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Consolidated assessment of the sustainability of the investment project. Coursework: Accounting for uncertainty and risk in evaluating the effectiveness of investment projects

Consolidated assessment of the sustainability of the investment project. Coursework: Accounting for uncertainty and risk in evaluating the effectiveness of investment projects

7. ACCOUNTING FOR UNCERTAINTY AND RISK IN ASSESSING THE EFFICIENCY OF INVESTMENT PROJECTS

7.2. Consolidated assessment of the sustainability of the investment project as a whole

When using this method, in order to ensure the sustainability of the project, it is recommended:
- use moderately pessimistic forecasts of technical and economic parameters of the project, prices, tax rates, exchange rates and other parameters of the economic environment of the project, production volume and product prices, deadlines and costs of certain types of work, etc. (at the same time, positive deviations of these parameters will be more likely than negative ones);
- provide for reserves of funds for unforeseen investment and operating expenses due to possible errors design organization, revision of design decisions during construction, unforeseen delays in payments for delivered products, etc.;
- increase the discount rate in the calculations of commercial efficiency by the amount risk adjustments (see 5.2.1.6.5).

7.3. An aggregated assessment of the sustainability of the project from the point of view of its participants

The stability of the IP from the point of view of the enterprise - a participant in the project, with possible changes in the conditions for its implementation, can be generally checked based on the results of calculations of commercial efficiency for the main (basic) scenario of the project implementation by analyzing the dynamics of real money flows. In this case, real money flows included in the calculation are calculated for all types of activity of the participant, taking into account the conditions for granting and repaying loans.

If an accident is possible at one or another step of the billing period, the liquidation of the consequences of which, including compensation for damage, requires additional costs, the cash outflows include the corresponding expected losses . They are defined as the product of the costs of eliminating the consequences of an accident by the probability of an accident occurring at a given step.

For an aggregated assessment of the sustainability of the project, indicators of the internal rate of commercial return and the index of return on discounted investments can be used. At the same time, the IP is considered stable if the value of GNI is large enough (at least 25 - 30%), the value of the discount rate does not exceed the level for small and medium risks, and loans at real rates that exceed GNI are not expected, and the index of return on discounted investments exceeds 1.2.

Subject to the requirements of Sec. 7.2 to the parameters of the main scenario for the implementation of the project, the project is recommended to be assessed as sustainable only if there is a certain financial reserve. Considering that the free financial resources of an enterprise include not only the accumulated balance of cash flow from all activities, but also reserve Money as part of the assets of the enterprise, the condition for the sustainability of the project can be formulated as follows.

At each step of the calculation period, the sum of the accumulated balance of cash flow from all types of activities (cumulative effect) and financial reserves must be non-negative.

To implement this recommendation, it may be necessary to change the norms of the financial reserve provided for by the project, to provide for deductions to reserve capital, or to adjust the project financing scheme. If such measures do not ensure the fulfillment of this requirement, a more detailed study of the impact of uncertainty on the feasibility and effectiveness of the IP is necessary (see below).

7. ACCOUNTING FOR UNCERTAINTY AND RISK IN ASSESSING THE EFFICIENCY OF INVESTMENT PROJECTS

7.2. Consolidated assessment of the sustainability of the investment project as a whole

When using this method, in order to ensure the sustainability of the project, it is recommended:
- use moderately pessimistic forecasts of technical and economic parameters of the project, prices, tax rates, exchange rates and other parameters of the economic environment of the project, production volume and product prices, deadlines and costs of certain types of work, etc. (at the same time, positive deviations of these parameters will be more likely than negative ones);
- provide for reserves of funds for unforeseen investment and operating expenses due to possible errors of the design organization, revision of design decisions during construction, unforeseen delays in payments for delivered products, etc.;
- increase the discount rate in the calculations of commercial efficiency by the amount risk adjustments (see 5.2.1.6.5).

7.3. An aggregated assessment of the sustainability of the project from the point of view of its participants

Subject to the requirements of Sec. 7.2 to the parameters of the main scenario for the implementation of the project, the project is recommended to be assessed as sustainable only if there is a certain financial reserve. Taking into account that the free financial resources of the enterprise include not only the accumulated balance of cash flow from all types of activities, but also the reserve of funds as part of the assets of the enterprise, the condition for the sustainability of the project can be formulated as follows.

At each step of the calculation period, the sum of the accumulated balance of cash flow from all types of activities (cumulative effect) and financial reserves must be non-negative.

