what is more important: less risk or more efficiency? Therefore, the need for a systematic approach to solving this issue is obvious. Objective evaluation methods are needed investment projects, which would take into account the economic, industrial, social, environmental and even political situation in each separate case. At the same time, speaking of environmental factors, one should not forget about the time factor as well.
Basic methods of investment appraisal
One of the main requirements for an enterprise in market conditions is its ability to create added value, which includes wage employees, loan interest, profit, minimum obligations to shareholders. If an enterprise does not have such an ability, then, having lost its competitiveness, it is forced out of the market.
The company develops through growth net income, which is formed from net profit (enrichment of the owner) and depreciation. Therefore, as an efficiency criterion, we can consider the value of the ratio of value added and the capital that was spent on its creation, and the more (services or products must be of high quality) the enterprise has profit per unit of costs, the more competitive it will be.
Some methods are based on this efficiency criterion. These include profitable (spectacular) and costly methods:
- The cost method is based on an analysis of the costs associated with the project. They provide an opportunity to evaluate the economic annual effect this project compared to the alternative.
- A profitable, or effective, method is based on an analysis of the results of investments, that is, profits (additional, balance sheet, products, annual economic effect. NPV is a reflection of the absolute result of investments, and PI and IRR (internal rates of return), including efficiency ratio - relative.
Methods for evaluating investment projects that take into account the time factor are divided into two main groups: static and dynamic.
Static costs, payback, profit, profitability) are based on indicators using accounting estimates, for example, efficiency ratio, reduced costs, payback period, economic annual effect.
Dynamic methods (accumulated value, annuity, discounting) use indicators that are based on net present value, the internal rate of the project's payback period, that is, on discounted estimates.
Methods for evaluating investment projects are also differentiated by the number of criteria used in the evaluation. From this position, evaluation models are divided into normative and multifactorial, and single- and multi-criteria methods are singled out in the methods.
With the multi-criteria optimality method, in addition to the profitability of the project, there are also such indicators as: stability of capital growth, safety, risk, payback period, social and environmental efficiency. Since in normative models the assessment is carried out only on the basis of financial and economic indicators, multi-criteria method should use multi-factor modeling.
Efficiency can be calculated in predictive or current prices:
- at the initial stage of development of an investment project, calculations can be carried out at current prices;
- the effectiveness of the entire project as a whole is produced both in forecast and current prices;
- forecast prices are used to develop a financing scheme and evaluate the effectiveness of participation in it.
Before assessing the effectiveness of investments, it is important to expertly determine the social significance of the industry in which investments are planned, and the project itself. Projects that affect the environmental, social and economic situation in the country and in the world are considered to be socially significant. Further, the assessment is carried out in two stages (Figure 5.3).
At the first stage, performance indicators as a whole are determined. The purpose of this stage is an aggregate economic assessment design solutions and creating the necessary conditions for the search for investors. If the project turns out to be socially significant, then its commercial effectiveness is evaluated. And with insufficient commercial efficiency of a socially significant project, the possibility of using various forms of its support is being considered.
Rice. 5.3. Stages of evaluating the effectiveness of investment projects
The second stage of the assessment is carried out after the development of the financing scheme. At this stage, the composition of participants and the effectiveness of participation in the project of individual enterprises and shareholders are specified. The efficiency of investments can be expressed in accounting for costs and results both in natural-material and in cost (cash) form. The cost indicators of the economic efficiency of investments, despite their shortcomings, are currently the main indicators of the justification of programs and projects.
According to the type of generalizing indicator, investment calculation methods are divided into:
Absolute (in which absolute values of the difference between capital investments and current costs of project implementation and monetary value its results);
Relative (in which generalizing indicators are defined as the ratio of the valuation of results and total costs);
Temporary (in which the return period (payback period) of investments is estimated).
Methods used in the analysis investment activity, can be divided into two groups depending on the consideration of the time parameter:
Based on discounted estimates;
Based on accounting estimates.
1. based on discounted estimates ("dynamic" methods):
Net Present Value - NPV(Net Present Value);
Return on investment index - PI(Profitability Index);
Internal rate of return - IRR(Internal Rate of Return);
Modified internal rate of return- MIRR(Modified Internal Rate of Return);
Discounted payback period of investment - DPP(Discounted Payback Period).
2. based on accounting estimates (“statistical” methods):
Payback period of investments - PP(Payback period);
Investment efficiency ratio - ARR(Accounted Rate of Return).
Net Present Value (NPV). This method is based on comparing the value of the original investment (IC) with the total discounted net cash receipts generated by it during the forecast period. Since the influx Money distributed over time, it is discounted by a coefficient r, set by the analyst (investor) independently based on the annual percentage return that he wants or can have on the capital he invests.
Suppose a forecast is made that an investment (IC) will generate, over n years, annual returns of P 1 , P 2 , ..., P n . The total accumulated value of discounted income (PV) and the net present effect (NPV) are respectively calculated by the formulas:
, (5.1)
. (5.2)
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, if possible, to take into account all types of receipts, both production and non-production nature, which can 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 salvage value equipment or part release working capital, they should be accounted for as income of the respective periods.
If the project involves not a one-time investment, but a consistent investment financial resources over m years, then the formula for calculating NPV is modified in the following way:
, (5.3)
where i is the projected average inflation rate.
Manual calculation using the above formulas is quite laborious, 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, and discounted value are tabulated. monetary unit etc. 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 time, i.e. NPV various 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.
Return on investment index. (PI). This method is essentially a consequence of the net present value method. Profitability Index (PI) is calculated by the formula:
. (5.4)
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.
The logic of the PI criterion is as follows: it 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.
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 that have approximately the same NPV values. or when completing an investment portfolio with the maximum total NPV value.
Internal rate of return of investment. (IRR). The second standard method for evaluating the effectiveness of investment projects is the method for determining the internal rate of return (IRR), i.e. the discount rate at which the net present value is zero.
IRR = r, where 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 financed entirely by a loan commercial bank, then the IRR value shows the upper bound acceptable level bank interest rate, the excess of which makes the project unprofitable.
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 it that the IRR indicator calculated for specific project, while the relationship between them is as follows.
