Annotation. On the economic evaluation of investment projects: types of economic efficiency, evaluation methods, possible classifications of investment projects.

What is an investment project? In general, a project is a well-founded proposal, a specially formulated intention to change an activity or business, which has a specific goal. Most projects require financial investments to be implemented. And when a project is considered from an investment point of view (how beneficial it will be for the investor and cost-effective), it is called an investment project. An economic assessment of an investment project helps an investor make the right decision.

Classification of investment projects during their economic assessment

There is no special classification of investment projects for their economic assessment. There are many different parameters by which you can combine the entire variety of projects into separate groups. A generalized classification of investment projects can be found in the diagram.

As you can see, there can be a lot of projects, but assessing the economic efficiency of investment projects of various types comes down to answering standard basic questions:

1. Is it possible to implement this project? Do its parameters (economic, technological, legal, organizational, etc.) correspond to real conditions?
2. Are there sufficient financial resources to support the project?
3. What is the effectiveness of the project and is it sufficient?
4. What will the risks be and are they acceptable?

Types of economic efficiency of projects

The economic efficiency of an investment project is understood as the level of its compliance with the expectations and goals of the participants involved in it. When assessing, the following types of economic efficiency of projects are considered:

Overall efficiency of the IP. Evaluating effectiveness in this case is usually carried out based on its commercial and social components, which are analyzed from the point of view of a participant planning to finance the project entirely with its own funds.

The objectives of overall performance evaluation are:

• determining interest in the project from potential participants;
• search for additional sources and methods of financing.

Efficiency of participation in individual entrepreneurs. Participants in an investment project can be not only shareholders and the enterprise implementing the project, but also many other persons and organizations: banks, leasing companies, insurance companies, etc. In addition, completely different structures, industries, and regions may be involved in the implementation of the project, which can also influence it. The project may even require support from the state budget.

Thus, it turns out that several different individuals are involved in the project, and the interests of these individuals and their expectations from it also differ. In this case, the effectiveness of the participation of each person involved is determined separately.

The goals of assessing the effectiveness of participation in the project are as follows:

• analysis of the possibilities of implementing an investment project;
• determining the degree of interest in the project of each of the actual participants.

The economic efficiency of an investment project is assessed using both of the above methods in stages according to the following algorithm.

1. For small projects of local significance, their commercial effectiveness is first assessed, and only if it is considered sufficient, the project is analyzed further. The assessment of large-scale investment projects begins with an assessment of their social effectiveness. If it is too low, it is better not to implement the project. If the level of social efficiency is satisfactory, they move on to assessing the commercial components.
2. For a project of local importance, the effectiveness of participation of individual organizations in it is assessed. For large-scale projects, first of all, regional and sectoral efficiency is calculated, and if their indicators are good, the efficiency of individual participating enterprises is assessed.

Methods for economic evaluation of investment projects

Income approach

When using this method, future potential income is predicted and determined using the discounted cash flow method. Cash flow is discounted at a barrier rate determined for a specific company, at the weighted average cost of capital, or at a risk-adjusted discount rate determined taking into account the specifics of the project.

The income approach is the main one in assessing the cost of investment projects. This approach often uses data from business plans and business strategies. The approach has an undoubted advantage - it almost always gives results of high reliability. Its disadvantages are the complexity of calculations, and sometimes it may not give a very correct estimate (in case of uncertainty of planned cash flows).

Comparative approach

In this case, the cost of comparable investment projects available on the market, similar in terms of: industry scale, income level, production efficiency, operating activities, functions, profitability indicator, competition, risks, etc., is analyzed. As the name suggests, this approach is used when availability of objects for comparison.

It has the following advantages: the method is easy to use and uses current market information. Disadvantages: Some standard indicators (for example, industry indices) can provide too rough information, and it is often difficult to find a comparable project.

Cost-effective approach

This approach determines the replacement cost of project assets (or replacement cost), as well as the level of cost reduction after implementation of the project. It is used to assess the starting cost of a project and to analyze the degree of flexibility of the enterprise strategy in relation to a given project. Can be used to evaluate investment projects planning to launch relatively new technologies.

Advantages of the cost approach: solves the problems of uncertainty and lack of information. Disadvantages - the costs of implementation and development of the project are difficult to correlate with its future value. The cost approach, as well as the comparative one, is used to assess the effectiveness of investment projects much less often than the profitable one.

In the fourth section, we will study the potential ability of the project to ensure sufficient growth rates of invested funds. The analysis is based on determining the efficiency indicators of investment projects.

The methods used in the economic assessment of the effectiveness of investment projects are divided into static (simple) and dynamic (complex).

Static methods are used for quick and approximate assessment of the attractiveness of investment projects; they are used at the preliminary stage of project examination.

The main feature of simple indicators for assessing the effectiveness of projects is that their calculation does not take into account the inequality of cash flows arising at different points in time; the indicators are calculated without discounting.

In practice, the two most commonly used indicators are return on investment and payback period.

Return on Investment(ROI - return of investments) makes it possible to establish not only the fact of the project’s profitability, but also to assess the degree of this profitability. Return on investment (or rate of return) can be used to compare the effectiveness of a project with alternative investment options. In particular, a project can be considered economically profitable if its rate of return is not less than the bank discount rate.

Return on investment is calculated as the ratio of average annual profit (AP avg.) to the total investment costs (K) according to the formula:

(8)

If the calculated return on investment (rate of return) meets the level required by investors, then the project is attractive to them.

Payback period(PP - payback period) of the project determines the calendar period of time from the moment of the initial investment of capital in the investment project until the point in time when the cumulative total of net total income (net cash flow) becomes equal to zero. This is a period of time during which the project does not make a profit, that is, the entire amount of money generated by the project is used to return the initially invested capital.

To calculate the payback period you need:

2) determine at what year of life the cumulative cash flow takes a positive value;

3) find the part of the investment amount not covered by cash receipts in the period preceding the year determined in the previous step;

4) divide this uncovered balance of the investment amount by the amount of cash receipts in the period in which the cumulative flow takes a positive value.

The result obtained will characterize that portion of a given period, which, when added to the previous whole periods, forms the total payback period.

The payback period can also be calculated by gradually subtracting the amount of depreciation charges and net profit for the next planning interval from the total capital costs. The interval during which the balance is leveled off or becomes negative is the payback period. If this result is not achieved, then the payback period exceeds the established life of the project.

If the payback period is within the life of the project in question, then the relationship between the net annual flows of real money and the initial investment is favorable.

To calculate simple indicators of the effectiveness of an investment project, you should use Table 10.

Table 10 - Calculation of static indicators of the effectiveness of an investment project

Indicators	Years	Total
1.Net profit, thousand den. units (Table 8, paragraph 12)	-	-	1857,12	2990,32	3411,92	3833,52	4255,12	4676,72	5098,32	5519,92	5941,52	37584,48
2.Average annual profit, thousand den. units (clause 1/10)	-	-	-	-	-	-	-	-	-	-	-	3758,45
3.Total investment costs, thousand den. units (Table 5)	-	-	-	-	-	-	-	-	-	-	-
4.Return on investment, % (item 2/item 3)	-	-	-	-	-	-	-	-	-	-	-	9,28
5.Cash flow for operating and investment activities (Table 9, paragraph 6)	-40500	7315,28	9801,84	10170,32	10141,92	10113,52	10085,12	10056,72	10028,32	9999,92	13166,22	60379,18
6.Accumulated cash flow from operating and investing activities	-40500	-33184,72	-23382,88	-13212,56	-3070,64	7042,88	17128,00	27184,72	37213,04	47212,96	60379,18	-
7. Payback period, years (4+item 6 4th year/item 5 5th year)					4,30

Throughout the entire billing period, an increase in net profit is observed. In the second year, the net profit amounted to 1857.12 thousand. units, and in the tenth 5941.52 thousand den. units At the same time, the average annual profit is 3,758.45 thousand den. units Since in the first year the company had a loss, therefore this year there is no net profit (see Table 8). The loss is covered by pre-tax profits in the second year. The return on investment was 9.28%, and the payback period was 4.30 years. Calculated static indicators (return on investment and payback period) are used to quickly assess the attractiveness of an investment project.

For a more accurate assessment of the investment project, we will calculate dynamic indicators.

Dynamic Methods investment calculations are used to justify investment projects when we are talking about long-term projects that are characterized by income and expenses changing over time.

To assess the investment attractiveness of a project, all indicators of the future activity of the investment project are adjusted taking into account the decrease in the value of cash flows as the operations associated with it become more distant in time. For this purpose, discounting is used - an operation inverse to the calculation of compound interest, the process of recalculating a future amount of money into the present.

In practice, the most widely used methods for calculating net present value (NPV), return on investment index (PI), internal rate of return (IRR) and discounted payback period (DPP).

Net present value(NPV - net present value) is the difference between the current, discounted on the basis of the discount rate, cost of receipts and investment expenses.

The formula for calculating this indicator is as follows:

where IC t - investment costs in period t, den. units

Moreover, if:

NPV > 0, then the project should be accepted (the project is effective at a given discount rate);

NPV< 0, то проект следует отвергнуть;

NPV = 0, then the project is neither profitable nor unprofitable (brings neither profit nor loss).

One of the factors that determines the amount of net present value of a project is the scale of activity, which is expressed in the volume of investments, production and sales. Therefore, the use of this method is limited for comparing different projects: a large NPV value will not always correspond to the most efficient use of investments. In such a situation, it is advisable to calculate return on investment index(PI - profitability index) according to the formula:

Discounted investment costs, den. units

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 profitability index is a relative indicator, which makes it convenient when choosing one project from a number of alternative ones that have approximately the same NPV values, or when assembling a portfolio of investments with the maximum total value of net present value.