The sustainability of the project is its ability to maintain its effectiveness under various changes in the implementation conditions.

A project is considered absolutely sustainable if, under all alternative scenarios of its development, it turns out to be effective and financially viable, and possible Negative consequences adverse events can be eliminated with the help of the organizational and economic measures provided for in the project (diversification, risk distribution among participants, insurance, reservations, etc.). A project is unsustainable if it has proved to be ineffective or results in significant financial losses under scenarios that have a sufficiently high level of probability of occurrence.

An enlarged assessment of the sustainability of a project under risk conditions is a method of express analysis aimed at quickly obtaining a conclusion about the riskiness of a project without the use of complex statistical and mathematical risk assessment procedures.

When using an aggregated assessment of project sustainability as the main method for taking into account risk and uncertainty, it is recommended:

Use moderately pessimistic forecasts of 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 reserves of funds to cover the possible growth of investment and operating costs due to the adjustment of design decisions 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 evaluate the effectiveness of the project for the following scenarios:

An increase in investment costs, as well as a corresponding adjustment in 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%

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, unfinished production and finished products as part of working capital changes

Reducing the amount of revenue to 80% of its design value;

2-fold increase in the design time for delays in payments for goods supplied without prepayment;

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

If the project provides for insurance in case of changes in the relevant project parameters, 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 aggregated assessment of the sustainability of the project, indicators of the internal rate of return and the index of profitability of discounted investments can be used. The project is considered sustainable if. All of the following conditions apply:

The IRR value is quite large - at least 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;

Discounted Investment Return Index (PI) exceeds 1.2

In addition, the project is recommended to be assessed as sustainable only if there is a certain financial reserve - all free financial assets of the enterprise, including the total accumulated cash flow balance for the project and cash balances in the assets of the enterprise 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 is at least 5% of the net operating and investment costs of the corresponding period.

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

Changing the size and terms of attracting loans;

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

Adjustment of the terms of settlements 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, should be reflected as a separate item of cash outflows "Expected losses" Their volume by steps. The settlement period is defined as the product of possible financial losses and the probability of their occurrence at a given step anomaly.

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

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

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

aggregated sustainability assessment;

calculation of break-even levels;

parameter variation method;

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

Each subsequent method is more accurate, although more laborious, and therefore the use of each of them makes the use of the previous ones unnecessary. All methods, except for 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 for measures to prevent or redistribute the resulting losses.

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

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

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

provide insurance for project participants for certain insured events.

In cases where the project remains unsustainable even with these adjustments, its implementation is recognized as inexpedient if there is no additional information sufficient to apply the fourth of the methods listed above. The issue of the implementation of the project according to the fourth method is solved without taking into account the results of all the previous ones.

Consolidated assessment of the sustainability of an investment project. In 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 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 product prices, the timing and cost of certain types of work V. etc. In this case, positive deviations of these parameters will be more likely than negative ones;

provide for reserves of funds for unforeseen investment and operating expenses due to possible errors of the design organization, revision of simple decisions during construction, unforeseen delays in payments for delivered products, etc.;

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

The sustainability of the IP from the point of view of the organization participating in the project, with possible changes in the conditions for its implementation, can be generally checked based on the results of calculations of commercial efficiency for the main (basic) scenario of project implementation by analyzing the dynamics of real money flows. In this case, real money flows included in the calculation are calculated for all types activities of the participant, taking into account the conditions for granting and repaying loans.

For an aggregated assessment of the sustainability of a project, indicators of the internal rate of return and the index of return on discounted costs can sometimes be used. At the same time, the IP is considered sustainable if the value of the IRR is large enough (at least 25-30%), the value of the discount rate does not exceed the level for small and medium risks (up to 15%) and at the same time it is not supposed to use loans at real rates exceeding the IRR, and the index of return on discounted costs exceeds) ,2.

Subject to these requirements for assessing the sustainability of an investment project as a whole to the parameters of the main scenario for its implementation, it is recommended that the project be assessed as sustainable only if there is a certain financial reserve.

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

Operating costs include: direct material costs, labor costs for production personnel, distribution costs, production management costs, depreciation, as well as taxes charged to cost and financial results.

