Determination of the payback period, profitability and economic sustainability of the investment project. Investment design Aggregated assessment of the sustainability of an investment project

General procedure for assessing stability. A project is considered sustainable if, under all scenarios, it turns out to be effective and financially feasible, and possible adverse consequences are eliminated by measures provided for by the organizational and economic mechanism of the project.

In order to assess the sustainability and effectiveness of a project under conditions of uncertainty, it is recommended to use the following methods:

aggregate sustainability assessment;

calculation of break-even levels;

method of variation of parameters;

assessment of the expected effect of the project, taking into account the quantitative characteristics of the uncertainty.

Each subsequent method is more accurate, although more laborious, and therefore the use of each of them makes it unnecessary to use the previous ones. All methods, except the first, are associated with the development of scenarios for the implementation of the project in the most probable or most dangerous conditions and the assessment of the financial consequences of the implementation of such scenarios. This makes it possible, if necessary, to provide in the project measures to prevent or redistribute the resulting losses.

change the size and (or) conditions for granting loans, for example, provide for a more flexible schedule of their repayment;

provide for the creation of the necessary reserves, cash reserves, deductions B additional risk fund;

adjust the terms of mutual settlements between project participants, if necessary, provide for hedging transactions or indexing prices for goods and services supplied to each other;

provide for insurance of project participants for certain insured events.

In those cases when, even with these adjustments, the project remains unstable, its implementation is considered inappropriate if there is no additional information sufficient to apply the fourth of the above methods. The issue with the implementation of the project according to the fourth method is resolved without taking into account the results of all the previous ones.

Aggregated assessment of the sustainability of an investment project.With an integrated assessment of the sustainability of an investment project as a whole, in order to ensure its sustainability, it is recommended:

use moderately pessimistic forecasts of the technical and economic parameters of the project, prices, tax rates. exchange rates and other parameters of the economic environment of the project, the volume of production and prices for products, the timing and cost of certain types of work V. etc. Moreover, positive deviations of these parameters will be more likely than negative;

provide for reserves for unforeseen investment and operating expenses caused by possible mistakes of the design organization, revision of travel solutions during construction, unforeseen delays in payments for delivered products, etc .;

increase the discount rate by the amount of the risk adjustment.

The stability of the IP from the point of view of the organization - the project participant in case of possible changes in the conditions of its implementation can be broadly verified based on the results of calculations of commercial efficiency for the main (baseline) scenario of the project implementation by analyzing the dynamics of real money flows In this case, the flows of real money included in the calculation are calculated for all types the activity of the participant, taking into account the conditions for the provision and repayment of loans.

For an integrated assessment of the sustainability of a project, sometimes indicators of the internal rate of return and the index of profitability of discounted costs can be used. risks (up to 15%) and at the same time it is not supposed to use loans at real rates exceeding the SID, and the profitability index of discounted costs exceeds), 2.

If these requirements for assessing the stability of the investment project as a whole to the parameters of the main scenario of its implementation are met, the project is recommended to be assessed as sustainable only if there is a certain financial reserve.

Since the free financial resources of the organization include not only the accumulated balance of cash flow from all types of activities (page 4 of Table 2.1), but also the cash reserve as part of the organization's assets, the condition for the sustainability of the project can be formulated as follows: at each step of the calculation period, the amount of accumulated the balance of cash flow from all types of activities (accumulated effect) and financial reserves must be non-negative. It is recommended that it be at least 5% of the total operating costs and investments made at this step.

Operating costs include: direct material costs, labor costs of production personnel, sales costs, production management, depreciation, and taxes attributable to cost and financial results.

To implement this recommendation, it may be necessary to change the provisions of the project for the reserve of financial resources, deduction to the reserve capital, or adjustments to the project financing scheme. If these measures do not ensure the fulfillment of the specified requirement, a more detailed study of the influence of uncertainty on the feasibility and efficiency of the IP is necessary, the methods of which will be discussed below.

Calculation of break-even boundaries. The degree of project stability in relation to possible changes in the implementation conditions can be characterized by indicators of break-even boundaries and limit values ​​of such project parameters as production volumes, prices of products, etc. Such indicators are used only to assess the impact of possible changes in project parameters on its financial feasibility and efficiency , but they themselves do not relate to IP performance indicators and their calculation will not replace the calculation of integral performance indicators (net discounted (reduced) income (effect) NPV, discounted investment profitability index IDI, internal rate of return IRR).