Internal rate of return(IRR - internal rate of return) characterizes the effectiveness of investments in a project at a certain stage of time. The internal rate of return is the discount rate at which the net present value equals zero. Therefore, at this discount rate, the value of discounted cash receipts equals discounted investment costs. In the case where investments and the return on them are given in the form of a stream of payments, the internal rate of return is determined as a solution to the equation:

The internal rate of return is found by iterative selection of discount rate values ​​when calculating the net present value of the project. The algorithm for determining the internal rate of return using the selection method is as follows:

1) two values ​​of the discount rate are selected and NPV is calculated. At one value of the discount rate, the NPV value should be greater than zero, and at another, less than zero;

2) the values ​​of the coefficients and NPV values ​​are substituted into the formula (interpolation):

,

(12)

where r 1 is the discount rate at which NPV is positive;

r 2 - discount rate at which NPV is negative;

NPV 1 - the value of the positive NPV value;

NPV 2 - the value of the negative NPV value.

In order for a project to be accepted, it must provide a certain rate of return. The project's internal rate of return is compared with the investor's required rate of return on invested capital.

In the case where the internal rate of return is equal to or greater than the investor's required rate of return on capital, investment in this investment project is justified, and the issue of its adoption can be considered. Otherwise, investment in this project is inappropriate.

If comparisons of alternative (mutually exclusive) investment projects based on net present value and internal rate of return lead to opposite results, preference should be given to net present value.

Thus, the internal rate of return (profitability) for any project represents the maximum interest rate that can be used to finance the project without harming the interests of the firm and shareholders. An enterprise can make any investment decisions, the level of profitability of which is not lower than the price of funds raised for this project.

Discounted payback period(DPP) - the number and duration of periods during which full recovery of invested funds occurs.

The choice of investment decision is carried out according to the principle: the shorter the payback period; the more effective they are. According to this principle, any project can be accepted whose payback period is less than a certain predetermined period (for example, the payback standard).

This indicator can be effectively used along with the indicators of net present value or internal rate of return.

The discounted payback period is equal to the minimum number of years (n) at which

Obviously, in the case of discounting, the payback period will increase. Consequently, a project acceptable under the PP criterion may not be acceptable under the DPP criterion.

If the net present value is positive, the profitability index is greater than one, and the internal rate of return significantly exceeds the threshold rate of return for the company, then the project can be accepted because it satisfies all criteria for assessing the economic efficiency of investment projects.

The calculation of complex indicators of the effectiveness of an investment project is shown in Table 11. The accumulated discounted cash flow for operating and investment activities is shown in Figure 3.

Table 11 - Calculation of dynamic performance indicators of an investment project

Indicators	Years	Total
1.Cash flow from operating and investment activities, thousand den. units (Table 9, paragraph 6)	-40500	7315,28	9801,84	10170,32	10141,92	10113,52	10085,12	10056,72	10028,32	9999,92	13166,22	60379,18
2. Discount factor r =14		0,877	0,769	0,675	0,592	0,519	0,456	0,400	0,351	0,308	0,270	-
3. Discounted cash flow from operating and investment activities, thousand den. units (item 1*item 2)	-40500	6415,50	7537,61	6864,97	6004,02	5248,92	4598,81	4022,69	3519,94	3079,98	3554,88	10347,32
4. Accumulated discounted cash flow from operating and investment activities, thousand den. units	-40500	-34084,50	-26546,89	-19681,92	-13677,90	-8428,98	-3830,17	192,52	3712,46	6792,44	10347,32	-
5.Discounted positive cash flow, thousand den. units (item 3 all positive values)	-	-	-	-	-	-	-	-	-	-	-	50847,32

Continuation of table 11

Indicators	Years	Total
6. Discounted cost of investment costs, thousand den. units (Table 5)	-	-	-	-	-	-	-	-	-	-	-
7. Net present value, thousand den. units (item 5-item 6)	-	-	-	-	-	-	-	-	-	-	-	10347,32
8. Return on investment index (item 5/item 6)	-	-	-	-	-	-	-	-	-	-	-	1,26
9. Internal rate of return, %	-	-	-	-	-	-	-	-	-	-	-	19,88
10. Payback period taking into account discounting, years (6+page 4 year 6/page 3 year 7)							6,95

Rice. 3 Accumulated discounted cash flow from operating and investing activities

Discounted positive cash flow amounted to 50847.32 thousand den. units, the discounted value of investment costs is equal to 40,500 thousand den. units, thus, net present value amounted to 10,347.32 thousand den. units (NPV>0). The return on investment index is 1.26 (PI>1), the internal rate of return is 19.88% - this is the maximum interest rate that can be used to finance the project without damaging the interests of the company and shareholders. Figure 3 shows the payback period of the project is 6.95 years.

Thus, the calculated indicators reflect the economic efficiency of the investment project.

The internal rate of return is calculated in Table 12 and shown in Figure 4.

Table 12 - Calculation of the internal rate of return of an investment project

Indicators	Years	Total
1.Cash flow from operating and investment activities, thousand den. units (Table 11 p.1)	-40500	7315,28	9801,84	10170,32	10141,92	10113,52	10085,12	10056,72	10028,32	9999,92	13166,22	-
2. Discount factor at r = 20		0,833	0,694	0,578	0,482	0,402	0,335	0,279	0,233	0,194	0,162	-
3. Discounted cash flow at r = 20 (item 1*item 2)	-40500	6093,63	6802,48	5878,44	4888,41	4065,64	3378,52	2805,82	2336,60	1939,98	2132,93	-177,55
4. Discount factor at r = 19		0,840	0,706	0,593	0,498	0,418	0,351	0,295	0,248	0,208	0,175	-
5. Discounted cash flow at r = 19 (item 1*item 4)	-40500	6144,84	6920,10	6031,00	5050,68	4227,45	3539,88	2966,73	2487,02	2079,98	2304,09	1251,77
6. Internal rate of return, %	-	-	-	-	-	-	-	-	-	-	-	19,88

Rice. 4 Determination of internal rate of return

The economic assessment of investment projects occupies a central place in the process of justification and selection of possible options for investing funds in operations with real assets. Despite all the other favorable characteristics of the project, it will never be accepted for implementation if it does not provide:

Reimbursement of invested funds from income from the sale of goods or services;

Obtaining a profit that ensures a return on investment not lower than the level desired for the enterprise;

Return on investment within a period acceptable to the enterprise.

Determining the reality of achieving precisely these results of investment activity is the key task of assessing the financial and economic parameters of any project for investing in real assets.

Carrying out such an assessment is always quite a difficult task, which is explained by a number of factors:

Firstly, investment expenses can be made either one-time or repeatedly over a fairly long period of time (sometimes up to several years);

Secondly, the process of obtaining results from the implementation of investment projects is also long (in any case, it exceeds one year);

Thirdly, the implementation of long-term transactions leads to increased uncertainty in the assessment of all aspects of investments and to the risk of error.

It is the presence of these factors that has given rise to the need to create special methods for evaluating investment projects, allowing one to make fairly informed decisions with the lowest possible level of error (although, of course, there cannot be an absolutely reliable decision when evaluating investment projects).

The basis of all calculations carried out in the justification and analysis of investment projects is a comparison of the costs that need to be carried out at the present time and the cash flows that can be received in the future.

An approach that involves determining the current (modern) value of an annuity helps in solving this problem. On this basis, you can clearly imagine how today's investment will pay off with tomorrow's benefits.

It will be easier to understand the meaning of such an analysis if we take as an example an investment project that involves receiving 1 million rubles. at the end of each of the next five years. We can determine the present value (based on the interest rate - the discount rate - at the level of 10% per annum) for each of the future inflows of money using formula (5.2) and adj. 3. The results obtained are shown in table. 5.2.

Table 5.2

Calculation of the current value of an annuity

	Cash flows (cash receipts), million rubles.	Current value future cash receipts, million rubles.
		1,00
		1,00
Total current value 3.79

Graphically this process is depicted in Fig. 5.2.

Rice. 5.2. Scheme for forming the current value of an annuity

The logic of such recalculation will be unchanged for any number of years of life of the object created as a result of investment. The calculation was carried out according to formula (5.2) as follows:

Hence the general equation for calculating the present value of an annuity:

, (5.5)

where PMT t is future cash receipts at the end of period t;

E – rate of return on investments;

k is the number of periods during which future income from modern investments will be received.

If cash receipts are the same in each period, the formula can be simplified and presented as follows:

Where - current (modern) value of an annuity worth 1 ruble. at the end of each of k periods with a rate of return at level E.

You can find the desired value using formulas (5.5) and (5.6) using spreadsheet systems or lookup tables (Appendix 4). If to solve this problem we used a lookup table containing the values ​​of an annuity of one ruble, then, in fact, we found the coefficient for reducing the future value to the modern value (discount factor), and then we simply need to multiply this coefficient by the real amounts of the annuity.

Example 5.3. Let’s assume that to purchase new equipment, funds in the amount of 100 thousand rubles are needed, which will ensure an annual receipt of cash receipts after taxes in the amount of 25 thousand rubles. for six years without significant annual fluctuations. Although the equipment will not be completely worn out after six years of operation, nevertheless, it is hardly possible to assume that at this point in time its value will exceed the cost of scrap. Liquidation costs will be reimbursed from proceeds from the sale of scrap. Linear depreciation for these six years (16,667 rubles per year) will accordingly be included in the amount of cash receipts of 25 thousand rubles.

To evaluate this project as a very first approximation, it is enough to estimate whether the current (modern) value of future cash receipts will cover the costs that the company will have to undertake now. In reality this means that we should define net present value, which the company will receive from the implementation of such a project.

When making calculations, we will proceed from the rate of return (discount rate) at the level of 10% per annum.

The calculation results are summarized in table. 5.3.