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

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

One of the most common indicators of the break-even boundary of the 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 volume (production) to the project one at this step. Break-even is the volume of sales at which net profit is zero. The break-even calculation is based on the assumption that production equals 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 volume;

income from non-operating activities and expenses for this activity do not depend on sales volumes;

total current costs can be divided into conditionally fixed (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 revenue per nth step;

full current production costs - production costs plus depreciation, taxes and other deductions attributable to prime cost (including transport, land, water, unified social tax, as well as fees for issuing licenses and the right to produce and sell ethyl alcohol, alcohol-containing and alcoholic products, payments for maximum allowable 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 profit taxation (including property tax) at the /?-th step;

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

OSp - income from non-operating activities minus expenses for this activity at the first step.

If the project involves the production of several types of products, formula (3.13) does not change, and all the quantities included in it are taken over the entire project (without separation by type of product). 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 design capacities. Break-even close to 1

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

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

proceeds from the sale of IP (IR) 116; total costs, SS 25;

including

variable costs, US 14;

fixed costs, GS 11.

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

According to the results of the calculation, the break-even level does not exceed the established limits with a large margin (0.11 Break-even limits can also be determined for each project participant. The criterion for reaching the limit is the net profit of this participant turning to zero. 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.

Parameter variation method. Limit values of parameters.

The output indicators of the project can change significantly if there is an unfavorable change (deviation from the design) values of some parameters. The method of parameter variations considers possible changes in parameters during the calculation period and evaluates the results of the project due to these parameters, or factors.

investment costs (or their individual components);

production volume;

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

interest on a loan;

forecasts of the general inflation index, target indices and domestic inflation index (or other measure of changes in purchasing power) foreign exchange;

payment delays;

the duration of the settlement period (until the termination of the project resolution);

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 limits of change in 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)

increase in investment. At the same time, the cost of work performed by Russian contractors and the cost of Russian-delivered equipment increase by 20%, the cost of work and equipment of foreign companies - by 10%. Accordingly, the cost of fixed assets and the amount of depreciation and prime cost change; 2)

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

reduction in revenue to 80% of its design value; four)

increase by 100% of the time of delays in payments for products supplied without prepayment; 5)

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

These scenarios are recommended to be considered against the background of unfavorable development of inflation set by experts. If the project provides for insurance against changes in any project parameters or the values of these parameters are fixed in contracts prepared for conclusion, the scenarios corresponding to these cases are not considered.

The project is considered sustainable in relation to possible changes in parameters if, under all considered scenarios:

NPV is positive;

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

If under 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, clarify the upper limits of these fluctuations. If, even after such clarification, the conditions for project sustainability are not met, it is recommended:

smart tel p meter> vestn>

if there is no additional information, reject the project:

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

effect of smallness 1 ivn "C

meanopti

Sustainability can also be assessed by defining limit values for project parameters, i.e. such their values at which the integral effect of the participant becomes equal to zero. One of these indicators is VID, which reflects the marginal value of the discount rate. To estimate the limit values of parameters that change by calculation steps (prices of products AND MAIN technological equipment, volumes of Production*I, volume of credit resources, rates of the most significant taxes, etc.), it is recommended to calculate the limit integral levels (IL) 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 project participant) becomes zero.

Let's estimate the marginal RI of the volume of sales for the project considered in example 3.7. This solution complements and refines the calculation of break-even limits. As in example 3.7, it is assumed that the volume of production is equal to the volume of sales, all costs are divided into conditionally fixed and conditionally variable (proportional to the volume of production) and only material costs are variables.

To determine the IR, revenue, semi-variable costs, and revenue-proportional taxes are multiplied at each step by a common multiplier \x. The rest (investment and semi-fixed production costs, non-revenue taxes) remains unchanged, and the factor q is chosen so that the NPV becomes zero or, equivalently, the IRR becomes equal to the discount rate (11% per year). The multiplier µ selected in this way is the IE.

For calculation we use the formula (2.2)

D7>K \u003d y - * 1 _ a, -

where in the composition of costs without depreciation (34 - 20 million rubles), we single out their conditionally variable and conditionally constant parts. By condition, we are from IT

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

To determine the IU in formula (2.2), we multiply the revenue related to IP (FVA = 116 million rubles) and the variable part of the costs VS =) 4 million rubles by | q and equate NPV to zero. Then we find the multiplier \x using the "Search for a solution" or "Selection of a parameter" function 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 c- (116 - 14) \u003d 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 a difference:

tp \u003d 1 - c \u003d I - 0.951806 \u003d 0.048194 (4.82%).