One of the most common indicators of the break-even limit of a project for a certain step of the calculation period is the break-even level. It is usually determined for the project as a whole by formula (3.13).

The break-even level at step n is the ratio

break-even sales (production) to the project at this step. Break-even is the volume of sales at which the net profit is zero. The calculation of the break-even level is based on the assumption that the volume of production is equal to the volume of sales. When determining this indicator, it is assumed that at step p.

the volume of production is equal to the volume of sales;

revenue changes in proportion to sales;

income from non-sales activities and expenses for these activities do not depend on sales volumes;

total current costs can be divided t conditionally constant (not changing when the volume of production) and conditionally variable, changing in direct proportion to the volume of production.

The calculation of the break-even level is carried out according to the formula

where AGR is the amount of proceeds at the n-th step;

full current production costs - production costs plus depreciation, taxes and other deductions attributed as cost (including transport, land, water, unified social tax, as well as fees for issuing licenses and the right to produce and turnover of ethyl alcohol, alcohol-containing and alcoholic beverages, payments for maximum permissible emissions, discharges of pollutants, waste disposal, levels of harmful effects), and on financial results, except for income tax, those that reduce

SSp - US, - OS

base for taxation of profits (including property tax) at /? - th step;

USp is the conditionally variable part of the total current production costs at the n-th step,

OSP - income and non-sales activities minus the costs of these activities at the nth step.

If the project involves the production of several types of products, formula (3.13) does not change, and all the values ​​included in it are taken throughout the project (without dividing by types of products). When using formula (3.13), all prices and costs should be taken into account without VAT.

Typically, a project is considered sustainable if, in the calculations for the project as a whole, the break-even level does not exceed 0.6-0.7 after the development of the design capacity. The closeness of the break-even level to 1

(100%), as a rule, indicates the insufficient stability of the project to fluctuations in demand for products at this stage. But even satisfactory values ​​of the break-even level (compliance with the established limits) at each step do not guarantee the effectiveness of the project (positive NPV).

At the same time, high values ​​of the break-even level not at all steps can be considered as a sign of unrealizability, inefficiency of the project. For example, at the stage of development of commissioned capacities or during the overhaul of expensive high-performance equipment, they can exceed 100%.

proceeds from the sale of IP (IR) 116; full costs, CC 25;

including

variable costs, CS 14;

fixed costs, HS 11.

According to the formula (3.13), the break-even level will be equal to:

According to the calculation results, the break-even level does not exceed the established limits with a large margin (0.11 The break-even limits can be determined for each project participant. The criterion for reaching the border is the zero profit of this participant. To do this, it is necessary to determine how the income and costs of this participant change *, when changing the values ​​of the parameter for which the border values ​​are determined.

Method of variation of parameters. Limit values ​​of parameters.

The output indicators of the project can change significantly in the event of an unfavorable change (deviation from the design) values ​​of some parameters. In the method of variation of parameters, possible changes in parameters during the calculation period are considered and the results of the project due to these parameters or factors are evaluated.

investment costs (or their individual components);

production volume;

production and sales costs (in trade, distribution costs) or their individual components;

interest for a loan;

forecasts of the general inflation index, indexes and the index of internal inflation (or other characteristics of changes in purchasing power) of foreign currency;

delays in payments;

the duration of the billing period (until the termination of the decision of the project);

other parameters provided for in the assignment for the development of project documentation.

In the absence of information about the possible, from the point of view of the project participant, the range of variation of the values ​​of these parameters, it is recommended to carry out variant calculations of the feasibility and effectiveness of the project sequentially for the following scenarios - 1)

increased investment. At the same time, the cost of work performed by Russian contractors and the cost of equipment for Russian supplies increase by 20%, the cost of work and equipment of foreign companies - by 10%. Correspondingly, the cost of fixed assets and the amount of depreciation and the cost price change; 2)

a 20% increase in the design level of costs and a 30% increase in specific (per unit of production) direct material costs for the production and sale of products. Accordingly, the cost of stocks of raw materials, materials, work in progress and finished goods in the composition of working capital changes; 3)

decrease in the volume of proceeds to 80% of its design value; 4)

100% increase in delays in payments for products delivered without prepayment; 5)

an increase in interest on a loan by 40% of its design value for loans in rubles and by 20% for loans in foreign currency.