Table 5.3

Calculation of the present value of cash flows

Time period (years)	Investments (RUB)	Cash receipts	Current value 1 rub. cash flows of different years (discount factors at a rate of 10%)	Current value monetary flows of different years, rub.
0 (today)
Net present value of the project

As calculations showed, for this project the net present value turned out to be positive. In other words, the implementation of the investment project led to an increase in the company’s capital by 8,850 rubles. in modern terms. Consequently, the investment turned out to be beneficial and led to an increase in the value of the firm.

5.2.1.5. Discount coefficient. Discount rate

5.2.1.5.1. Moment of reduction

Discounting cash flows is called bringing their values ​​at different times (related to different calculation steps) to their value at a certain point in time, which is called moment of bringing and is denoted by t 0 . The reduction moment may not coincide with the base moment (the beginning of the time count, t 0). We understand the discounting procedure in an expanded sense, i.e. as leading not only to more early point in time, but also to more late(in case t 0 > 0) . As the moment of reduction, most often (but not always) they choose either the base moment (t 0 = t 0) or the beginning of the period when, as a result of the implementation of the investment project, the enterprise begins to receive net profit.

For greater clarity, we will show the most frequently used points in charting the financial profile of a hypothetical investment project with a single cash flow (Fig. 5.3).

Rice. 5.3. The most commonly used reduction moments

5.2.1.5.2. Discount rate

The main economic standard used in discounting is discount rate (E), expressed as a fraction of a unit or as a percentage per year.

Discounting of cash flow at the m-th step is carried out by multiplying its value of NDP m (CF m) by discount coefficient, calculated by formula

, (5.7)

where t m is the moment of completion of the mth calculation step, E is expressed in fractions of a unit per year, and t m – t 0 – in years.

Formula (5.7) is valid for a constant discount rate, i.e. when E is constant over the economic life of the investment or calculation horizon.

Discount rate (E) is an exogenously specified basic economic standard used in assessing the effectiveness of individual entrepreneurs.

In some cases, the value of the discount rate can be selected differently for different calculation steps (variable discount rate), this may be advisable in the following cases:

Time-varying risk;

Time-variable capital structure when assessing the commercial efficiency of individual entrepreneurs;

Time-varying interest rate on loans, etc.

The definition of discount rates in the case of a variable discount rate will be outlined below.

5.2.1.5.3. Classification of discount rates

The following discount rates differ:

A commercial;

Project participant;

Social;

Budget.

As mentioned earlier, in this tutorial we will consider only the commercial discount rate and the project participant discount rate.

Commercial discount rate (E) used in assessing the commercial viability of a project; it is determined taking into account alternative efficiency use of capital. In other words, the commercial discount rate is the desired (expected) rate of profitability (profitability), i.e. the level of return on invested funds that can be ensured when they are placed in publicly accessible financial mechanisms (banks, financial companies, etc.). Thus, E is the choice price (opportunity cost) of a commercial strategy that involves investing money in an investment project.

Project participant discount rate reflects the effectiveness of participation in the project of enterprises (or other participants). It is chosen by the participants themselves. In the absence of clear preferences, it can be used as a commercial discount rate.

5.2.1.5.4. Discount rate as cost of capital

To assess the commercial effectiveness of the project as a whole, foreign financial management experts recommend using a commercial discount rate established at the cost of capital level.

Any enterprise needs sources of funds to finance its activities. Attracting one or another source of financing is associated with certain costs for an enterprise: shareholders need to pay dividends, banks need to pay interest on loans provided to them, investors need to pay interest on the funds they have invested, etc.

The total amount of funds that must be paid for the use of a certain volume of financial resources as a percentage of this volume is called at the cost of capital (cost of capital).

The cost of capital is not limited to calculating the relative amount of cash payments that need to be transferred to the owners who provided financial resources, but also characterizes the level of return on invested capital that the enterprise must provide in order not to reduce its market value.

If the investment project is carried out at the expense equity firm, then the commercial discount rate used to assess the commercial effectiveness of the project as a whole can be set in accordance with the requirements for the minimum acceptable future return on invested funds, determined depending on the deposit rates of banks of the first reliability category.

In the economic assessment of investment projects carried out at the expense of borrowed money, The discount rate is assumed to be equal to the interest rate on the loan.

Since in most cases it is necessary to attract capital not from one source, but from several (equity capital and borrowed capital), the cost of capital is usually formed under the influence of the need to ensure a certain average level of profitability. That's why weighted average cost of capital WACC Weighted Average Cost of Capital can be defined as the level of return that an investment project must produce in order to ensure that all categories of investors receive a return similar to what they could receive from alternative investments with the same level of risk.

In this case, WACC is formed as a weighted average of the required profitability for various sources of funds, weighted by the share of each source in the total investment.

The general formula for determining the weighted average cost of capital is as follows:

where n is the number of types of capital;

E – discount rate i th capital;

d i – share i th capital in total capital.

5.2.1.5.5. Discount rate and risk adjustment

1. Depending on the method by which the uncertainty of the conditions for the implementation of an investment project is taken into account when determining the expected net present value (NPV), the discount rate in efficiency calculations may or may not include a risk adjustment. The inclusion of a risk adjustment is usually made when a project is assessed under a single scenario for its implementation. Discount rate excluding risk premiums ( risk-free discount rate ), reflects the profitability of alternative risk-free investment directions. The discount rate, which includes a risk adjustment, reflects the profitability of alternative investment directions that are characterized by the same risk as the investment in the project being evaluated.

2. Discount rate that does not include risk adjustment ( risk-free discount rate ), is determined in the following order.

Risk-free commercial discount rate , used to assess the commercial effectiveness of the investment project as a whole, can be set in accordance with the requirements for the minimum acceptable future return on invested funds, determined depending on the deposit rates of banks of the first reliability category (after excluding inflation).

The risk-free commercial discount rate, used to assess the effectiveness of the enterprise’s participation in the project, is set by the investor independently.

3. In size risk adjustment In general, three types of risks associated with the implementation of an investment project are taken into account:

Country risk;

The risk of unreliability of project participants;

Risk of non-receipt of the project income.

An adjustment for each type of risk is not introduced if the investment is insured for the corresponding insured event (in this case, the insurance premium is a certain indicator of the corresponding type of risk). However, the investor's costs increase by the amount of insurance payments.

4.Country risk usually seen as the possibility:

Confiscation of property or loss of property rights when they are purchased at a price below the market price or provided for by the project;

Unforeseen changes in legislation that worsen the financial performance of the project (for example, increasing taxes, tightening requirements for production or manufactured products compared to those provided for in the project);

Changes in personnel in government bodies interpreting legislation of indirect effect.

The amount of adjustment for country risk is assessed by experts:

In Russia, country risk is determined in relation to the risk-free, non-inflationary discount rate.

5.Risk of unreliability of project participants is usually seen in the possibility of unexpected termination of the project due to:

Misuse of funds intended for investment in this project or for creating financial reserves necessary for the implementation of the project;

Financial instability of the company implementing the project (insufficient supply of its own working capital, insufficient coverage of short-term debt with turnover, lack of sufficient assets to secure loans, etc.);

Bad faith, insolvency, legal incapacity of other project participants (for example, construction organizations, suppliers of raw materials or consumers of products), their liquidation or bankruptcy.

The size of the premium for the risk of unreliability of project participants is determined by experts by each specific project participant, taking into account its functions, obligations to other participants and the obligations of other participants to them. Typically, the adjustment for this type of risk does not exceed 5%, but its value significantly depends on how detailed the organizational and economic mechanism for implementing the project is, and how much the concerns of the project participants are taken into account.

6.Risk of non-receipt of project income caused primarily by technical, technological and organizational decisions of the project, as well as random fluctuations in production volumes and prices for products and resources. The adjustment for this type of risk is determined taking into account the technical feasibility and validity of the project, the availability of the necessary scientific and development resources and the thoroughness of marketing research.

The question of the specific values ​​of adjustments for this type of risk for different industries and different types of projects is poorly understood. If there are no special considerations regarding the risks of this particular project or similar projects, the amount of amendments can be approximately determined in accordance with Table. 5.4.

Table 5.4

Approximate amount of adjustments for the risk of non-receipt of the income provided for by the project

The risk of not receiving project income is reduced:

Upon receipt of additional information about the feasibility and effectiveness of a new technology, about mineral reserves, etc.;

In the presence of representative marketing research confirming the moderately pessimistic nature of the demand volumes and prices adopted in the project and their seasonal dynamics;

In the case when the project documentation contains a project for organizing production at the stage of its development.

5.2.1.5.6. Factorial calculation of risk adjustment

Risk adjustment, in addition to the method outlined above, can be determined by factor calculation. In this case, the amendment summarizes the influence of the factors taken into account. First of all, these factors include:

The need to conduct R&D with previously unknown results by specialized research and/or design organizations and the duration of R&D;

The novelty of the technology used (traditional, new, different from traditional in various features and resources used, etc.);

The degree of uncertainty in demand volumes and price levels for manufactured products;

The presence of instability (cyclicality) in demand for products;

The presence of uncertainty in the external environment during the implementation of the project (mining, geological, climatic and other natural conditions, aggressiveness of the external environment, etc.);

The presence of uncertainty in the process of mastering the equipment and technology used.