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

From previous calculations, we know the following results:

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

net present value (NPV) NPV= 3.24 mln rub. > 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 break-even indicator, we see that the judgment of the sustainability of MP based on the values of the break-even level may be unreasonably optimistic. Evaluation of the expected effect of the project, taking into account the quantitative:: characteristics of uncertainty. More accurate methods for assessing the effectiveness of IP under conditions of uncertainty include the method of calculating and evaluating the expected effect of the project. The Eyug method allows you to directly calculate the general indicator of the project's effectiveness - the expected integral effect (expected NPV). Estimation of the expected effectiveness of the project, taking into account the uncertainty, is carried out in the presence of more detailed information about the various scenarios for the implementation of the project, the probabilities of their implementation and the values of the main technical and economic indicators of the project in each of the scenarios. Such an assessment can be carried out both with and without taking into account the financing scheme of the project.

Calculations are carried out in the following order:

describe the entire set of 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 similar parameters of the project);

for each scenario, they study how the organizational and economic mechanism for the implementation of the project will operate under specific conditions, how the cash flows of the participants will change in this case;

for each scenario, for each step of the billing period, inflows and outflows of real money and generalized performance 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 the participants, insurance, reservations and other elements of the organizational and economic mechanism for the implementation of the project. According to scenarios that provide for emergency situations (accidents, natural disasters, abrupt changes in market conditions, etc.), additional costs arising from this are taken into account. When determining the NPV for each scenario, the discount rate is assumed to be risk-free;

check the financial feasibility of the project. Violation of the realizability conditions is considered as necessary condition termination of the project (taking 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 factors of uncertainty is presented in the form of probabilities of individual scenarios or intervals of change of these probabilities. Thus, a certain class of admissible (consistent with the available information) probability distributions of project performance indicators is determined. In special cases, this class may consist of a single probability distribution or of all distributions on the set of possible combinations of performance indicators,

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

evaluate the risk of project inefficiency - the total probability of scenarios in which the integral effect (NPV) becomes negative;

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

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

Probable! us uncertainty. With probabilistic uncertainty, for each scenario, the probability of its implementation is considered to be known (given). It can be determined expertly. 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 depreciation of fixed assets (reduction in the strength of structures of buildings and structures, equipment failures, etc.) or natural and climatic conditions (weather, soil characteristics or reserves minerals, the possibility of earthquakes or floods, etc.), d also the uncertainty of changes in the market related to IP on the part of suppliers, buyers, creditors and debtors involved in the formation of cash flows, market instability, the emergence of new competitors or products substitutes in 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,

Price fluctuations for different types goods are interdependent. Therefore, for example, from the fact that the prices of gasoline and road transport are highly likely to deviate from the average by 10%, it does not follow that with a high probability one of these prices will fall by 10%, and the other will increase by 10%.

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

y^ozh \u003d Eltruk-Rk "(314)

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

Pk - the probability of this scenario.

At the same time, the risk of project inefficiency Pe and the average damage from the implementation of the project in case of its inefficiency Y are determined by the formulas

KRUk - rk

Ue \u003d * - , (316)

where the summation is carried out only for those scenarios (j) for which the integral effects (NPV) of 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 Table. 3.3.

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

Let us determine the expected integral effect by formula (3.14). To do this, we multiply the integral effect (NPV) for each scenario (rows in column 1) by the probabilities for each scenario (rows in column 2) and add the numbers obtained. We get No. RUozh \u003d 1.97 million rubles. (total for gr. 3).

Table 3.3. Calculation of the expected integral effect

and possible damage Scenario number, to inte

rub. Probability of realization of the k-th scenario, pk Calculation of the expected integral effect, А7%zh, mln rub. Calculation of the risk of project inefficiency, Re Calculation of the average possible damage,

mln rub. 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). To do this, we summarize the probabilities of the scenarios for which the integral effects (NPV) of the MRU k 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 expected integral effects for scenarios with negative integral effects by the risk of project inefficiency (total column 4 of Table 3.3):

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

Integral effects of scenarios NRUk and the expected effect of NRUexp depend on the value of the discount rate (r). The premium (#) for the risk of non-receipt of income provided for by the main scenario of the project is determined from the condition of equality between the expected effect of the project No. Uzh (r), calculated at the risk-free discount rate r, and the effect of the main scenario MRU0S(r + g), calculated at the discount rate (r + #) including risk adjustment

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

In this case, the average losses from not receiving the incomes envisaged by the main scenario under unfavorable scenarios are covered by the average gain from obtaining higher incomes under favorable scenarios.