If: IRR > CC. then the project should be accepted;
IRR< CC, то проект следует отвергнуть;
IRR = CC, then the project is neither profitable nor unprofitable.
Practical use 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 where r 1 is the value of the tabulated discount factor at which f(r 1)>0 (f(r 1)<0); r 2 - the value of the tabulated discount factor at which f(r 2)<О (f(r 2)>0). The 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 r (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 r (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 "+". Payback period of investment.(PP). This method is one of the simplest and widely used in world practice, 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. When a fractional number is received, it is rounded up to the nearest whole number. 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: РР = n, at which Рк > IC. The indicator of the payback period of investments is very simple in calculations, 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. Second, because this method is based on undiscounted estimates, it does not distinguish between projects with the same amount of cumulative returns, but different distribution them by year. Investment efficiency ratio. (ARR). This method has two character traits: it does not involve discounting income indicators; 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 original amount 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 value (RV) is allowed, its valuation should be excluded. 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). Example: The company is faced with a choice between two investment projects characterized by the following data: Rank projects according to IRR, PP, NPV criteria if r = 10%. Solution. 1) net present value for project A: for project B: 2) payback period of the project: for project A: 1 year + = 1.5 years or 1 year and 6 months for project B: 1 year + = 1.53 years or 1 year and 6 months 3) the internal rate of return of the project is calculated by the formula: r 1 is the value of the discount factor at which NPV > 0 (NPV<0); r 2 - the value of the discount factor at which NPV<0 (NPV > 0); IRR is calculated using a linear approximation. For project A: NPV 1 (r=10%) = NPV 2 (r=25%) = For project B: NPV 1 (r=10%) = NPV 2 (r=25%) = Comparison of two projects according to the calculated criteria indicates that preference should be given to project A, since its net present value and internal rate of return are higher than those of project B. Therefore, project A is more expedient than project B. SUMMARY Investments are, first of all, cash, securities, other property, including property rights having a monetary value, invested in objects of entrepreneurial and (or) other activities in order to make a profit and (or) achieve another beneficial effect. Distinguish, first of all, real and financial investments. Any organization can face the problem of alternative implementation of real or financial investments. At the same time, it is recommended to optimize the ratio of the volumes of real and financial investment in the process of developing the appropriate policy of the enterprise based on a number of factors: the functional orientation of the enterprise, the stage life cycle enterprises, the size of the enterprise, the nature of strategic changes operating activities enterprises, projected interest rate in the financial market, projected inflation rate. An investment project is a planned and ongoing set of measures to invest capital in various industries and sectors of the economy in order to increase it. In form, it is a set of documents to justify the economic feasibility, volume and timing of capital investments, including the necessary design and estimate documentation developed in accordance with the legislation of the Russian Federation and duly approved standards (norms and rules), as well as a description practical actions for the implementation of investments (business plan). All financial sources of investment are divided into own (internal) and external. To own funds of enterprises and organizations implementing investment projects, include: depreciation charges on existing funds (for their renovation); profit from production and economic activities directed to production development; amounts received from insurance companies in the form of compensation for damage as a result of natural disasters and accidents; funds from the sale of unnecessary surplus fixed assets and the immobilization of surplus working capital; funds from the sale of intangible assets (government securities, securities of other enterprises, patents, ownership of industrial product designs, production methods, etc.). The own sources of investment of enterprises and organizations also include funds attracted by them from other sources: funds received as a result of the issue and sale of shares and other securities by the investor; funds of other enterprises and organizations involved in the investment project as partners and on the relevant terms of participation in the distribution of dividends; funds allocated by superior holding and joint-stock companies, industrial and financial groups on an irrevocable basis; state subsidies, various kinds of monetary contributions and donations from regional and local budgets, entrepreneurship support funds, etc., provided free of charge. To external sources of investment include various forms borrowed money, as well as: appropriations from the federal, regional and local budgets, various entrepreneurship support funds provided free of charge; foreign investments provided in the form of financial or other tangible and intangible participation in the authorized capital of joint ventures. The investment strategy is a part of the overall financial strategy of the enterprise, the main purpose of which is a profitable investment of funds and the timely and complete renewal of the non-current assets of the enterprise. The initial prerequisite for the formation of an investment strategy is the general strategy for the economic development of the company (firm). In relation to it, the investment strategy is subordinate and must be consistent with it in terms of goals and stages of implementation. At the same time, the investment strategy is considered as one of the main factors for ensuring the effective development of the company in accordance with the general economic strategy chosen by it. The classification of investment strategies of enterprises involves the allocation of so-called "pure" (if there is only one motive) and "mixed" investment strategies (if more than one motive is indicated). All "pure" strategies are typical, and among the mixed ones - motivated as "maintaining capacities with intensification" and "modernization of production", "expansion of production with product renewal" (note that they are used even somewhat more often than "pure" investment strategies, corresponding to the second motive), “intensification and modernization of production with its expansion” and “maintenance of capacities with product renewal”. If the motives of investment activity are ranked according to their “progressiveness”, from relatively conservative “capacity maintenance” to “new product release”, then the types of “pure” investment strategies can be defined as: conservative (the corresponding investment activity motive is “capacity maintenance”); extensive ("expansion of existing production"); intensive (“intensification and modernization of production”); progressive ("release of new products"). The "mixed" types of strategies include: conservative-intensive ("capacity maintenance with intensification and modernization of production"); extensively progressive (“expansion of production with the renewal of products”); extensive-intensive (“expansion of production with its intensification and modernization”); conservative-progressive (“maintaining capacities with product renewal”). The methods used in the evaluation of investment projects can be divided into two groups depending on the time parameter taken into account: those based on discounted valuations (net present value, return on investment index, internal rate of return, modified internal rate of return, discounted payback period of investments) and those based on accounting estimates (payback period, investment efficiency ratio). Test questions 1. What are investments and what are their main types? 