Each factor, depending on its assessment, can be assigned a risk adjustment value for this factor, generally speaking, depending on the industry to which the project belongs and the region in which it is being implemented. In cases where these factors are independent and complement each other in terms of risk, risk adjustments for individual factors should be added to obtain an overall adjustment that takes into account the risk of not achieving the project's planned income. However, to avoid double counting, the risk adjustment values ​​for individual factors cannot always be added together. For example, an adjustment for the risk associated with the need for R&D is unlikely to be added to an adjustment for the associated uncertainty in the application of the technique or technology used, since the risk associated with the need for R&D may include such uncertainty. Let us note that if we understand risk as the possibility of not receiving the income envisaged by the project as a result of the implementation of the corresponding unfavorable project implementation scenario, which is typical for the current Russian economy, then the most consistent and reliable way to take it into account should be based on an analysis of a representative set of possible project implementation scenarios. However, in cases where it is not possible to reasonably select a representative set of scenarios, introducing a risk adjustment makes it possible to take into account the risk at least approximately. At the same time, this method should be used with some caution. For example, for some projects, when a risk adjustment is introduced into the discount rate, the integral economic benefit (NPV) increases, so that with risk taken into account, the project will seem more efficient than without risk taken into account (projects with extraordinary cash flow). In these cases, risk adjustment is not recommended.

It should also be noted that a calculation based on an adjustment to the discount rate, which is the same for positive and negative elements of cash flow (albeit possibly variable over time), may lead to an unjustified overestimation of the efficiency of the project as a whole (for projects with cash flows of which take negative values ​​not only at the beginning of the billing period), but also the effectiveness of participation in the project. However, today it is impossible to completely abandon this method of calculation, since other methods of taking into account the risk of non-receipt of the income provided for by the project, which are more consistent with Russian economic realities, are not sufficiently developed to replace it . In those cases where the risk is adequately taken into account by appropriately adjusting cash inflows and outflows, when specifying different project implementation scenarios or in some other correct way, additional risk adjustments should not be introduced into the discount rate, as this would lead to a double taking into account risks.

5.2.1.5.7. Interest rates

Interest rates on deposits and borrowed funds are often the basis (starting point) in determining the discount rate. In addition, taking into account that the use of discount rates that take into account investors' inflation expectations is one of the methods of accounting for inflation in investment analysis, it is necessary to pay attention to such an economic category as interest rates.

Interest rate (rate of interest) is the relative (in percentage or fraction) amount of payment for using a loan (credit) for a certain time.

The interest rate charged by a bank on loans is called credit interest rate P kr. A special case of a credit interest rate is refinancing rate Central Bank. This is the interest rate at which the Central Bank issues loans to commercial banks to replenish their reserves.

The interest rate paid to banks on deposits is called deposit interest rate P d. Credit and deposit interest rates can be nominal, real and effective.

Nominal ( nominal interest rate) is called the interest rate P n announced by the lender. As a rule, it takes into account not only the lender’s income, but also the inflation index.

Real interest rate ( real interest rate) P 0 is the nominal interest rate reduced to a constant price level, i.e. adjusted for inflation (“inflation-free”).

The relationship between nominal and real interest rates is given by Fisher's formula:

(5.9)

or symmetrically

where (all indicators are expressed in fractions of unity)

P nsh – nominal interest rate for one interest calculation step;

P 0ш – real interest rate for one interest calculation step;

i sh – inflation rate (price growth rate), average for the interest calculation step.

Effective interest rate P ef characterizes the lender's income due to the capitalization of interest paid during the period for which the nominal interest rate is announced.

So, if the nominal interest rate for the year is equal to Pn (in fractions of one), and interest payments under the terms of the loan occur m times a year, then the bank almost always determines the interest rate for each payment equal to P n/m. In this case, the effective interest rate P ef (in fractions of one) is determined by the formula

. (5.11)

5.2.1.5.8. Accounting for changes in the discount rate over time

However, from general considerations, one can highlight the presence of a general trend towards a decrease in the discount rate over time.

First of all, the country’s financial markets are improving and their government management is becoming more and more efficient, and the refinancing rate of the Central Bank of the Russian Federation is decreasing, which leads to a reduction in the scope of obtaining excessively high returns on invested capital. Therefore, if today an investor invests in a project with an annual return (in hard currency) of at least 15%, then in a few years he will agree to 10%. In addition, as legislation improves, the political risk of long-term investment decreases, and the development of foreign economic and foreign trade relations contributes to the convergence of discount rates for Russian commercial structures with lower standards for developed countries (the discount rate there is determined by the yield of long-term government securities, adjusted for the rate of inflation ).

For these reasons, it is theoretically correct at present to carry out calculations of the effectiveness of investment projects taking into account the gradually decreasing discount rate.

The need to take into account changes in the discount rate by steps of the calculation period may also be determined by the method of establishing this rate.

Thus, when using a commercial discount rate set at the weighted average cost of capital (WACC), as the capital structure and dividend policy change, the WACC will change.

Discounting cash flows with a discount rate varying over time differs, first of all, in the calculation formula for determining the discount rate.

In the case when the beginning of the calculation period (t 0 =0) is taken as the reduction moment, the discount factor for the m-th step is calculated using the formula

, (5.12)

where E 0,..., E m are the discount rates at the 0th,..., mth steps, respectively,

D 0 , …, D m – the duration of these steps in years or fractions of a year.

5.2.1.5.9. Recalculation of the discount rate

When determining the effectiveness of investment projects, the problem often arises of determining the discount rate for steps of different durations (six months, quarter, month), with a known discount rate for a step lasting one year.

This problem arises, in particular, when assessing an investment project with a variable step. The conversion formula for the case of a constant discount rate E is determined as follows.

Let the discount rate E(D 1) be known for the duration of the step D 1 (for example, a year), and it is required to find the discount rate E(D) for the step size D (for example, a quarter), expressed in the same units as D 1, provided that both these standards must correspond to the same efficiency of capital.

Then E(D) is defined as the solution to the equation

(5.13)

where D 1 and D are reasonable to calculate in quarters.

Then D 1 = 4 (quarters), D = 1 and

Previous

Posted on the website 05/14/2009

In the context of the global economic crisis, the construction sector of the Russian economy is experiencing serious difficulties, in particular, limited access to credit resources. The article discusses an example of assessing the effectiveness of an investment project for the construction of a multifunctional complex.

A.V. Zemtsov, independent expert

Criteria and methods for evaluating investment projects

Financial and economic assessment of investment projects occupies a central place in the process of justification and selection of possible options for investing funds in operations with real assets. It is largely based on design analysis. The purpose of project analysis is to determine the outcome (value) of the project. To do this, use the expression:

Project result = project price - project costs.

It is customary to distinguish between technical, financial, commercial, environmental, organizational (institutional), social, economic and other assessments of an investment project.

Predictive assessment of a project is quite a complex task, which is confirmed by a number of factors:

1) investment expenses can be made either on a one-time basis or over a fairly long period of time;

2) the period for achieving the results of the investment project may be greater than or equal to the calculated one;

3) carrying out long-term operations leads to an increase in uncertainty in assessing all aspects of investments, that is, to an increase in investment risk.

The effectiveness of an investment project is characterized by a system of indicators that reflect the ratio of costs and results depending on the interests of its participants.

Assessing the overall effectiveness of the project for the investor

Investment projects can be either commercial or non-commercial. Even with non-commercial projects, there are opportunities expended and opportunities gained.

The difference between investment projects and current activities is that costs intended for the one-time acquisition of some opportunities are not considered investments. It turns out that an investor is a person who invests his capabilities for repeated use, making them work to create new opportunities.

If there are ways to evaluate effectiveness for commercial projects, then how to evaluate the effectiveness of non-commercial projects? Efficiency in general refers to the degree of compliance with the goal 1. The goal must be set precisely, in detail and allow only an unambiguous answer - whether it has been achieved or not. At the same time, you can achieve your goal in different ways, and each path has its own costs.

To decide on the implementation of a commercial project, an assessment of its economic efficiency is carried out. In the case of a non-profit project, if it is decided to achieve a goal, then the choice is to determine the most effective way. In this case, non-financial criteria should take precedence over financial ones. But at the same time, the goal must be achieved in the least expensive way.

Also when evaluating a non-profit project:

The investor’s resilience to the implementation of the project should be taken into account - will the investor withstand the implementation of the project;

When identifying alternatives of equal quality, the cheapest one is usually chosen;

It is advisable to plan the movement of costs (investments) over time in order to calculate forces in advance, anticipate shortages and take care of attracting additional resources, if necessary.

Assessment of project externalities

The second aspect of project evaluation is that the project may have value not only for the investor. For example, investments in the knowledge of some people no longer brought benefits to themselves, but to society as a whole, which then used the discoveries and inventions of scientists for its needs. In addition to commercial significance, ordinary commercial investment projects of companies also have the following effects:

Social;

Tax;

Budget;

Ecological.

All the effects of the project for other parties are important, since the company and the project are surrounded by society, people, the state, and nature. If the project improves the environment, then it is better for the company implementing the project, because everything in the world is interconnected.

1. The social effect is assessed by the benefit of the project for the population either living around the project site or working on the project, and consists of:

In increasing the level of salaries;

Development of infrastructure and other opportunities for the population around the project site.

2. The tax effect is assessed by the volume of taxes collected from the project into the local, regional and federal budget.

3. The budgetary effect is assessed if the project is fully or partially financed from the budget (federal, regional, local). It is determined how much money the project returns to the budget through taxes, after the budget has invested in the project, over a certain number of years.

4. An environmental effect occurs if the project somehow affects the environmental situation.

Economic approach to assessing the effectiveness of an investment project

The vast majority of decisions made by market economy entities are based on a preliminary assessment of the expected consequences. Individual assessment of the acceptability (effectiveness, value) of each investment project is carried out using various methods and taking into account certain criteria. We have analyzed Russian and foreign methods for evaluating investment projects and shown the application of these methods using practical examples.

General approaches to determining the effectiveness of investment projects

Investment decision-making is based on an assessment of the economic efficiency of investments. A market economy requires taking into account the influence on the efficiency of investment activity of environmental factors and time factors, which are not fully assessed in the calculation of these indicators.