It is recommended to consider these scenarios against the background of unfavorable development of inflation, set by experts. If the project provides for insurance in the event of a change in any of the project parameters or the values ​​of these parameters are fixed in the contracts prepared for the conclusion, the scenarios corresponding to these cases are not considered.

The project is considered stable in relation to possible changes in parameters if, for all considered scenarios:

NPV is positive;

the necessary reserve of financial feasibility of the project is provided, g. subject to the assumption of worsening scenarios in accordance with the variant calculations of the feasibility and efficiency of the project, the project remains profitable.

If in any of the considered scenarios at least one of the specified conditions is not met, it is recommended to conduct a more detailed analysis of the limits of possible fluctuations of the corresponding parameter and, if possible, to clarify the upper limits of these fluctuations. If, after such a clarification, the conditions for the sustainability of the project are not met, it is recommended:

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in the absence of additional information, reject the project:

if information is available, taking into account the quantitative characteristics of the uncertainty, which will be discussed below, evaluate the effectiveness of the IP using the more accurate methods described there.

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The sustainability assessment can also be carried out by determining the limit values ​​of the project parameters, i.e. such their values, at which the integral effect of the participant becomes equal to zero. One of these indicators is the type, which reflects the maximum value of the discount rate. To assess the limiting values ​​of parameters that vary by calculation steps (prices of products AND BASIC technological equipment, production volumes * I, volume of credit resources, rates of the most significant taxes, etc.), it is recommended to calculate the limiting integral levels (IS) of these parameters, i.e. ... such coefficients (constant for all calculation steps) to the values ​​of these parameters, when applied, the NPV of the project (or the project participant) becomes zero.

Let us estimate the limiting IU of the volume of product sales for the project considered in example 3.7. This solution complements and clarifies the calculation of the break-even boundaries. As in example 3.7, it is considered that the volume of production is equal to the volume of sales, all costs are divided into conditionally constant and conditionally variable (proportional to the volume of production) and only material costs are variables.

To determine the IU, revenue, notional variable costs and taxes proportional to revenue are multiplied at each step by a common factor \ x. The rest (investment and conditionally fixed production costs, taxes not related to revenue) remains unchanged, and the multiplier q is selected so that the NPV becomes zero or, equivalently, the VID becomes equal to the discount rate (11% per year). The multiplier q chosen in this way is the IU.

For the calculation, we use the formula (2.2)

D7> K = y - * 1 _ a, -

where in the composition of costs without amortization (З4 - 20 million rubles) we will single out the conditionally variable and conditionally constant parts of them. By condition, we from- IT

veilma variable part of the costs of US - 14 million rubles. Therefore, 34 = 20 = 14 + 6

To determine the IU in formula (2.2), the proceeds related to the sole proprietorship (FVA = 116 million rubles), and the variable part of the costs CA =) 4 million rubles, multiply by | d and equate NPV to zero. Then we find the factor \ x using the "Search for a solution" or "Selection of parameter" functions of the Microsoft Excel software application or as an unknown variable in the equation, where NPV is 0.

116 - ji - 14? ji - 6

(1 + 0, P) 4 q- (116 - 14) = 60 (1 + 0.11) 4 + 6;

The calculation shows that in this example IU = 0.951806.

For a more accurate assessment, it is required to determine the stability margin in the form of the difference:

tp = 1 - q = I - 0.951806 = 0.048194 (4.82%).

It follows from the calculation that the margin of stability in terms of revenue is small.

We know the following results from previous calculations:

the internal rate of return (IRR) exceeds the discount rate IRR = 0.124682> 0.11;

net present value (NPV) NPV = 3.24 mln rubles. > 0;

the break-even level does not exceed the established limits with a large margin () 4b = 0.11 The listed indicators positively characterize the effectiveness of the project. However, these positive results have a small margin of stability: Comparing the margin of stability with the indicator of the break-even level, we believe that the judgment about the stability of the MP based on the values ​​of the break-even level may turn out to be unreasonably optimistic. Estimation of the expected effect from the project, taking into account the quantitative characteristics of the uncertainty. The more accurate methods for assessing the effectiveness of IP in conditions of uncertainty include the method of calculating and assessing the expected effect of the project. The Eughian method allows you to directly calculate a generalizing indicator of the project's effectiveness - the expected integral effect (expected NPV). The assessment of the expected project efficiency, taking into account the uncertainty, is carried out in the presence of more detailed information about various scenarios of the project implementation, the probabilities of their implementation and the values ​​of the main technical and economic indicators of the project for each of the scenarios. Such an assessment can be carried out both taking into account and not taking into account the project financing scheme.