2. What characterizes the investment activity of the enterprise? 3. What criterion underlies the division of investments into direct and portfolio ones? How do these forms of investment compare with real and financial investments? 4. What factors should be considered when choosing investment projects? 5. What criteria for evaluating investment projects do you know? Give a brief description and evaluate the scope of each investment criterion. 6. How does the inflation rate affect the performance of investment projects? 7. Should a 15-year project requiring an investment of $150,000 be accepted if no income is expected in the first 5 years and an annual income of $50,000 in the next 10 years? LEARNING SITUATION Canadian company Agrimax Inc. undertook to invest 168 million dollars. in the development of technologies based on the Russian "discovery" - an autonomous energy source based on materials such as quartz sand. The contract providing for these investments was signed in February 200X in the presence of the Russian prime minister and his Canadian counterpart. They hardly guessed that official science considers the “discovery” of pure water to be charlatanism. The authors of the project - specialists from the Volgograd research and production center "GRUS" - could not clearly explain the essence of their discovery at a special press conference. In addition, there were no scientific publications on the declared topic at all. Meanwhile, the authors of the project will receive royalties from the construction of two new plants (one each in Russia and Canada) for the implementation of "alternative energy technology." In general, the business of Katsabanis, the owner of Agrimax Inc., has nothing to do with high technologies. Questions: 1. What type of investments are included in the described project? 2. How promising is this investment project? 3. What risks are inherent in the implementation of this investment project? 1. Baranov V.V. Financial management / V.V. Baranov. – M.: Delo, 2002. 2. Melkumov Ya.S. Economic assessment of the effectiveness of investments and financing of investment projects / Ya.S. Melkumov. - M.: Finance and statistics, 1997. 3. Limitovsky M.A. Fundamentals of evaluation of investment and financial decisions / M.A. Limitovsky. – M.: DeKA, 1997. 4. Chetyrkin E.M. Financial analysis of industrial investments / E.M. Chetyrkin. – M.: Delo, 1998. 5. Grechishkina M.V. The choice of the optimal investment option (optimization approach) / M.V. Grechishkina, D.E. Ivakhnik // Financial management. - 2006. - No. 3. - S. 82-96. 6. Kovalev V.V. Methods for evaluating investment projects / V.V. Kovalev. - M., 2004. Modern methods for evaluating the effectiveness of investments include simple methods that do not involve discounting (methods of a simple rate of return, payback period) and methods based on discounted cash flows (methods of discounted payback period, net present value, internal rate of return, modified internal rate of return and profitability investments). Usually the project is evaluated not by one method, but by several. This is due to the fact that the individual methods used are imperfect. Simple rate of return(AROR - Accounting Rate of Return) shows what part investment costs reimbursed in the form of profit within one planning interval. This indicator is calculated on the basis of net profit and is equal to the ratio of net profit on the project for the analyzed period to the total capital costs (investments). Comparing it with the minimum or average level of profitability, the investor can come to the conclusion about the advisability of further analysis of the investment project. Advantages of the method AROR is the ease of calculation and the ability to assess the profitability of the project. The disadvantages include that the time aspect of the value of money is not taken into account; profit is used as an assessment of the profitability of projects, although in real practice, investments are returned in the form cash flow, consisting of the sum of net profit and depreciation; income from the liquidation of old assets being replaced by new ones, as well as the possibility of reinvesting the income received are not taken into account. Payback period(PP - Payback Period) is the minimum time interval (measured in months and years) from the start of the project, for which investment costs are covered by net cash receipts from it, i.e. received net profit under the project and depreciation allowances will cover the capital costs (investments) incurred. This indicator is used in cases of low inflation, low project risk, etc. It is this indicator, along with internal norm profitability, is chosen as the main one in the methodology for evaluating investment projects participating in the competitive distribution of centralized investment resources. The calculation of the payback period is carried out according to the formula where C 0 - initial investment costs; C 1 , C 2 , … C t future net cash flows; T- the minimum number of years when the initial investment equals future cash flows; t- specified period of time. The calculation of the payback period is based on forecasting the net cash flows of the first few years and comparing the accumulated return with investment costs. The advantage of this indicator is the simplicity of its calculation. The payback period is the simplest indicator of the liquidity of an investment project (shows how long financial resources will be "bound" in this investment project). In addition, the payback period characterizes the level of risk associated with the implementation of the project (the farther the forecast period from the present time, the lower the degree of reliability of cash flow forecasts, which means that the uncertainty of their values increases, i.e. risk). This method is convenient for small companies with a small cash turnover, as well as for quick evaluation of projects in a resource-poor environment. The disadvantages of the method include the fact that it does not have a target criterion for selecting projects, does not contribute to maximizing the value of the company, does not take into account the difference in the cost of money over time and the difference in the time of receipt of income within the payback period, does not take into account the cash flows (profitability) of the project after payback period, and, therefore, cannot be used when comparing options with the same payback periods, but different lifetimes. The accuracy of calculations using this method largely depends on the frequency of dividing the life of the project into planning intervals. The risk is also estimated very roughly. Considering that the main drawback of the payback period indicator as a measure of efficiency is that it does not take into account the entire period of investment operation and, therefore, it is not affected by all the return that lies beyond it, this indicator should not serve as a selection criterion, but be used only as a constraint in decision making. Accordingly, if the payback period of the project is longer than the accepted limit, then it is excluded from the list of possible investment projects. Analyzing simple methods for evaluating the effectiveness of investments, it should be noted their inherent disadvantages: Discounted payback period(DPP - Discounted Payback Period) - an analogue of the payback period in simple valuation methods. Determining the payback period for the discount method is similar to the previous one, with the only difference being that the values of net cash flows over the years are given at a pre-selected discount rate to the initial point in time (the time of the initial investment). The resulting payback period is compared with the acceptable one for the company. This method is usually used in an unstable economic situation. The advantages of the DPP method are that it takes into account the time value of money, allows calculations for a longer payback period than PP, and takes into account a large number of cash flows from capital investments. In addition, the method has a clear criterion for the acceptability of projects (recoupment of the project during its lifetime) and takes into account the liquidity of the project. The disadvantages of this method