They quite fully reflect the results of scientific research by domestic and foreign economists in the field of efficiency assessment methods. According to the Methodological Recommendations, the performance indicators of investment projects are divided into the following types 3:

Indicators of commercial efficiency, taking into account the financial consequences of the project for its direct participants;

Budget efficiency indicators reflecting the financial consequences of the project for the federal, regional or local budgets;

Indicators of economic efficiency that take into account the results and costs associated with the implementation of an investment project, going beyond the direct financial interests of the project participants and allowing for cost measurement.

The identification of such types is artificial and is associated with the determination of a single indicator of economic efficiency, but in relation to different objects and levels of the economic system: the national economy as a whole (a global criterion of economic efficiency), regional, sectoral, enterprise level or a specific investment project.

According to methodological recommendations, investment efficiency is characterized by a system of indicators that reflect the ratio of investment-related costs and results and allow one to judge the economic advantages of some investments over others.

Investment efficiency indicators can be classified according to the following 4 criteria:

1) by type of general indicator, serving as a criterion for the economic efficiency of investments:

Absolute, in which general indicators are defined as the difference between the cost estimates of the results and costs associated with the implementation of the project;

Relative, in which generalizing indicators are defined as the ratio of cost estimates of project results to the total costs of obtaining them;

Temporary, which estimates the payback period of investment costs;

2) using the method of comparing monetary costs and results at different times:

Static, in which cash flows arising at different points in time are assessed as equivalent;

Dynamic, in which cash flows caused by the implementation of the project are reduced to an equivalent basis by discounting them, ensuring comparability of cash flows at different times.

Static methods are also called methods based on accounting estimates, and dynamic methods are called methods based on discounted estimates 5.

TO group of static methods include: payback period of investments (Payback Period, PP); investment efficiency ratio (Accounting Rate of Return, ARR).

TO dynamic methods include: net present value, net present value (Net Present Value, NPV); return on investment index (Profitability Index, PI); internal rate of return (Internal Rate of Return, IRR); modified internal rate of return (Modified Internal Rate of Return, MIRR), discounted payback period of investment (Discounted Payback Period, DPP).

It should also be noted that the assessment of the effectiveness of each investment project is carried out taking into account criteria that meet certain principles, namely:

The influence of the value of money over time;

Opportunity costs;

Possible changes in project parameters;

Carrying out calculations based on real cash flow rather than accounting indicators;

Inflation and its reflections;

Risk associated with the implementation of the project.

Let us consider the main methods for assessing the effectiveness of investment projects in more detail and find out their main advantages and disadvantages.

Static estimation methods

Payback Period (PP)

The most common static indicator for evaluating investment projects is the term payback period (PP).

The payback period is understood as the period of time from the start of the project until the operation of the facility, when the income from operation becomes equal to the initial investment (capital costs and operating costs).

This indicator answers the question: when will the full return of the invested capital occur? The economic meaning of the indicator is to determine the period within which an investor can return the invested capital.

To calculate the payback period, the elements of the payment series are summed up on an accrual basis, forming the balance of the accumulated flow, until the amount takes a positive value. The serial number of the planning interval, in which the balance of the accumulated flow takes a positive value, indicates the payback period expressed in planning intervals. The general formula for calculating the PP indicator is:

where P k is the value of the accumulated flow balance;
I 0 is the amount of initial investment.

When a fraction is obtained, it is rounded up to the nearest whole number. Often the PP indicator is calculated more accurately, that is, the fractional part of the interval (calculation period) is also considered; in this case, the assumption is made that within one step (calculation period) the balance of the accumulated cash flow changes linearly. Then the “distance” x from the beginning of the step to the moment of payback (expressed in the duration of the calculation step) is determined by the formula:

where P k- is the negative value of the balance of the accumulated flow at the step until the payback period;
Р k+ is the positive value of the balance of the accumulated flow at the step after the payback moment.

As a meter, the “payback period” criterion is simple and easy to understand. However, it has significant disadvantages, which we will consider in more detail when analyzing the discounted payback period (DPP), since these disadvantages apply to both static and dynamic indicators of the payback period. The main disadvantage of the static indicator “payback period” is that it does not take into account the time value of money, that is, it does not distinguish between projects with the same balance of income flow, but with different distributions over the years.

Accounting Rate of Return (ARR)

Another indicator of the static financial assessment of a project is the investment efficiency ratio (Account Rate of Return or ARR). This ratio is also called the accounting rate of return or the project profitability ratio.

There are several algorithms for calculating ARR.

The first calculation option is based on the ratio of the average annual profit (minus contributions to the budget) from the implementation of the project for the period to the average investment:

I av 0 - the average value of the initial investment, if it is assumed that upon expiration of the project, all capital costs will be written off.

Sometimes the profitability of a project is calculated based on the initial investment:

Calculated on the basis of the initial investment volume, it can be used for projects that create a stream of uniform income (for example, an annuity) for an indefinite or rather long period.

The second calculation option is based on the ratio of the average annual profit (minus deductions to the budget) from the implementation of the project for the period to the average investment, taking into account the residual or liquidation value of the initial investment (for example, taking into account the liquidation value of equipment upon completion of the project):

where Р r is the average annual profit (minus contributions to the budget) from the implementation of the project;
I 0 is the average value (value) of the initial investment.

Dynamic estimation methods

Net present value (Net Present Value, NPV)

In modern published works, the following terms are used to name the criterion of this method: net present value 6 ; net present value 7; net present value 8 ; net present value 9 ; total financial result from the implementation of the project 10; current value 11.

The value of net present value (NPV) is calculated as the difference between the discounted cash flows of income and expenses incurred in the process of implementing the investment over the forecast period.

The essence of the criterion is to compare the current value of future cash receipts from the project with the investment costs necessary for its implementation.

The application of the method involves the sequential passage of the following stages:

1) calculation of the cash flow of the investment project;

2) selection of a discount rate that takes into account the profitability of alternative investments and the risk of the project;

3) determination of net present value.

The NPV or NPV for a constant discount rate and a one-time initial investment is determined by the following formula:

where I 0 is the amount of initial investment;

i is the discount rate.

Cash flows must be calculated in current or deflated prices. When forecasting income by year, it is necessary, if possible, to take into account all types of income, both production and non-production, that may be associated with a given project. Thus, if at the end of the project implementation period it is planned to receive funds in the form of the liquidation value of equipment or the release of part of working capital, they should be taken into account as income of the corresponding periods.

The basis of calculations using this method is the premise that the value of money varies over time. The process of converting the future value of a cash flow into the current value is called discounting(from English discount- reduce).

The rate at which discounting occurs is called the rate discounting (discount), and the factor F = 1/(1 + i) t - discount factor.

If the project does not involve a one-time investment, but a sequential investment of financial resources over a number of years, then the formula for calculating NPV is modified as follows:

where I t is the cash flow of the initial investment;
C t is the cash flow from the sale of investments at time t;
t — calculation step (year, quarter, month, etc.);
i is the discount rate.

The conditions for making an investment decision based on this criterion are as follows:

If NPV > 0, then the project should be accepted;

If NPV< 0, то проект принимать не следует;

If NPV = 0, then accepting the project will bring neither profit nor loss.

This method is based on following the main target set by the investor - maximizing its final state or increasing the value of the firm. Following this target setting is one of the conditions for a comparative assessment of investments based on this criterion.

A negative net present value indicates the inexpediency of making decisions on financing and implementing the project, since if the NPV< 0, то в случае принятия проекта ценность компании уменьшится, то есть владельцы компании понесут убыток и основная целевая установка не выполнится.

A positive net present value indicates the advisability of making decisions on financing and implementing a project, and when comparing investment options, the option with the highest NPV value is considered preferable, since if NPV > 0, then if the project is accepted, the value of the company, and therefore the welfare of its owners will increase. If NPV = 0, then the project should be accepted provided that its implementation will increase the flow of income from previously implemented capital investment projects. For example, expanding a hotel's parking lot will increase the property's income stream.

The implementation of this method involves a number of assumptions that must be checked for the degree of their correspondence to reality and the results that possible deviations lead to.

Such assumptions include:

The existence of only one objective function - the cost of capital;

The specified duration of the project;

Data reliability;

Payments belong to certain points in time;

Existence of a perfect capital market.

When making decisions in the investment field, you often have to deal not with one goal, but with several goals. If a cost of capital method is used, these objectives should be considered when arriving at a solution outside of the cost of capital process. In this case, methods for making multi-objective decisions can also be analyzed.

The useful life must be established in the performance analysis before applying the net present value method. For this purpose, methods for determining the optimal service life may be analyzed, unless this has not been established in advance for technical or legal reasons.

In reality, there is no reliable data when making investment decisions. Therefore, along with the proposed method for calculating the cost of capital based on predicted data, it is necessary to analyze the degree of uncertainty, at least for the most important investment objects. Methods of investing under conditions of uncertainty serve this purpose.

When forming and analyzing the method, it is assumed that all payments can be attributed to certain points in time. The time period between payments is usually one year. In reality, payments can be made at shorter intervals. In this case, you should pay attention to the compliance of the calculation period step (calculation step) with the conditions for granting the loan. For the correct application of this method, it is necessary that the calculation step be equal to or a multiple of the period for calculating interest on the loan.

The assumption of a perfect capital market, in which financial resources can be attracted or invested at any time and in unlimited quantities at a single calculated interest rate, is also problematic. In reality, such a market does not exist, and interest rates for investing and borrowing funds tend to differ from each other. This raises the problem of determining an appropriate interest rate. This is especially important since it has a significant impact on the value of capital.

When calculating NPV, discount rates that vary from year to year can be used. In this case, it is necessary to apply individual discount factors to each cash flow, which will correspond to this calculation step. In addition, it is possible that a project acceptable at a constant discount rate may become unacceptable at a variable one.