Calculations are carried out in the following order:

describe all the many possible scenarios for the implementation of the project (either in the form of an enumeration, or in the form of a system of restrictions on the values ​​of the main technical, economic and other similar parameters of the project);

for each scenario, they study how the organizational and economic mechanism for implementing the project will operate in specific conditions, how the participants' cash flows will change;

for each scenario, for each step of the billing period, inflows and outflows of real money and generalizing efficiency indicators are determined (calculated or set by analytical expressions). Inflows and outflows of real money include, in addition to the main cash flows, flows associated with mutual sanctions of participants, insurance, reservations and other elements of the organizational and economic mechanism for the implementation of the project. For scenarios involving contingencies (accidents, natural disasters, abrupt changes in market conditions, etc.), additional costs are taken into account. When determining NPV for each scenario, the discount rate is assumed to be risk-free;

check the financial feasibility of the project. Violation of the conditions of feasibility is considered as a necessary condition for the termination of the project (this takes into account the losses and income of the participants associated with the liquidation of the project due to its financial insolvency);

The initial information about the uncertainty factors is presented in the form of the probabilities of individual scenarios or the intervals of changes in these probabilities. Thus, a certain class of admissible (consistent with the available information) probability distributions of project performance indicators is determined. In particular cases, this class can consist of a single probability distribution or of all distributions on a set of possible combinations of performance indicators,

assess the risk of unrealizable ™ of the project - the total probability of scenarios in which the conditions of financial feasibility of the project are violated;

assess the risk of project inefficiency - the su * mmar probability of scenarios in which the integral effect (NPV) becomes negative;

estimate the average damage from the implementation of the project in the case of its inefficiency;

based on the indicators of individual scenarios, generalizing indicators of the project's efficiency are determined, taking into account uncertainty factors, i.e. indicators of expected performance. The main such indicator used to compare various projects (project options) and choose the best one is the indicator of the expected integral effect (NPV), No.RUozh (national economic - for the national economy or region, commercial - for an individual participant). The same indicators are used to substantiate the rational size and forms of reservation and insurance. Methods for determining the indicators of the expected effect depend on the available information about the uncertain conditions of the project implementation.

Probable! To us uncertainty. With probabilistic uncertainty for each scenario, the probability of its implementation is considered known (specified). It can be determined ekpertno. A probabilistic description of the conditions for the implementation of the project is justified and applicable when the effectiveness of the project is primarily due to the uncertainty of the processes of operation and wear of fixed assets (decrease in the strength of structures of buildings and structures, equipment failures, etc.) or natural and climatic conditions (weather, characteristics of soil or reserves minerals, the possibility of earthquakes or floods, etc.), d also the uncertainty of changes in the market related to individual entrepreneurs from suppliers, buyers, creditors and debtors involved in the formation of cash flows, market instability, the emergence of new competitors or goods substitutes on the market, possible fluctuations in financial results and financial stability related to the project. With a certain degree of conventionality, fluctuations in deflated prices for manufactured products and consumed resources can also be described in probabilistic terms,

Fluctuations in prices for different types of goods are interdependent. Therefore, for example, from the fact that prices for gasoline and road transportation with a high probability of М01УТ deviate from the average by 10%, it follows that with a high probability one of these prices will fall by 10%, while the other will grow by 10%.

If the number of scenarios is finite and their probabilities are specified, the expected integral effect of the project is calculated using the mathematical expectation formula:

y ^ ex = Eltruk-Rk "(314)

where A [RUk - integral effect (NPV) according to the k-th scenario;

Рк is the probability of this scenario being realized.

At the same time, the risk of inefficiency of the project Re and the average damage from the implementation of the project in the event of its inefficiency U are determined by the formulas

KRUk - rk

Ue = * -, (316)

where the summation is carried out only for those scenarios (k) for which the integral effects (NPV) AGRUk are negative.