include the fact that it does not take into account the impact of cash inflows of subsequent years after the completion of the project implementation period, does not distinguish between the accumulated cash flows and their distribution over the years. Net present value method(NPV - Net Present Value) takes into account the time value of money and is based on a comparison of investment costs with the present value of all future net cash flows over the years of the project. The calculation of the value of net present value includes: Formula for calculation NPV as follows: where t= 1, …, T- years of operation of the project, d- discount rate. If a NPV greater than zero, i.e., the estimate of future net cash flows exceeds the current estimate of investment costs, then the project is accepted. In this case, the investment costs of this project generate net cash flows with higher returns than alternative options in the market with the same level of risk. Negative meaning NPV means that the profitability of the project is less than the amount of funds invested in it, and there are more attractive investment options on the market. Manual calculation using the above formulas is time-consuming, therefore, for methods based on discounted estimates, special statistical tables have been developed in which the values of compound interest, discount factors, the discounted value of the monetary unit, etc. are tabulated, depending on the time interval and the value of the discount factor . By the amount NPV the structure of the cash flow has a significant impact. The greater the cash inflows in the first years of the economic life of the project, the greater the final value NPV and, accordingly, the sooner the costs incurred will be reimbursed. Advantages of the method NPV is that it has clear decision criteria; takes into account the different time value of money and the risk of a particular investment; takes into account the entire life of the project; the correct calculation of the indicator leads to the selection of projects that maximize the value of the real estate portfolio; has the property of additivity in time aspect ( NPV different projects can be summarized), which allows you to use NPV as the main one in the analysis of the optimality of the investment portfolio. The disadvantages of this method include: The next method for evaluating the effectiveness of an investment project is internal rate of return method(IRR Internal Rate of Return). The internal rate of return is defined as the estimated discount rate that equalizes the amount of discounted net cash flows for the project under consideration with the current estimate of investment costs. If the investment is made in the year t= 0 in size C 0 and projected net cash flows by year t= 1, …, T, at the rate of C t, then the internal rate of return is the constant discount rate d, at which equality is achieved: If you move C 0 to the right, then we get a formula for finding the value IRR: to be decided on d. On the right side there is an expression for determining NPV Therefore, the internal rate of return is the discount rate at which NPV = 0. IRR can only be calculated if the cash flows in all future time periods are non-negative. Otherwise, get an unambiguous answer about the value IRR impossible. In practical calculations IRR use the method of successive iterations (search for a solution by successive replacement of values in the calculations). Accordingly, to determine IRR you need to choose such a discount rate d, with which NPV will become zero. The internal rate of return determines the quality of the project itself, this is the minimum return that the project can provide while remaining break-even (that is, covering investment and current costs with a return). The company may accept investment decisions, the level of profitability of which is not lower than the current value of the level of expenses for attracting investment investments (or the price of the source of funds for this project). The indicator is compared with the relative level of investment spending IRR calculated for a particular project. If the value IRR more than this indicator, then the project is profitable and should be accepted; if less, the project is unprofitable and should be rejected; if equality is observed, the project is neither profitable nor unprofitable. In particular, if the source of project financing is a loan from a commercial bank, then the value IRR shows the upper limit of the acceptable level of interest rate, the excess of which makes the project unprofitable. To the advantages of the method IRR refer to the fact that it has clear decision-making criteria; it can be used for both equity and total invested capital, both pre-tax and post-tax; takes into account the discounted value of future cash flows; takes into account cash flows during the life cycle of the project, gives an estimate of the relative profitability of the project. In addition, it can be easily adapted to compare projects with different levels of risk: projects with a high level of risk should have a large internal rate of return. Limitations in using this method include: For non-standard cash flows, the application of the internal rate of return method is incorrect. Therefore, it applies modified internal rate of return method(MIRR - Modified Internal Rate of Return). MIRR is the discount rate at which the future estimate of receipts and the current estimate of costs are equalized. For determining MIRR all positive cash flows are increased at the discount rate at the final point in time (the end of the project), and all negative flows are given at the same rate at the initial point in time (the moment of investment). If we designate all accrued income FV, and all the reduced costs PV, then MIRR is found from the following equation: where T- number of years of project operation. Method MIRR has a number of advantages: When evaluating the effectiveness of investments, it is also of interest return on investment calculation method(PI - Profitability Index). The return on investment shows the extent to which the value of the company increases per ruble of invested funds, and is calculated by the formula: In a similar situation, but when investments are made not at once, but in parts - over several months or even years, the formula takes the following form: where - investment costs in the period t. According to the profitability index method, if the profitability index is greater than 1, then the project is accepted; if it is less than 1, then the project is rejected; if the index is 1, then large bases are needed. The profitability index is a relative indicator and allows, unlike the method NPV, quantitatively compare the costs and the effect of them. The indicator is used when choosing from alternative projects with similar values NPV but different investment costs. In addition, the indicator is good for projects with different life cycles. The disadvantage of the method is that it does not contribute to the selection of projects with maximum profitability and may contradict the method NPV when choosing projects. Large values PI do not always correspond to a high value NPV and vice versa, since projects with a high net present value are not necessarily efficient, and therefore have very little PI. Indicators NPV, IRR, PI, used in investment analysis, are different versions of the same concept and therefore are interconnected by certain ratios, which for one project look like this: if NPV> 0, then PI> 1 and IRR > d; if NPV < 0, то PI < 1 и IRR < d; if NPV= 0, then PI= 1 and IRR = d, where d is the required rate of return. When evaluating an investment project, experts focus on certain indicators, analyzing: An investment appraisal is conducted to find out three key points. If the investment appraisal is carried out professionally, the enterprise can: A company should assess how attractive a project is from an investment point of view if it: As a rule, the score investment attractiveness of the project is interesting, first of all, to the investor himself. Sometimes the implementation of one particular project may not bring the expected results. financial results. That is why firms often consider several options in order to choose the most promising ones. The assessment is carried out in order to: 1.
Grade financial efficiency.