The net present value indicator takes into account the time value of money, has clear decision criteria and allows you to select projects for the purpose of maximizing the value of the company. In addition, this indicator is absolute and has the property of additivity, which allows you to add the values ​​of the indicator for various projects and use the total indicator for projects in order to optimize the investment portfolio, that is, the following equality is valid:

NPV A + NPV B = NPV MB.

For all its advantages, the method also has significant disadvantages. Due to the difficulty and ambiguity of forecasting and generating cash flow from investments, as well as the problem of choosing a discount rate, there may be a danger of underestimating the risk of the project.

Profitability Index (PI)

The profitability index (profitability, profitability) is calculated as the ratio of the net present value of cash inflows to the net present value of cash outflows (including initial investments):

where I 0 is the enterprise’s investment at time 0;
i is the discount rate.

The profitability index is a relative indicator of the effectiveness of an investment project and characterizes the level of income per unit of cost, that is, the efficiency of investments - the higher the value of this indicator, the higher the return on the monetary unit invested in this project. This indicator should be given preference when compiling an investment portfolio in order to maximize the total NPV value.

The conditions for accepting a project according to this investment criterion are as follows:

If PI > 1, then the project should be accepted;

If PI< 1, то проект следует отвергнуть;

If PI = 1, the project is neither profitable nor unprofitable. It is easy to see that when evaluating projects involving the same amount of initial investment, the PI criterion is fully consistent with the NPV criterion.

Thus, the PI criterion has an advantage when choosing one project from a number of projects with approximately the same NPV values, but different volumes of required investments. In this case, the one that provides greater investment efficiency is more profitable. In this regard, this indicator allows you to rank projects with limited investment resources.

The disadvantages of the method include its ambiguity when discounting cash inflows and outflows separately.

Internal Rate of Return (IRR)

Under internal rate of return, or internal rate of return, investment (IRR) understand the value of the discount rate at which the NPV of the project is equal to zero:

IRR = i, at which NPV = f(i) = 0.

The meaning of calculating this coefficient when analyzing the effectiveness of planned investments is as follows: The IRR shows the maximum acceptable relative level of costs that can be associated with a given project. For example, if a project is financed entirely by a loan from a commercial bank, then the IRR value shows the upper limit of the acceptable level of the bank interest rate, exceeding which makes the project unprofitable.

In practice, any enterprise finances its activities from various sources. As payment for the use of financial resources advanced to the activities of the enterprise, it pays interest, dividends, remunerations, etc., that is, it bears some reasonable expenses to maintain its economic potential. An indicator characterizing the relative level of these incomes can be called at the price of advanced capital (capital cost, CC). This indicator reflects the minimum return on capital invested in its activities at the enterprise, its profitability and is calculated using the weighted arithmetic average formula.

The economic meaning of this indicator is as follows: an enterprise can make any investment decisions, the level of profitability of which is not lower than the current value of the CC indicator (price of the source of funds for this project). It is with this that the IRR calculated for a specific project is compared, and the relationship between them is as follows:

If IRR > CC, then the project should be accepted;

If IRR< СС, то проект следует отвергнуть;

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

Another interpretation option is to treat the internal rate of return as a possible discount rate at which the project is still profitable according to the NPV criterion. The decision is made based on comparison of IRR with standard profitability; Moreover, the higher the internal rate of return and the greater the difference between its value and the selected discount rate, the greater the margin of safety the project has. This criterion is the main guideline when an investor makes an investment decision, which does not at all detract from the role of other criteria. To calculate IRR using discount tables, two values ​​of the discount factor r are selected< i 2 таким образом, чтобы в интервале (i, …, i 2) функция NPV = f(i) меняла свое значение с «+» на «-» или с «-» на «+». Далее применяют формулу:

where r 1 is the value of the discount factor at which f (i 1) > 0 (f (i 1)< 0);
r 2 - the value of the discount factor at which f (i 1)< 0 (f (i 1) > 0).

The accuracy of the calculations is inversely proportional to the length of the interval (i 1, ..., i 2), and the best approximation is achieved in the case when i 1 and i 2 are the closest values ​​of the discount factor that satisfy the conditions.

Accurate calculation of the IRR value is only possible using a computer.

The corresponding assumption of the method for determining the internal rate (investment at the internal interest rate), as a rule, does not seem appropriate. Therefore, the method of determining the internal rate of return without taking into account specific reserve investments or other modification of conditions should not be used to assess absolute profitability if complex investments take place and thus a process of reinvestment occurs. This type of investment also poses the problem of multiple positive or negative IRRs, which can make it difficult to interpret the results obtained by the IRR method.

The method of determining the internal rate of return for assessing relative profitability should not be applied, as noted above, by comparing the internal interest rates of individual properties. Instead, the investment must be analyzed to determine the difference. If we are talking about investments made in isolation, then we can compare the internal interest rate with the calculated one to make it possible to compare profitability. If the investments for comparison of profitability are complex, then the use of the method for determining profitability is inappropriate.

The advantage of the internal rate of return method over the net present value method is the possibility of its interpretation. It characterizes the accrual of interest on capital expended (return on capital expended).

In addition, the internal interest rate can be considered as the critical interest rate for determining the absolute profitability of an investment alternative if the net present value method is used and the “hard data” assumption does not apply.

Thus, investment evaluation using this method is based on determining the maximum discount rate at which projects will break even.

The NPV, IRR and PI criteria most commonly used in investment analysis are actually different versions of the same concept, and therefore their results are related to each other. Thus, we can expect the following mathematical relationships to be satisfied for one project:

If NPV > 0, then IRR > CC(r); PI > 1;

If NPV< 0, то IRR < CC (r); PI < 1;

If NPV = 0, then IRR = CC (r); PI = 1.

There are techniques that adjust the IRR method for use in a particular non-standard situation. One of these methods is the modified internal rate of return (MIRR) method.

Modified Internal Rate of Return (MIRR)

The modified rate of return (MIRR) eliminates the significant shortcoming of the project's internal rate of return, which arises in the event of repeated cash outflows. An example of such repeated outflow is the purchase by installments or construction of a real estate project carried out over several years. The main difference of this method is that reinvestment is carried out at a risk-free rate, the value of which is determined based on financial market analysis.

In Russian practice, this may be the profitability of a fixed-term foreign currency deposit offered by Sberbank of Russia. In each specific case, the analyst determines the value of the risk-free rate individually, but, as a rule, its level is relatively low.

Thus, discounting costs at a risk-free rate makes it possible to calculate their total current value, the value of which allows a more objective assessment of the level of return on investments, and is a more correct method in the case of making investment decisions with irrelevant (extraordinary) cash flows.

Discounted Payback Period (DPP)

Discounted payback period of investment (Discounted Payback Period, DPP) eliminates the disadvantage of the static payback period method and takes into account the time value of money, and the corresponding formula for calculating the discounted payback period, DPP, is:

Obviously, in the case of discounting, the payback period increases, that is, always DPP > PP.

The simplest calculations show that this technique, under conditions of a low discount rate, characteristic of a stable Western economy, improves the result by an insensible amount, but for a significantly higher discount rate, characteristic of the Russian economy, this results in a significant change in the calculated payback period. In other words, a project acceptable under the PP criterion may be unacceptable under the DPP criterion.

When using the PP and DPP criteria in assessing investment projects, decisions can be made based on the following conditions:

a) the project is accepted if payback occurs;

b) the project is accepted only if the payback period does not exceed the deadline established for a particular company.

In general, the determination of the payback period is of an auxiliary nature relative to the net present value of the project or the internal rate of return. In addition, the disadvantage of such an indicator as the payback period is that it does not take into account subsequent cash inflows, and therefore can serve as an incorrect criterion for the attractiveness of the project.

Another significant drawback of the “payback period” criterion is that, unlike the NPV indicator, it does not have the property of additivity. In this regard, when considering a combination of projects, this indicator must be handled with caution, taking into account this property.

However, the “payback period” criterion is indifferent to the amount of initial investment and does not take into account the absolute volume of investment. Thus, this indicator can only be used to analyze investments with a comparable amount of initial investment.

In some cases, the application of the payback period criterion may be critical for investment decision-making purposes. In particular, this can happen if the investment involves a high risk, and then the shorter the payback period, the more preferable such a project is. In addition, the company's management may have a certain limit on the payback period, and this is primarily due to the problem of liquidity, since the company's main goal is for investments to pay off as soon as possible. Thus, the PP and DPP criteria make it possible to judge the liquidity and riskiness of a project as follows: the shorter the payback period, the less risky the project; The more liquid project is the one that has a shorter payback period. It is advisable to apply these criteria when the company is interested in increasing liquidity, as well as in industries in which investments are associated with a high level of risk (for example, in industries with rapid changes in technology: computer systems, mobile communications, etc.).

Cash flows of investment projects: analysis and assessment

Relevant cash flows

The most important stage in the analysis of an investment project is the assessment of the projected cash flow 12, which consists (in the most general form) of two elements: the required investments (outflows of funds) and cash receipts minus current expenses (inflows of funds).

In financial analysis, it is necessary to carefully consider the distribution of cash flows over time. Income statements are not linked to cash flows and therefore do not reflect when cash inflows or outflows occur during the reporting period.

When developing cash flow, the time value of money must be taken into account.

To compare cash flow values ​​at different times, a discounting mechanism is used, with the help of which all cash flow values ​​at various stages of the investment project are brought to a certain point, called the reduction moment. Typically, the moment of reduction coincides with the beginning or end of the basic stage of the investment project, but this is not a prerequisite, and any stage at which it is necessary to evaluate the effectiveness of the project can be selected as the moment of reduction.

As noted above, the most important indicator of project efficiency is net present value. The indicators of net present value and internal rate of return (IRR) allow you to compare different investment projects with each other in order to select the most effective one. However, such comparisons are subject to projects with comparable implementation periods, volumes of initial investments and relevant cash flows.