Example 3.8. Determine the expected integral effect and the average damage from the implementation of the project in case of its inefficiency according to the table. 3.3.

Solution. To simplify the average damage from the implementation of a project in case of its inefficiency, we will agree to call the average possible damage.

Let's define the expected integral effect by the formula (3.14). To do this, we multiply the integral effect (NPV) for each scenario (rows for column 1) by the probabilities for each scenario (rows for column 2) and add the resulting numbers. We get No. Ouzh = 1.97 million rubles. (total for column 3).

Table 3.3. Calculating the expected integral effect

and possible damage Scenario number, to Inte

rub. Probability of the k-th scenario, pk Calculation of the expected integral effect, A7% w, mln rub. Calculation of the risk of project inefficiency, Re Calculation of the average potential damage,

RUB million A 1 2 A 5 1 3.5 0.2 0.7 2 3.24 0.3 0.97 3 -0.5 0.2 “0.1 0.2 -0 1 4 2.5 0.2 0.5 5 -1 od -0.1 0.1 "0.1 Project result - 1 1.97 0.3 -0.67 Next, we calculate the risk of project inefficiency (Re) using formula (3.15). For this Let us summarize the probabilities of the scenarios for which the integral effects (NPV) of the MRU are negative:

Re = 0.2 + OD = 0.3.

The average damage from the implementation of the project in case of its inefficiency is calculated by the formula (3.16). According to this formula, we divide the sum of the expected integral effects for scenarios with negative integral effects by the risk of project inefficiency (total of column 4 of Table 3.3):

The calculation shows that as a result of the operation of the project, the effect of the project is expected, taking into account the uncertainty, in the amount of 1.97 million rubles. with possible damage under the worst-case scenarios - 0.67 million rubles. ?

The integral effects of scenarios No.RUk and the expected effect of NRUozh depend on the value of the discount rate (d). The premium (#) for the risk of non-receipt of incomes stipulated by the main project scenario is determined from the condition of equality between the expected effect of the project # Woj (r), calculated at the risk-free discount rate r, and the effect of the main scenario MRU0C (r + g), calculated at the discount rate (r + #) including risk adjustment

KRUzh (r) = NPVoc (r -?).

In this case, the average losses from non-receipt of incomes provided for by the main scenario under unfavorable scenarios are covered by the average gains from obtaining higher incomes under favorable scenarios.

The size of the premium g depends on which scenario is adopted as the main one. In the absence of information on the probabilities of individual scenarios, in order to simplify the assessment of efficiency, it is recommended to use moderately pessimistic rather than average estimates of expenses and incomes in this scenario, i.e. focus on a reduced risk premium.

Suppose that the process of functioning of an object is considered as discrete and starts from the 1st step (year). The service life of the object is unlimited. At each n-th step, the object provides a non-random (annual) effect Ф0) - RU „- 3“.

At the same time, the project is terminated at some step, if a catastrophe occurs at this step - a sharp deterioration in the results of the NP operation due to the appearance on the market of a cheaper substitute product, a serious equipment failure, natural disaster or other unfavorable coincidence. The probability that a catastrophe will occur at some step, provided that it was not at the previous steps, does not depend on the step number and is equal to p. The expected integral effect is defined here as follows. The probability that no catastrophe will occur at the 1st step is 1 p. The probability that it will not occur at either the 1st or the 2nd step, according to the rule of the product of probabilities, is equal to (1 - p) 2, etc. Therefore, either until the end of step n, the catastrophe will not occur and the effect of the project at this step will be equal to Ф0м, or such an event will occur and the effect will be equal to zero. This means that the mathematical expectation (average value) of the effect at the n-th step will be equal to Ф0ах (1 “p) n. Summing up these values, taking into account the difference in timing, we find the mathematical expectation of the NPV of the project:

cr \ "ex = ^ Ф °" "(1 ~ p) - a = ^ (" P "~ 3" * 11 p '- a. (3.17) * O + rG "(I + r)"

It can be seen from this formula that the multi-temporal effects of Ф, provided under normal conditions, i.e. in the absence of disasters. are reduced to the base point in time using the coefficient (1 - p) n: (1 + r) n, which does not coincide with the usual discount factor 1: (1 + r) r of these factors gave the same result, it is necessary that a different value of c was taken as the discount rate, such that 1 - + + c = (1 + r): (1 - p). From this we obtain c = (r + p): (1 - p). For small values ​​of the probability p, this formula takes the form gr = r + + py, confirming that in this situation, taking into account the risk is reduced to calculating the NPV under normal conditions, but with the discount rate gr exceeding the risk-free r by the value of the "risk premium", which reflects in In this case, the (conditional) probability p of termination of the project during the nth year.