The assessment of financial efficiency involves the calculation of the net present value of the project, defined as the difference between the inflow and outflow of funds during each settlement period (month, year), reduced to present value(inflation is taken into account). If the net present value is greater than 0, it is advisable to invest in the project. If the indicator is less than 0, it is better to refuse it. Thanks to the assessment of financial efficiency, a company can understand how profitable investments are, that is, learn about the ratio of funds already invested and the profit received. When evaluating financial attractiveness, not only the net present value indicator is calculated, but also the payback period, index and internal rate of return. Comprehensive assessment values of all indicators allows you to understand how effective the project is. That is, an assessment of the return on investment will be carried out. 2.
Assessment of socio-economic efficiency. Socio-economic evaluation of investments helps to judge how the project can benefit the state, citizens and other enterprises. The indicators of socio-economic efficiency are the main results of the implementation of the investment project, namely: The social results of the investment project implementation are: 3.
Assessment of budgetary efficiency. When evaluating budgetary efficiency, they compare the size of investments from a certain budget and the total income for the entire budget system. At the same time, experts evaluate how the results achieved are reflected in the revenue and expenditure parts of the budgets of all levels. The main indicator for assessing the budgetary efficiency of investments is the amount of net present value of a certain budget. It is calculated as the difference between the amount of revenues (taxes and fees, amounts used to repay loans, etc.) and total costs (for the implementation of state functions and the provision intergovernmental transfers in the form of subsidies, grants, subventions). They also use the indicator of the integral budget effect, calculated as the sum of the reduced (discounted) annual budget effects during the implementation of the investment project or as the excess of integral budget revenues over budget costs. There are various criteria for evaluating the effectiveness of investments, the main of which is profit. It is also possible to evaluate the effectiveness of an investment project on the basis of the return on investment parameters measured over a certain period - several months or years. When evaluating an investment project, risks are also taken into account. It should be emphasized here that if investments in a project are very risky, other indicators should not even be given attention. 1.
Criteria in financial terms. In this case, we are talking about the general indicators of return on investment in the currency of their full settlement, reduced to a previously determined settlement date. This indicator is indispensable if you need to choose a more profitable investment option from a number of available ones. 2.
Relatively pronounced criteria. There are much more such indicators than financial ones. Their main advantage lies in the visibility and the ability to reflect the variety of probable results. Don't forget one of key indicators evaluation - the life cycle of an investment project. It is needed in the conditions of urgent optimization of the main production apparatus of the organization, the need for which is dictated by modern scientific and technological progress. It is this criterion that directly affects the overall profitability (attractiveness) of the investment project. 1.
Conditional selection. The conditional allocation method is effective if the investment project exists separately from the company. It works like this. Imagine an investment project as a separate legal entity with its own assets and liabilities, which receives revenue and bears expenses, and evaluate how financially sound it is. Then ask yourself if you would cooperate with him or not. Using the conditional selection method, it is possible to evaluate financial solvency investment project. However, it also has disadvantages, since the project and independent entity- still not the same thing. However, the overall picture can be formed. 2.
An association. line up financial plan enterprise that implements the project, make a forecast of profit, balance, cash flow and enter all the data in the report. To accomplish this task, you need to have a good understanding of how the organization works, to have the necessary information. If you do not have the information, and you cannot get reliable data, you should not use the aggregation method. 3.
Comparison. When using the method, they describe the budget plan of the company implementing the investment project. Next, the current production process is considered, but the project is not taken into account, after which the financial viability of the enterprise is assessed. Then they compare the profit of the company with and without the investment project. 4.
Change analysis. In this case, the revenue that the company will receive from the implementation of the project is calculated by comparing its size with the amount of investments. The method has a clear advantage - thanks to it, you can very easily get the information you need. 5.
Overlay. When applying the overlay method, the solvency of the investment project is determined, and it is carefully studied. Next, they develop a financial plan for the enterprise without taking into account the project, after which the results obtained are superimposed on each other. Based on the results of the calculation, a conclusion is made about the financial viability of the organization, taking into account the implementation of the investment project. There are also alternative methods for evaluating the effectiveness of investments. Companies use the value added method, the adjusted value method, the chain repetition method, and a special method based on real options. In accordance with the adjusted cost method, the entire financial flow is divided into several components, each of which is considered separately. This is the most convenient method for evaluating projects financed from different sources. The value added method is based on the fact that the total return on investment should be significantly higher than the cost of total capital. This method allows you to identify all inefficient options for the use of funds in projects. The most flexible of all existing methods is based on real options. It is possible to buy or form assets within a certain period. Thanks to this method, you can correctly determine how valuable the project is in general. If there are doubts about whether it is correct to compare investment projects with different implementation periods using the described criteria, you can use the chain repetition method. Here, the least common multiple of n of the implementation periods of n1 and n2 of the investment projects being evaluated is determined. They build new financial flows from the implementation of several investment projects, expecting that costs and profits will remain at the same level (the next project begins to be implemented when the previous one ends). Net present profit indicators will change. And the internal rate of return will remain the same, regardless of the number of repetitions. At the same time, new financial flows may be non-standard if the initial investment exceeds the income in the last period of the investment project. The application of this method may cause the need for complex calculations when considering several projects and the coincidence of all deadlines. Each of the calculations can be performed several times. The chain repeat method has one major drawback. It consists in the assumption that the conditions under which projects will be implemented, and, accordingly, the necessary investments and profits, will remain at the same level. In the setting modern market it's almost impossible. In addition, it is not always possible to re-implement a project, especially if it is not long enough or belongs to an industry where manufactured products are quickly updated technologically. Each of the investment appraisal methods has its pros and cons. To obtain the most accurate results, it is necessary to find out the degree of uncertainty of an investment project, which, accordingly, can have one outcome or several development options. All this is associated with risks, on which, as a rule, the overall assessment of investments in the project depends very much. Static indicators are an assessment of the effectiveness of an investment project in certain period, usually in this moment. Static indicators are also called the arithmetic mean of all financial investments during the life cycle of the project. At the same time, indicators become less valuable, since they do not take into account temporary changes. The most important of them are the following: 1.
Return on invested capital (P). Here we are talking about the degree of profitability of the project. The ROI is used when you need to: The degree of return on investment is calculated as the total profit divided by the amount of capital invested. The indicator is expressed as a percentage. 2.