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

Let us assume that the process of the object functioning 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) - РУn - 3н.

At the same time, the project is terminated at a certain step if a catastrophe occurs at this step - a sharp deterioration in the results of the NP, due to the appearance on the market of a cheaper substitute product, a serious equipment failure, natural disaster or other unfavorable set of circumstances. 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 equal to 1 р. The probability that it will not happen neither at the 1st nor at the 2nd step, according to the rule of product of probabilities is equal to (1 - p)2, and so on. Therefore, either the catastrophe will not occur until the end of step n and the effect of the project at this step will be equal to Ф0m, or such an event will occur and the effect will be equal to zero. The above means that the mathematical expectation (mean value) of the effect at the n-th step will be Summing up these values, taking into account the time difference, we find the mathematical expectation of the NPV of the project:

kr\"ozh \u003d ^ F ° "" (1 ~ p) - a \u003d ^ ("P "~ 3" * 11 p' - a. (3.17) * O + gG "(I + r)"

It can be seen from this formula that the multi-temporal effects F provided under normal conditions, i.e. in the absence of disasters. are reduced to a reference point in time using a factor (1 - p)n: (1 + r)n, which is not the same as the usual discount factor 1: (1 + r)r\ In order for ordinary discounting without taking into account risk factors and calculating of these factors gave the same result, it is necessary that a different value of gr be taken as the discount rate, such that 1 - + + gr \u003d (1 + r): (1 - p). From here we get gr = (r + p) : (1 - p). For small values of the probability p, this formula takes the form r = r + + py, confirming that in this situation, risk accounting is reduced to calculating the NPV under normal conditions, but with a discount rate r, exceeding the risk-free r by the “risk premium”, reflecting in In this case, the (conditional) probability p of terminating the project within the n-th year.

Example 3.9. The amount of income (/V) from IP after 4 years of investment will be equal to 116 million rubles. The amount of costs 3 for the same period will be 20 million rubles. Capital investments C/ in the amount for this investment period are 60 million rubles. Suppose that the probability p of the appearance during one calculation step (within a year) on the market of a cheaper substitute product that can lead to a sharp deterioration in the performance of this IP (probability of a catastrophe) is 0.0171 (1.71%) for 1 calculation step. The discount rate is set at 11% per head.

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

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

60 = -1.00 million rubles

According to previous calculations, which can be called the baseline scenario, the NPV of the project has a positive value (IV RC = 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), during the investment period 4 becomes negative (-1 million rubles). This change occurred due to the small margin of stability of the project f = 0.048194 (4.82%), previously determined when calculating the limiting integral level c. As a result, a small deviation in the predicted implementation of the project 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

№Y0Ж = X NPVm^iX + (1 - X). (2-18)

where A!RUmax and MRUm(n - the largest and smallest integral effects (NPV) for the scenarios under consideration;

X - 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 calculations of 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 IP operation, the maximum possible NPV in the amount of 3.55 million rubles is predicted. and the minimum possible NPV in the amount of -1.00 million rubles. Calculate the expected integral effect of IP, if the standard for taking into account the uncertainty of the effect (X) is set by management 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 integral effect, taking into account the interval uncertainty, positive, which indicates the probable profitability of IP?

In the general case, if there are additional restrictions on the probabilities of individual scenarios pp, it is recommended to calculate the expected integral effect using the formula (2.19)

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

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

P] "Pl D

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

Example 3.11. Calculate the expected integral effect for IP according to Table. 3.4 with given intervals of change of probabilities (gr. 2-3). A special standard for taking into account the uncertainty of the effect, reflecting the system of preferences of the relevant economic entity under conditions of uncertainty?v, is taken equal to 0.3.

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

When calculating it, one should multiply the values of the integral effects at k-m scenarios(NPVk) (rows in group 1) to their corresponding probabilities from the interval (/?*), providing the greater expected effect (lines in group 2). The results are recorded in gr. 4. Summing up the results for gr. 4 will give the maximum possible integral effect (NPV) with the best combination

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

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

P\ *Pi »??? to

calculation, it is necessary to multiply the values of the integral effects according to the i-th scenario (NPVk) (rows in group 1) by the corresponding probabilities from the interval of their values (pk), providing a smaller expected effect (lines in group 3). The results are recorded in gr. 5. Summation of the obtained results for gr. 5 will give the lowest possible integral effect (NPV) with the worst combination of probabilities | min ^(NPVk ? pk)) is the total for th. 5. We substitute the obtained results for the 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

mln rub. Interval of change in the probability of re-release of the k-th scenario Pk Maximum integral effect, min?(7VPV"p), mln rub. gr.1 * gr.3 Expected integral effect

RUB mln А 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 RURexp = 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 effectiveness of IG). ?