Example 3.9. The amount of income (/ V) from individual entrepreneurs in 4 years of investment will be equal to 116 million rubles. Costs 3 for the same period will amount to RUB 20 million. Capital investments С / in the amount for this investment period are equal to 60 million rubles. Suppose that the probability p of a cheaper substitute product appearing on the market during one calculation step (within a year), which can lead to a sharp deterioration in the results of the work of this IP (the probability of a catastrophe), is 0.0171 (1.71%) for 1 calculation step. The discount rate is set at 11% per goal.

Solution. Under such conditions, the expected integral effect, calculated by the formula (3.17), will be:

(116- 20) (1 - 0,0171)2 _

60 = -1.00 million rubles

According to earlier calculations, which can be called the baseline scenario, the NPV of the project has a positive value (IV RU = 3.24 million rubles). However, the expected integral effect (NPV), taking into account the probability of a catastrophe equal to 1.71% per one calculation step (guide), becomes negative during the investment period of 4 yd (-1 million rubles). This change occurred due to the small margin of stability of the project φ = 0.048194 (4.82%), which was previously determined when calculating the limiting integral level of c. As a result, a small deviation in the projected project implementation leads to a negative result. ?

Interval uncertainty. If there is no information about the probabilities of the scenarios (it is only known that they are positive and add up to 1), the calculation of the expected integral effect is carried out according to the formula

No. У0Ж = X NPVm ^ iX + (1 - X). (2-18)

where L! Rmax and MRUt (n - the largest and smallest integral effects (NPV) for the scenarios under consideration;

X is a special standard for taking into account the uncertainty of the effect, reflecting the system of preferences of an economic entity * in conditions of uncertainty. In calculating the expected integral national economic effect, it is recommended to take it at the level of 0.3.

Example 3.10. As a result of the IP operation, the maximum possible NPV is predicted in the amount of 3.55 million rubles. and the minimum possible NPV of -1.00 million rubles. Calculate the expected integral effect of IP, if the standard for accounting for the uncertainty of effect (X) by management is set at 0.3.

Solution. The calculation of the expected integral effect is carried out according to the formula (3.18):

MRU0zh - 0.3 3.55 + (1 - 0.3) - (- 1) = 0.37 million rubles.

Is the expected integrative effect, taking into account the interval uncertainty, positive, which indicates the probable profitability of the IP?

In the general case, in the presence of additional restrictions on the probabilities of individual scenarios pn, the calculation of the expected integral effect is recommended to be carried out according to the formula (2.19)

NPVm = X? max I (JVPK * pk) +

(one -/-)? mm Y. (NPVk-i "k)

P] "Pl D where / VPKfc is the integral effect (NPV) for the k-th scenario, and pip and

max are calculated for all admissible (consistent with the available information) combinations of the probabilities of individual scenarios at given intervals of their changes.

Example 3.11. Calculate the expected integral effect for PI according to the table. 3.4 with specified intervals of probability change (column 2-3). A special standard for taking into account the uncertainty of the effect, reflecting the system of preferences of the corresponding economic entity in conditions of uncertainty? V, is taken equal to 0.3.

Solution. Let's calculate the expected integral effect according to the formula (3.19). For this, we first find the maximum integral effect (NPV) with the best combination of probabilities I max? (NPVk - pk)].

When calculating it, the values ​​of the integral effects for the kth scenario (NPVk) (rows in column 1) should be multiplied by the corresponding probability values ​​from the interval (/? *), Providing a larger expected effect (rows in column 2). We write the results in gr. 4. Summation of the results for gr. 4 will give the maximum possible integral effect (NPV) with the best combination

probabilities [max ^ (NPVk pk)] - total for gr. 4.