Payback period of investments (PP). Estimating the payback period of an investment is very important for a company making a decision to implement a project. It should be noted that not all investments pay off directly, even if the enterprise has achieved the set results during the implementation of the project. As a rule, this situation arises with socio-economic projects. The difficulty in evaluating the effectiveness lies in the fact that the funds invested for the implementation of social goals (in the development educational institution, hospitals or highway laying) pay off indirectly. Improving through investment human capital and other factors of similar importance. At the same time, it is almost impossible to accurately calculate the payback period. But the criteria for the effectiveness of investments in human capital can be defined as a payback ratio showing the amount of invested financial units per unit of profit: PP=I/YNB, The payback period is the period after which the company begins to receive income from investments. The rest of the time she receives dividends from the business. Their amount and correlation with the reflected indicators in the business plan of the organization are not advertised. It should be emphasized that the overall assessment of the return on investment also involves taking into account the period of the project's existence. Often, investment projects with a longer life cycle can bring more benefits even if long term payback. 3.
Investment Effectiveness Ratio (ARR). When calculating ARR, the average profit for the period under study is divided by the total amount of investments for it: ARR = P(av)/ (1/2)I(av), The indicator is especially significant when investing borrowed funds, since it allows you to calculate the probable period of debt repayment. 1.
Net present value (NPV). The indicator is calculated as the difference between the discounted financial income and expenses that the company incurs when implementing the project during the forecast period. This value is determined in order to compare the current value of the expected profit from the investment project with the costs necessary for its implementation. Below are the conditions based on which the enterprise can decide on the implementation of the project: The basis of this way of evaluating investments is to follow the goal of the investor, whether it be maximizing the end state or increasing the value of the firm. Following the target setting of the investor is one of the conditions for a comparative assessment of investments based on this indicator. Despite the fact that this criterion has many advantages, it also has disadvantages. Since it is difficult to choose a discount rate, predict and generate a financial flow from investments, and the result may be ambiguous, a company may underestimate the risks of an investment project. 2.
Index of return on investment (Profitability index, PI). The return on investment index is a relative indicator of the effectiveness of an investment project, which reflects the level of income per unit of expenditure. Thus, it demonstrates how expedient it is to invest in the project. The higher the value of the criterion, the more company can earn. When forming an investment portfolio in order to maximize the total value of NPV, it is better for an enterprise to use this indicator. Here are the conditions based on which a firm can make an investment decision: Note that when evaluating projects with the same amount of initial investment, PI fully complies with the NPV criterion. 3. Internalnormprofitability(Internal rate of return, IRR). Considering the dynamic methods of estimating investments, it is necessary to dwell on the internal rate of return. This indicator is calculated with the following goal. IRR shows the maximum allowable relative level of costs that a company can incur in the implementation of the project. For example, if an investment project is fully implemented with a loan from a commercial bank, IRR will show the upper limit of the bank interest rate, the excess of which means the project is unprofitable. From an economic point of view, the internal rate of return means the following: a company can make any investment decisions, the profitability of which is not lower than the current value of the CC indicator (the cost of the source financial resources for an investment project). It is with him that the IRR value calculated for this project is compared. These indicators are related as follows: The internal rate of return method, compared with the net present value method, has the advantage that it can be interpreted. It means the accrual of interest on the funds spent (the level of return on capital spent). As part of investment analysis The most commonly used criteria for evaluating the effectiveness of investments are NPV, IRR and PI. In fact, these are different versions of the same concept, and therefore their results are correlated. That is, for one investment project, the following mathematical relationships are possible: There are investment risk assessment methods that adjust the IRR for use in certain non-standard situations. In particular, we are talking about the modified internal rate of return (MIRR) method. 4.
Modified internal rate of return (MIRR). The modified rate of return (MIRR) makes it possible to eliminate a significant minus of the internal rate of return of an investment project that occurs with repeated outflows of funds. An example of such an outflow is the purchase on an installment plan or the process of building a property lasting several years. The method differs, first of all, in that reinvestment is carried out at a risk-free rate. The size of the bet is calculated based on the results of the analysis financial market. Applied to Russian companies it might be urgent currency deposit offered by Sberbank. In each specific situation, the expert determines the amount of the risk-free rate in separately. Usually it is small. That is, by discounting expenses at a risk-free rate, it is possible to calculate their total present value, the size of which allows us to give an objective assessment of the profitability of investments. This method is most convenient if you need to make investment decisions with extraordinary (irrelevant) financial flows. 5.