Relevant cash flows mean those flows in which a flow with a minus sign changes to a flow with a plus sign once. Relevant cash flows are typical for standard, typical and simplest investment projects, in which the initial investment of capital, that is, the outflow of funds, is followed by long-term receipts, that is, the inflow of funds.

Analysis of the cash flow of an investment project is not limited to studying its structure. It is also important to identify the cash flow, ensure its relevance/irrelevance, which will ultimately simplify the procedure for selecting evaluation indicators and selection criteria, as well as improve the comparability of different projects.

Irrelevant cash flows

Irrelevant cash flows are characterized by a situation where the outflow and inflow of capital alternate. In this case, some of the considered analytical indicators may change in an unexpected direction with changes in the initial parameters, that is, conclusions drawn on their basis may not always be correct.

If we recall that IRR is the root of the equation NPV = 0, and the function NPV = f (i) is an algebraic equation of the kth degree, where k is the number of years of project implementation, then, depending on the combination of signs and absolute values ​​of the coefficients, the number of positive roots equations can range from 0 to k. In particular, if cash flow values ​​alternate in sign, several values ​​of the IRR criterion are possible.

If we consider the graph of the function NPV = f (r, Pk), then it can be represented differently depending on the values ​​of the discount factor and the signs of cash flows (“plus” or “minus”). We can distinguish two most realistic typical situations (Fig. 1).

The given types of graph of a function

NPV = f (r, Pk) correspond to the following situations:

Option 1 - there is an initial investment of capital with subsequent receipts of funds;

Option 2 - there is an initial investment of capital; in subsequent years, inflows and outflows of capital alternate.

The first situation is the most typical: it shows that the function NPV = f (r) in this case is decreasing with increasing r and has a single IRR value. In the second situation, the type of graph may be different.

Project effectiveness assessment

Let's consider an example of assessing an investment project for the construction of a multifunctional complex within the third transport ring.

Assumptions

Any investment project is considered in the context of complex macro- and microeconomic processes. The process of modeling and evaluating an investment project is influenced by many, if not all, macro- and microenvironmental factors, if this concerns real investments in the construction sector that will be discussed. It is impossible to take into account absolutely everything, but there are indicators that can and even need to be taken into account: inflation, commercial loan rate, share of the fund’s profit, taxes, desired investor profit and others. It is easy to notice that some indicators, such as inflation and taxes, are conditionally constant, that is, their quantitative characteristics can be taken as constant over a certain period of time. Others, such as the commercial loan rate, the fund's profit share, the investor's desired return and others, may vary depending on the "appetite" of the participants. To analyze the effectiveness of the proposed investment project, a model was created in which it is possible to change the indicators described above, and the computer automatically recalculates the analytical part, but for this study it is necessary to fix some indicators in the form of economic assumptions 13:

Bank loan interest rate, 27% per annum;

Bank profit share, 0%;

Copyright holder profit, 84%;

Income tax rate, 24%;

Development fee, 3% of revenue;

Marketing costs, 2% of revenue;

Land rental cost, $91,000/ha per year;

Fixed portion of operating costs, $15,000 per month.

In addition to the assumptions described above, it is worth saying that there are several strategies for the development of the proposed investment project. To minimize risks and provide a faster return on investment, we propose to consider the situation of financing the project using 100% of funds raised with the parallel sale of areas under construction as they are being built.

Logic of the study

To determine investment needs, as well as to analyze the economic efficiency of an investment project, it is necessary to go through several stages 14:

1) investment forecasting: project estimate;

2) investment forecasting: investment plan;

3) revenue forecast;

4) drawing up a cash flow report;

5) determination of net present value (NPV) and internal rate of return (IRR);

6) calculation of the investment payback period (PP), discounted payback period (DPP) and investment profitability index (PI);

7) determination of financing needs.

Let's take a closer look at the key points.

Description of the investment project

Let's consider an investment project for the construction of a multifunctional complex within the third transport ring, which is a multi-storey complex on an area of ​​1.08 hectares with underground parking, offices, retail space, a hotel, restaurant and apartments.

Project effectiveness assessment. Investment forecasting: project estimate

Let's consider a specific example of assessing the effectiveness of an investment project for the construction of a multifunctional complex in Moscow. Let's draw up an estimate for the project (Table 1).

Preparation of a cash flow statement

Determining Net Present Value (NPV)

To determine NPV, the profit/loss (or cash flow) line from the cash flow statement is taken. For clarity, we present a method for calculating NPV.

NPV calculation:

conclusions

In the context of the global economic crisis, the construction sector of the Russian economy is experiencing serious difficulties, in particular, access to credit resources is limited even for such large companies as the Mirax Group, the PIK group of companies, and Glavmosstroy. Almost all developers now have to rely exclusively on their own funds, which are generally not enough to implement new and complete existing projects, not to mention those companies that carried out construction exclusively with borrowed funds.

Nevertheless, promising investment projects continue to exist on the market, and the use of the correct methodology for assessing them is still relevant. In this case, it is necessary, of course, to make amendments to the values ​​of current indicators for the cost of credit resources, exchange rates, discount rates and other indicators, and to modernize the general approach to the formation of project financing sources.

Table 1. Project estimate

Table 2. Cash flow statement

Cash flow statement
	1st year				2nd year
	I	II	III	IV	I	II	III	IV
Revenue
Sale of hotel space			$239 200 000
Sale of apartments		$54 000 000	$54 000 000	$54 000 000	$54 000 000	$54 000 000	$54 000 000	$54 000 000
Sale of parking spaces		$17 460 000		$17 460 000		$17 460 000		$17 460 000
Sale of restaurant space					$23 700 000
Sale of retail space			$3 760 000	$3 760 000	$3 760 000
Sale of office space				$5 460 000	$5 460 000	$5 460 000
Sales costs		$ (2 143 800)	$ (8 908 800)	$ (2 420 400)	$ (2 607 600)	$ (2 307 600)	$ (1 620 000)	$ (2 143 800)
Net revenue		$69 316 200	$288 051 200	$78 259 600	$84 312 400	$74 612 400	$52 380 000	$69 316 200
Expenses
Preparation of a package of documents	$125 598 000
Construction of hotel areas		$15 946 667	$15 946 667	$15 946 667
Construction of apartments					$16 800 000	$16 800 000	$16 800 000
Construction of a parking lot	$55 500 000
Construction of restaurant areas								$7 900 000
Construction of retail space		$3 760 000
Construction of office space		$4 680 000
Construction of technical premises	$750 000	$750 000	$750 000	$750 000	$750 000	$750 000	$750 000	$750 000
Preparation for finishing		$628 857	$628 857	$628 857	$628 857	$628 857	$628 857	$628 857
Finishing of technical premises	$187 500	$187 500	$187 500	$187 500	$187 500	$187 500	$187 500	$187 500
Finishing of general office and retail spaces	$1 600 000
Parking lot finishing	$436 500	$436 500
Showroom organization		$900 000
Marketing costs		$1 386 324	$5 761 024	$1 565 192	$1 686 248	$1 492 248	$1 047 600	$1 386 324
Obtaining BTI								$4 402 000
Current expenses	$15 000	$15 000	$15 000	$15 000	$15 000	$15 000	$15 000	$15 000
Development Fee	$5 474 610	$908 725	$698 671	$572 796	$602 028	$596 208	$582 869	$458 090
Interest on borrowed funds		$12 687 409	$11 115 643	-	-	-	-	-
Total expenses	$187 961 610	$46 030 782	$44 012 162	$22 086 412	$23 277 233	$22 777 413	$21 631 826	$17 871 572
	$385 649 010
Total interest paid	$23 803 052
Profit Loss	$(187 961 610)	$23 285 418	$244 039 038	$56 173 188	$61 035 167	$51 834 987	$30 748 174	$51 444 628
Cumulative total	$(187 961 610)	$(164 676 192)	$79 362 846	$135 536 034	$196 571 200	$248 406 187	$279 154 361	$330 598 990

1 - Tslaf V. Evaluation of non-commercial investment projects // New markets. 2002. No. 3.

3 - Zavlin P.N. Assessing the economic efficiency of investment projects: Modern approaches. - St. Petersburg: Nauka, 1995.

4 - Zavlin P.N., Vasiliev A.V. Assessing the effectiveness of innovations. - St. Petersburg: Publishing house "Business Press", 1998.

5 - Kovalev V.V. Methods for evaluating investment projects. - M.: Finance and Statistics, 2000. P. 54.

6 - Beret V., Khavrapek P.M. Guidelines for preparing industrial feasibility studies. - M: Interexpert, 1995.

7 - Blech Yu., Goetze U. Investment calculations / Edited by A.M. Chuikina, L.A. Galutina. - Kaliningrad: Amber Tale, 1997.

8 - Foreign investments in St. Petersburg // Economics and life. St. Petersburg regional issue. 1997. No. 6.

9 - Gitmap L.J., Jonk M.D. Fundamentals of investing. - M.: Delo, 1998.

10 - Gazeev M.X., Smirnov A.P., Khrychev A.N. Indicators of investment efficiency in market conditions. - M.: PMB VNIIOENGa, 1993.

11 - Financial analysis of the company’s activities. - M.: East service, 1994.

12 - Cash flow of an investment project is a dependence on the time of cash receipts and payments during the implementation of the project generating it, determined for the entire billing period covering the time interval from the start of the project to its termination (see: “Methodological recommendations for assessing the effectiveness of investment projects”, approved by the Ministry of Economy of the Russian Federation, the Ministry of Finance of the Russian Federation, the Civil Code of the Russian Federation on construction, architectural and housing policy No. VK 477 dated June 21, 1999).

13 - All assumptions are based on in-depth market analysis, using data from well-known analytical companies.

14 - Mindich D.A. Finance for a growing business. - M.: JSC "Expert RA", 2007.