After that, we find the minimum integral effect (NPV) for the worst combination of probabilities [min ^ (NPVk pk)]. With him

P \ * Pi "??? To

the calculation should multiply the values ​​of the integral effects for the / s-th scenario (NPVk) (rows for column 1) by the corresponding probability values ​​from the interval of their values ​​(pk), providing a smaller expected effect (rows for column 3). We write the results in gr. 5. Summation of the results obtained by gr. 5 will give the lowest possible integral effect (NPV) with the worst combination of probabilities | min ^ (NPVk? рк)) - total for th. 5. The obtained results are substituted by B formula (3.19).

Table 3.4. Calculation of the literal effect with given intervals of scenario probabilities Scenario number k Integral effect for the k-th scenario

RUB million The interval of changes in the probability of realization of the k-th scenario Pk Maximum integral effect, shah? (7URU "p), mln rubles group I х group 2 MipimOlNi integral effect min? (7VPV" p), mln rubles group 1 * group 3 Expected integral effect

RUB mln A 1 2 3 4 5 6 1 3.5 From 0.2 to 0.1 0.7 0.35 2 3.24 From 0.3 to 0.3 0.97 0.97 3 -0.5 From 0 , 1 Up to 0.2 -0.05 -0.1 1.74 4 2.5 From 0.3 to 0.2 0.75 0.5 5 -1 From 0.1 to 0.2 -0.1 -0.2 Total - 1 1 2.27 1.52 IRU = 0.3 2.27 + (1 - 0.3) 1.52 - 1.74 million rubles.

The result is entered in gr. 6.

The positive value of the expected integral effect indicates the expected efficiency of the IG). ?

Formula (3.19) can also be used to calculate the maximum and minimum possible values ​​of the expected integral effect in the absence of specified intervals of probabilities for individual scenarios. In this case, the maximum expected integral effect [shah ^ SHRuk "Pk)] is calculated when using

Рі * Р2 * "" к

excluding from the calculation of scenarios k with negative integral effects (ЛТ ^,), and the minimum | mn 1 (A ^ p,.) \ - for

Рі * Р2> “" к

exclusion of scenarios with positive integral effects (IRUku). This version of the calculation by formula (3.19) is advisable to apply if there is a probability of complete exclusion

scenarios with positive or negative integral effects in the implementation of nriskta.

Table 3.5. Calculation of the expected integral effect in the presence of data on the probabilities of individual scenarios Scenario number k Integral effect for the k-th scenario

RUB million The probability of realization of the k-th scenario

Pk Maximum integral effect max (NRU "p), rub. Minimum integral effect mip (krU-r), million rubles. Expected integral effect

RUB million A I 2 3 4 5 1 3.5 0.2 0.7 2 3.24 0.3 0.97 3 -0.5 0.2 -0.1 0.51 4 2.5 0.2 0, 5 5 -1 0.1 -0.1 Total - 1 2.17 -0.20 Decision. The calculation of the expected integral effect will be carried out according to the formula (3.19). To do this, we first find the maximum possible integral effect (NPV) with the best combination of probabilities. When calculating it, one should multiply the positive integral effects (NPVk) for each of the k scenarios (rows in column I) by the corresponding probability values ​​(rows in column 2) scenarios. We will write the results in the corresponding lines for gr. 3, Summing up the results obtained for gr. 3 we obtain the maximum possible integral effect (NPV) with the best combination of probabilities I gnax? (A / RG *? /? /)] - the total for gr. 3.

RHURII- k

The minimum possible integral effect (NPV) with the worst combination of probabilities is determined by multiplying the negative integral effects NPVk for each of the k scenarios (rows for group I) by the corresponding probability values

(lines for group 2) scripts. We will write the results in gr. 4. Summing up the results obtained for group 4, we obtain the minimum possible integral effect (NPV) with the worst combination of probabilities [min y] (NPVk? Рк)] - the total for gr. 4.

We substitute the obtained results into the formula (3.19) at X = 0.3: NPVax = 0.3? 2.17 + (I - 0.3)? (-0.2) = 0.51 million rubles.