Discounted payback period (DPP). Discounted payback period (DPP) eliminates the downside static method payback period of investment and takes into account the cost of finance over time. It is clear that when discounting, the payback lasts longer, that is, DPP is always greater than PP. Based on the results of simple calculations, we can conclude that such a technique at a low discounted rate, which characterizes a stable economy in the West, improves the result by an imperceptible amount. But in relation to a larger discount rate, typical for the economy in Russia, it significantly changes the calculated value of the payback period. That is, a project that is acceptable on the basis of the PP criterion may not be acceptable on the basis of the DPP. Using the PP and DPP criteria when evaluating investment projects, a company can make decisions based on the following conditions: The criterion has a significant drawback, which is the absence of the additivity property, which differs from NPV. That is why, when considering combinations of projects, a company should be careful about this criterion, not forgetting this nuance. Generally speaking, the evaluation of the payback period of an investment is done for ancillary purposes relative to the net present value of an investment project or internal rate of return. In addition, the minus of the payback period is that it does not take into account subsequent inflows of finance, which may become an incorrect indicator of the attractiveness of an investment project. Stage 1.Forecasting the likely level of income of the investment project. To understand whether the project is effective, the level of income is estimated relative to the costs incurred. Profit in this case is not an increase in income in itself. Profit is important, compensating for the constant depreciation of funds throughout the life of the project. That is, in fact, you need to predict what new services or products the company will offer, what new technologies the project will allow to introduce, what it will bring to financially adjusted for inflation. It must be remembered that when investing there are always considerable risks. The investment is carried out in partly uncertain conditions - market conditions are constantly changing, and it is impossible to predict the success of a particular project. That is why investment decisions are often made by companies relying on intuition. But at the same time, it is also important economic calculations. The main thing here is to understand what income the company will receive from the project, taking into account inflation and all risks. Stage 2.Analysis of current expenses. When calculating income, the company must take into account expenses. After all, in case of excess of expenses over profit, the project will bring only losses. Operating costs are understood as the payment of salaries to employees, the maintenance of premises and production process, expenses for materials, equipment, purchase of products, provision of assets. When calculating, you need to take into account operating costs. Taking into account the specifics of the company, analysts can calculate the costs for these purposes in advance. Operating costs are annual (recurring) expenses for the use of assets. Stage 3.Accounting for investments that may be useful in the future. Very often, companies go bankrupt due to optimistic forecasts, which underestimate the future costs of implementing an investment project. In order for the assessment of investments to be objective, all expenses must be taken into account - capital, at the initial stage, and further (one-time and systematic). It is also necessary to remember about contingencies in the amount of 5-20%, depending on the area where the project is being implemented, the cost of paying taxes and ambiguous costs. When implementing investment projects, enterprises often need additional investments needed for construction purposes, installation of communications, and unforeseen investments in working capital. Think in advance where you will get the funds from. If you can't cover unexpected costs on time, the project will fail. Stage 4.Careful study of funding sources. Don't forget the golden rule of investors: long term investment funded by long-term financial resources. You need to know where you will get funds for the project, and do not doubt the stability financial sources. If it is impossible to take funds from at least one source, the project will slow down and cause losses. Stage 5.Accounting for basic taxes. An assessment of the economic efficiency of investments must necessarily take into account the amount of taxes that will be levied on profits. Get advice from lawyers and find out how much the state will have to pay after the project is implemented. Situations are common when, as a result of calculations, profitable projects become unprofitable. The assessment of risks associated with the implementation of an investment project must be carried out in two directions. Firstly, to comprehensively analyze the market environment, and secondly, to analyze the internal business model from a technical point of view. When assessing the risks of investment activity, the following is taken into account: Evaluate investment risks project is necessary, starting from the specific conditions of the business. However, there are general principles on which this analysis is based: These principles can be fully applied in forecasting, determining and insuring the risks of investment projects. Investment analysis and modeling are carried out using the following methods: The investment policy is based on an accurate calculation of the expected results of investing money, since this directly affects financial condition and activity of the enterprise. Evaluation of the effectiveness of investment projects includes a number of indicators, which together give a detailed picture of the prospects of the initiative. Consider the main criteria and methods for evaluating investment projects. Any investment in some kind of undertaking goes through several mandatory stages: Investing money in an investment endeavor involves not only making a profit, but also achieving the goals set by a businessman (or several partners) in their own interests. Evaluation of efficiency will help an entrepreneur or financier to understand whether he will lose his money as a result of investments, and whether the expected profit is able to compensate him for abandoning other possible investment options. Conducting an assessment of the effectiveness of an investment project can take from several days to several years, depending on the scale and complexity of the undertaking. It is advisable to carry it out not only when determining the potential of a proposal, but also for an informed choice between several competitive options, as well as for ranking and establishing a plan for the sequence of execution of several initiatives, depending on the expected economic effect. Basic principles for evaluating the effectiveness of investment projects in accordance with methodological recommendations The RAS are as follows: At the same time, one should not forget about the focus of each specific initiative on a specific goal. If the proposal in question about the development of infrastructure (building bridges, roads, bicycle parking) or any social issues (education, sports, health care), then the methods economic analysis most often unacceptable. The level of effectiveness of such undertakings can be considered as improving the quality of life of citizens, while making a profit is secondary or not considered at all. Among the whole variety of indicators, the following main complementary criteria for evaluating the effectiveness of investment projects are distinguished: AT international practice different methods of evaluating the economic efficiency of investment projects are used. All of them can be conditionally divided into two groups: In order to reduce the probability of error and adequately assess the feasibility of investing, a combination of these methods is usually used.
Static (simplified) methods for evaluating the effectiveness of investment projects have been widely used since the time when discounting was not yet recognized as one of the most accurate methods of analysis. They are acceptable for small investment for a short period (less than a year), and are also necessary for obtaining additional information. Let's consider them in more detail. The payback period is simple. This refers to the time from the beginning of the implementation of the idea to the moment of payback. The start is usually the start of operations, and the payback point is the earliest point at which net cash receipts become non-negative and remain so in the future. The calculation is to determine the period of time for which the amount of cash receipts on an accrual basis will be equal to the volume of the initial investment. This method of evaluation allows you to understand whether it will be possible to recover costs over the period of the life cycle of an undertaking. Let's assume that initially 1 million rubles were invested in a project with a total duration of 10 years, and 150 thousand rubles will be returned on average annually. Applying the formula, we find the solution: PP = 1000000 / 150000 = 6.66 years. Therefore, the payback moment will come in 6 years and 7 months, after which profit can be expected. The modified formula looks a bit more precise: where the initial investment is divided by the net average annual profit Pch s.g. (i.e. after taxes but without depreciation). If in our example the net profit is 50 thousand rubles, then we get the following picture: PP = 1000000 / 50000 = 20 years. Thus, only after 20 years the net profit will be equal to the amount of the down payment. The problem is that in addition to the return of money, the investor expects a profit. In our example, there are prerequisites for obtaining it, although discounting is not taken into account here. If average income per year will be 100 thousand rubles, then the payback moment will coincide with the end of the life cycle, therefore, the entrepreneur will incur losses, since he could earn by investing this money in an alternative idea. Also, with annual inflows that increase or decrease during the project implementation, carry out a correct calculation in a simple way impossible. In addition, the one-time investment of capital is required. Calculated rate of return (ARR). This methodology for evaluating the effectiveness of investment projects characterizes the return on investment and has the form of a ratio of cash receipts relative to the initial contribution. Calculated as a percentage. In relation to our example, this indicator for evaluating an investment undertaking has the following value: ARR = 150000 / 1000000 = 0.15 * 100% = 15%. This indicator indicates that with a starting investment of 1 million rubles, the rate of return should be 15% to obtain the desired annual income. There are variations of this formula, where the numerator uses the values of the net average annual profit (after tax payments) or gross average annual profit (before interest and taxes). In addition, the initial cost can be taken as a one-time cost or as an average between the start and end points. The advantage of the method is ease and clarity, the disadvantages are ignoring the cheapening of money, the duration of the operation of assets, focusing more on an external user. In addition to those mentioned above, other simple methods for evaluating investment projects are also used. They give a vision of the most general indicators, based on which, you can move on to more detailed calculations. (NV, or NPV) is the positive balance of cash flow for the period under review This is the ratio of the flow from the main activity to the amount of the flow from the investment activity. It can be represented as a formula: wherein: This indicator indicates the profitability of investing funds relative to net cash flow and the total amount of investments. Maximum cash outflow(CO). Represents the maximum negative balance and shows which is the least amount external funding from any source is necessary so that the initiative can be implemented. For a more detailed and professional study of the issue, indicators are used to evaluate the effectiveness of investment projects based on the concept of discounting. Let's dwell on the most important of them. The most common and important criterion in evaluating and analyzing an undertaking is the indicator net present value or net present value(NPV, or NTS). This is the effect of cash flows, normalized to present value. Its formula looks like this: where the discount factor is taken into account, expressed as part of the formula NPV shows the ratio of investment costs and future cash flows, which are adjusted to current conditions. For its correct calculation, it is necessary to determine the norm (rate) of reduction, after which .