(Discounted payback period, DPP)

Criteria and methods for evaluating investment projects

Financial and economic assessment of investment projects occupies a central place in the process of justification and selection of possible investment options in operations with real assets. It is largely based on design analysis. The purpose of project analysis is to determine the outcome (value) of the project. Typically the following expression applies:

Project Result = Project Price - Project Costs

Predictive assessment of a project is quite a complex task, which is confirmed by a number of factors:

• investment expenses can be made either on a one-time basis or over a long period of time;
• the period for achieving the results of the investment project may be greater than or equal to the billing period;
• Carrying out long-term operations leads to increased uncertainty in assessing all aspects of investments, that is, to an increase in investment risk.

The effectiveness of an investment project is characterized by a system of indicators that reflect the ratio of costs and results depending on the interests of its participants.

Assessing the overall effectiveness of the project for the investor

Investment projects can be either commercial or non-commercial. Even with non-commercial projects, there are opportunities spent, and there are opportunities gained.

The difference between investment projects and the operating activities of an organization is that costs intended to obtain certain opportunities one-time are not considered investments. In this case, the investor is the person who invests his capabilities for repeated use, making them work to create new opportunities.

If for commercial projects there are ways to evaluate their effectiveness, then how to evaluate the effectiveness of non-commercial projects? Effectiveness generally refers to the degree to which a goal is met. The goal must be set precisely, in detail and allow only an unambiguous answer - whether it has been achieved or not. At the same time, you can achieve your goal in different ways, and each path has its own costs.

To decide on the implementation of a commercial project, an assessment of its economic efficiency is carried out. In the case of a non-profit project, if it is decided to achieve a goal, then the choice is to determine the most effective way. In this case, non-financial criteria should take precedence over financial indicators. But at the same time, the goal must be achieved in the least expensive way.

Also when evaluating a non-profit project:

1. one should take into account the investor’s resistance to the implementation of the project - will the investor withstand the implementation of the project;
2. when identifying alternative options of equal quality, the cheapest option is usually chosen;
3. It is advisable to plan the movement of costs (investments) over time in order to calculate forces in advance, provide for shortages and take care of attracting additional resources, if necessary.

Assessment of project externalities

The second nuance of project evaluation is that the project will have value not only in the eyes of the investor. For example, investing in the education of certain people will no longer benefit them themselves, but the community as a whole, which then used the discoveries and inventions of scientists for its needs.

Investment projects of commercial organizations, along with their commercial significance, also have the following effects:

1. The social effect is assessed by the benefit of the project for society, or those living around the place where the plan is implemented, or those working on the project, and consists of:

• in increasing the level of salaries;
• in the development of infrastructure and other opportunities for the population around the project site.

2. The tax effect is assessed by the volume of projected tax revenues to budgets of all levels (municipal, regional, federal).

3. The budgetary effect is assessed if the project is fully or partially financed from budgetary funds. It is determined how much money after the implementation of the project will be returned through tax payments over a certain period of time.

4. An environmental effect occurs if the project somehow affects the environmental situation.

All the results of the plan for other parties are significant, since the company and the project are surrounded by community, people, state, nature. If the plan improves the environment, then it is probably better for the commercial organization that is implementing the investment project, since everything in the world is interconnected.

General approaches to determining the effectiveness of investment projects

Investment decision-making is based on an assessment of the economic efficiency of investments. A market economy requires taking into account the influence on the efficiency of investment activity of environmental factors and time factors, which are not fully assessed in the calculation of these indicators.

Currently, Methodological Recommendations for assessing the effectiveness of investments and their selection for financing have been adopted (approved by the Ministry of Economy of the Russian Federation, the Ministry of Finance of the Russian Federation and the State Construction Committee of Russia, June 21, 1999 No. VK477).

They quite fully reflect the results of scientific research by domestic and foreign economists in the field of methods for assessing the effectiveness of investment projects.

Let us consider the main methods for assessing the effectiveness of investment projects in more detail and find out their main advantages and disadvantages.

Static estimation methods

Payback period (PP)

The most common static indicator for evaluating investment projects is the payback period ( Payback period, PP).

The payback period refers to the period of time from the start of the investment project to the moment the facility is put into operation, when income from current activities becomes equal to the initial investment (capital costs and operating costs).

This indicator answers the question: when will the full return of the invested capital occur? The economic meaning of the indicator is to determine the period within which an investor can return the invested capital.

As a meter, the PP criterion is simple and easy to understand. However, it has its drawbacks, which we will consider in more detail during the analysis ( DPP), since these shortcomings relate to both static and dynamic indicators of the payback period. The main disadvantage of this ratio is that it does not take into account the time value of funds, that is, it does not distinguish between projects with the same income stream balance, but with different distributions over the years.

Investment efficiency ratio (Account rate of return, ARR)

Investment efficiency ratio ( Account rate of return, or ARR) or accounting rate of return or project profitability ratio. There are several algorithms for calculating this indicator.

The first calculation option is based on the ratio of the average annual profit (minus contributions to the budget) from the implementation of the project for the period to the average investment:

The second option for determining the project profitability ratio is as follows:

Dynamic estimation methods

Net present value (NPV)

The NPV value is calculated as the difference between the discounted cash flows of income and expenses incurred in the process of implementing the investment over the forecast period. The essence of the criterion is to compare the current value of future cash receipts from the project with the investment costs necessary for its implementation.

The conditions for making an investment decision based on this criterion are as follows:

if NPV > 0, then the project should be accepted;
if NPV< 0, то проект принимать не следует;
if NPV = 0, then accepting the project will bring neither profit nor loss.

This method is based on following the main goal determined by the investor - maximizing its final state or increasing the value of a commercial organization. Following this target setting is one of the conditions for a comparative assessment of investments based on this criterion.

With all the advantages of this indicator, it also has significant disadvantages. Due to the difficulty and ambiguity of forecasting and generating cash flow from investments, as well as the problem of choosing a discount rate, there may be a danger of underestimating the risk of the project.

Profitability index (PI)

Profitability index- a relative indicator of the effectiveness of an investment project and characterizes the level of income per unit of cost, that is, the effectiveness of investments - the higher the value of this indicator, the higher the return on the monetary unit invested in this project. This indicator should be given preference when compiling an investment portfolio in order to maximize the total NPV value.

The conditions for accepting a project according to this investment criterion are as follows:

if PI > 1, then the project should be accepted;
if PI< 1, то проект следует отвергнуть;
if PI = 1, the project is neither profitable nor unprofitable. It is easy to see that when assessing projects involving the same amount of initial investment, the PI criterion is fully consistent with the NPV criterion.

Internal rate of return (IRR)

The meaning of the calculation internal rate of return when analyzing the effectiveness of an investment project is as follows: IRR shows the maximum permissible relative level of expenses that can be associated with a given project. For example, if a project is financed entirely by a loan from a commercial bank, then the IRR value shows the upper limit of the acceptable level of the bank interest rate, above which the project will be 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 (price of the source of funds for this project). It is with this that the IRR calculated for a specific project is compared, and the relationship between them is as follows:

if IRR > CC, then the project should be accepted;
if IRR< CC, то проект следует отвергнуть;
if IRR = CC, then the project is neither profitable nor unprofitable.

The advantage of the internal rate of return method over the net present value method is the possibility of its interpretation. It characterizes the accrual of interest on capital expended (return on capital expended).

The NPV, IRR and PI criteria most commonly used in investment analysis are actually different versions of the same concept, and therefore their results are related to each other. Thus, we can expect the following mathematical relationships to be satisfied for one project:

if NPV > 0, then IRR > CC(r); PI > 1;
if NPV< 0, то IRR < CC(r); PI < 1;
if NPV = 0, then IRR = CC(r); PI = 1.

There are techniques that adjust the IRR method for use in a particular non-standard situation. One of these methods is the modified internal rate of return (MIRR) method.

Modified internal rate of return (MIRR)

Modified rate of return ( MIRR) allows you to eliminate a significant drawback of the internal rate of return of the project, which arises in the event of repeated outflows of funds. An example of such repeated outflow is the purchase by installments or construction of a real estate project carried out over several years. The main difference of this method is that reinvestment is carried out at a risk-free rate, the value of which is determined based on financial market analysis.

In Russian practice, this may be the profitability of a fixed-term foreign currency deposit offered by Sberbank of Russia. In each specific case, the analyst determines the value of the risk-free rate individually, but, as a rule, its level is relatively low.

Thus, discounting costs at a risk-free rate makes it possible to calculate their total current value, the value of which allows a more objective assessment of the level of return on investments, and is a more correct method in the case of making investment decisions with irrelevant (extraordinary) cash flows.

Discounted payback period (DPP)

Discounted payback period of investment ( Discounted payback period, DPP) eliminates the disadvantage of the static payback period method and takes into account the time value of money.

Obviously, in the case of discounting, the payback period increases, that is, it always DPP > PP.

The simplest calculations show that this technique, under conditions of a low discount rate, characteristic of a stable Western economy, improves the result by an insensible amount, but for a significantly higher discount rate, characteristic of the Russian economy, this results in a significant change in the calculated payback period. In other words, a project that is acceptable under the PP criterion may not be acceptable under the DPP criterion.

When using the PP and DPP criteria in assessing investment projects, decisions can be made based on the following conditions:

1. the project is accepted if payback occurs;
2. the project is accepted only if the payback period does not exceed the deadline established for a particular company.

One of the significant disadvantages of this criterion is that, unlike the NPV indicator, it does not have the property of additivity. In this regard, when considering a combination of projects, this indicator must be handled with caution, taking into account this property.

In general, the determination of the payback period is of an auxiliary nature relative to the net present value of the project or the internal rate of return. In addition, the disadvantage of such an indicator as the payback period is that it does not take into account subsequent cash inflows, and therefore can serve as an incorrect criterion for the attractiveness of the project.