The positive value of the expected integral effect indicates the expected efficiency of the IP under the assumption of the probability of mutually exclusive realization of extremely opposite scenarios, A

Calculations of the expected efficiency of IP, taking into account uncertainty and risk, show that the obtained values ​​of the expected integral effect differ from the baseline (NPV) by values ​​that take into account the possible development of the investment project scenario in comparison with the baseline scenario. Each of the methods for calculating the expected NPV leads to different results. The deviations of the design results depend on which directions of the baseline scenario change are taken into account and what kind of uncertainty is taken into account in the methodology. In turn, the choice of the type of uncertainty and the direction of the scenarios depend on the specific investment conditions and should be determined directly for each specific case of investment planning. Experts can be involved to select and evaluate scenarios.

Sustainability of a project is its ability to maintain its effectiveness under various changes in the implementation conditions

A project is considered absolutely sustainable if, for all alternative scenarios of its development, it turns out to be effective and financially sound, and the possible negative consequences of adverse events can be eliminated using the organizational and economic measures provided for in the project (diversification, risk distribution among participants, insurance, reservation, etc. etc.). A project is unstable if it turns out to be efficient or leads to significant financial losses in scenarios with a sufficiently high level of possibility of occurrence.

The aggregate assessment of the sustainability of a project under risk conditions is a method of express analysis aimed at promptly obtaining a conclusion about the riskiness of a project without the use of complex statistical and mathematics and other procedures for assessing risk.

When applying an integrated assessment of the project's sustainability as the main method for taking into account risk and uncertainty, it is recommended:

Use moderately pessimistic forecasts of the technical and economic parameters of the project, prices, tax rates, exchange rates and other parameters of the economic environment of the project, production volumes and prices for products, deadlines and costs of certain types of work, etc.

Provide for reserves of funds to cover possible growth in investment and operating costs due to adjustments to design solutions in the process of its implementation

Use the risk-adjusted discount rate in performance criteria evaluations

At the same time, if there is no information about possible changes in the values ​​of individual parameters in the future, it is recommended to assess the effectiveness of the project for the following scenarios:

An increase in investment costs, as well as a corresponding adjustment of the amount of depreciation in the cost price in the following areas: the cost of work performed by domestic contractors and the cost of equipment. Anna of domestic supply - by 20%, the cost of work and equipment of foreign firms - by 10%

An increase by 20% of the design level of indirect production costs and by 30% of specific (per unit of production) direct material costs, respectively, the cost of stocks of raw materials, materials, work in progress and finished products in the composition of working capital changes

Reducing the volume of proceeds to 80% of its design value;

Increase in 2 times the design time of delays in payments for the delivered without prepayment;

Increase in interest for a loan by 1.4 times on loans in hryvnia and 1.2 times on loans in foreign currency

If the project provides for insurance in the event of changes in the relevant parameters of the project, or the values ​​of these parameters are fixed in the concluded agreements as part of the project documentation, the possibility of deterioration of these parameters is not considered.

For an integrated assessment of the sustainability of the project, the indicators of the internal rate of return and the index of profitability of discounted investments can be used. In this case, the project is considered sustainable if. All of the following conditions apply:

The IRR value is large enough - not less than 25-30%;

The value of the discount rate does not exceed the level acceptable for small and medium risks - 15%;

Interest rates on loans and other components of borrowed capital in project financing do not exceed IRR;

The discounted investment return (PI) exceeds 1.2

In addition, the project is recommended to be assessed as sustainable only if there is a certain financial reserve - all available financial resources of the enterprise, include the total accumulated balance of the project cash flow and cash balances within the company's assets from other activities (related to this project). At the same time, it is desirable that the volume of such a financial reserve for each step of the billing period be at least 5% of the amount of net operating and investment costs for the corresponding period.

Fulfillment of this requirement may require a revision of the project financing scheme with the subsequent adjustment of the entire cash flow forecast and estimates of performance indicators, namely:

Changes in the size and conditions for attracting loans;

Creation of the necessary stocks, cash reserves, deductions to the additional fund;

Adjustment of settlement terms between project participants;

Insurance of project participants against certain risks

At the same time, additional costs associated with the occurrence of risk, including compensation for losses, it is advisable to reflect as a separate item of cash outflows "Expected losses" Their volume step by step. The settlement period is defined as the product of possible financial losses and the likelihood of their occurrence at a given step-by-step rate.

In cases where, even after the revision of the financial plan, the project remains unstable according to the results of the aggregated assessment, its implementation is impractical.