Using its value, you can easily find the discounted amounts of inflows and outflows of funds, and the current net worth is the difference between them, which can have different meanings: Let's turn to our example. If we take a discount factor of 10% as a basis, we get the following result: NPV = -1000000 + 150000 / (1 + 0.1) + 150000 / (1 + 0.1)2 + 150000 / (1 + 0.1)3 + 150000 / (1 + 0.1)4 + 150000 / (1 + 0.1)5 + 150000 / (1 + 0.1)6 + 150000 / (1 + 0.1)7 + 150000 / (1 + 0.1)8 + 150000 / (1 + 0.1 )9 + 150000 / (1 + 0.1)10 = -1000 + 136.3 + 123.9 + 112.8 + 102.4 + 93.1 + 84.7 + 77 + 70 + 63.6 + 57 ,8 = - 78.4 thousand rubles. Thus, we see that at a discount rate of 10%, the undertaking does not cover the start-up costs and will become unprofitable. Therefore, it should be abandoned if there are no options for how to lower . At the same time, when considering options with a decrease in the discount rate, one must remember about the methods for assessing the risks of an investment project (shortage of profit, poor management, country risk). The net present value is a good indication of the minimum required return. A positive NPV value indicates a profit, a negative NPV indicates a loss, close to zero indicates a minimum payback. If in our example we take 9% as the discount rate, then we still get a negative value (-37.4 thousand rubles), so a plus is possible here at a rate not higher than 8%. Discounted Yield Index (DII), or, in other words, return on investment (PI). This is the ratio of the adjusted flow from domestic activities to the adjusted flow from investment activities. Our example here is calculated like this: PI = (136.3 + 123.9 + 112.8 + 102.4 + 93.1 + 84.7 + 77 + 70 + 63.6 + 57.8) / 1000 = 921.6 / 1000 = 0, 9216 Therefore, we can conclude that each ruble invested in this project will result in almost 8 kopecks of loss. This method is well suited for determining the more attractive initiative among several available options, especially if some of their other indicators have similar values. Typically, this criterion is calculated with the following assumptions: There is no specific IRR formula. Most often, it is found by plotting a graph with values plotted on it. Then, by the method of successive trials, the closest value of the rate of return is selected. You can also use formulas by which other key indicators for evaluating investment projects are recognized. The problem that we consider throughout the article can be solved in this case using the calculation of NPV. In this case, by calculating the discount interest rate at which the net worth is close to zero, you can determine the IRR, it is in the range of 0.08, that is, 8%. Sometimes the value of this indicator is taken from the value of other related criteria. So, if the initiative is fully financed by commercial Bank, then the maximum allowable interest rate will point to the IRR value. The IRR size criterion is suitable for screening out unpromising initiatives if the IRR is less than E, as well as for ranking several proposals with similar inputs, such as: Payback period discounted (DPP). This is a more accurate calculation of the time required to return the money spent. Unlike simple term payback, it takes into account the dynamics of the value of money over time. Let's return to our task. In contrast to the method of finding the value of PP by a simple method, here it is required to bring all annual receipts to the current state at the rate of 10% adopted by us earlier. By year (from the first to the tenth) it looks like this: 136.3 + 123.9 + 112.8 + 102.4 + 93.1 + 84.7 + 77 + 70 + 63.6 + 57.8 = 921.6 thousand rubles. The result obtained indicates that during the life cycle of the initiative (10 years) this investment will not pay off. Here you can clearly see the difference between the objectivity of calculations by a simple method and using the reduction of cash flows. If the investor will rely on a simple method that is poorly applicable in long-term projects, then he will incur losses, since the PP was equal to 6 years and 7 months. If DPP is taken as the basis, then the entrepreneur is likely to refuse this proposal altogether or in favor of another possible option.
, (5.5)
(5.6)Projects IC C1 C2
BUT -4000
B -2000
= 
= $752.07 = 
= $330.58
, where= $752.07
= -80 USD
= 23,56%.= $330.58
= -80 USD
= 22,08%.
Indicators that are analyzed when evaluating investments
In what areas is the evaluation of the effectiveness of investments
Investment evaluation criteria
Investment Appraisal Methods
Alternative methods for evaluating the effectiveness of investments
Static indicators of investment evaluation
Dynamic indicators for evaluating the effectiveness of investments
How is the analysis and evaluation of investments carried out: 5 stages
Investment risk assessment
How projects are evaluated
What methods are used to evaluate investment projects
Static evaluation methods
Dynamic (discount) methods of analysis
Rate of return (profit, discount) internal (IRR). In projects where there are upfront costs and a positive cash flow, the internal rate of return is the number with a "+" sign equal to the discount rate at which NPV is zero. If the IRR is higher than the discount rate, then the project may be attractive; if it is lower, then it threatens to lose capital.