Formula (3.19) can also be used in calculating the maximum and minimum possible values of the expected integral effect in the absence of specified probability intervals for individual scenarios. In this case, the maximum expected integral effect [max ^ShRuk "Pk)] is calculated when using

Рі*Р2*"” to

exclusion from the calculation of scenarios k with negative integral effects (ΔT^,), and the minimum | type 1(A^ p,.)\ - when

Рі*Р2>“" to

exclusion of scenarios k with positive integral effects (IRUku). This calculation option according to formula (3.19) is advisable to apply if there is a possibility of complete exclusion

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

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

mln rub. Probability of realization of the k-th scenario

Pk Maximum integral effect max (NRU "r), sc rubles Minimum integral effect typ (crU-r), million rubles Expected integral effect

mln rub. 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 Solution. We will calculate the expected integral effect using 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 (lines in group I) by the corresponding probabilities (lines in group 2) of the scenarios. We write the results in the corresponding lines for gr. 3, Summing up the results obtained for gr. 3 we get the maximum possible integral effect (NPV) with the best combination of probabilities 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 in group I) by the corresponding probabilities

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

We substitute the results obtained into 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 effectiveness of the IP, assuming the probability of mutually exclusive implementation 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 possible development investment project scenario compared to the baseline scenario. Each of the methods for calculating the expected NPV leads to different results. Deviations of the design results depend on which directions of change in the baseline scenario are taken into account and what type 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 design. Scenarios can be selected and evaluated by experts.

The stability of the investment project as a whole (excluding the scheme of its financing) with possible changes in the conditions for its implementation can be comprehensively verified based on the results of calculations of the economic and commercial efficiency of the base scenario for its implementation by analyzing the dynamics of cash flows. The cash flows included in the calculation are calculated only for investment and operating activities.

In order to ensure the sustainability of the project, when forming the baseline scenario, it is recommended to use moderately pessimistic forecasts of technical and economic parameters of the project and parameters of the economic environment (prices, tax rates).

reserves of funds for additional investment and operating expenses arising from possible errors of the design organization, revision of design decisions during construction, unforeseen delays in payments for delivered products, etc.;

an increase in the timing of certain types of construction, installation and other work due to unforeseen construction delays;

decrease in the design volumes of production and sales of products due to the possible failure of technological equipment and loss of products during their delivery to the consumer;

expenses for the replacement of low-quality products and compensation for damage from its consumption. This is important for projects involving the production of consumer goods or materials for potentially hazardous facilities.

Subject to these requirements, the project is recommended to be considered as sustainable in general, if it has sufficiently high values of integral indicators, in particular, a positive value NPV. In these calculations, it is often recommended to increase the discount rate by the amount risk premiums .

The higher the investor estimates the risk of the project, the higher the requirements he makes to its profitability. This is reflected in the calculations by increasing the discount rate by including a risk adjustment (risk premium) in it.

Risk-adjusted discount rate (or required rate of return) - this is the maximum of such discount rates, when using which at least one alternative and affordable investment direction for the investor, which has the same risk as this project, will provide him with a non-negative integral discounted effect.

The risk premium is determined for each participant, taking into account its functions, obligations to others and obligations of other participants to it. She is zero , if the income of this participant is guaranteed regardless of the results of the project (for example, with a guarantee of payment for the work performed by him, as well as in the case when the receipt of income is insured). The risk premium increases if, regardless of the nature of the project, this participant does not have verified information about the solvency and reliability of other economic entities that must jointly participate in financing the project or pay for the products (works, services) it produces.

It is important to take into account that the risk of the project for its different participants is different and is assessed by them in different ways. Thus, the lender may consider the project risky (by analogy with other previously financed projects in the relevant sector of the economy), while the borrower is risk-free (due to the measures provided for in the project to reduce various types of risk, which the lender may either "not see" in the design materials, or not assessed). Therefore, when discounting cash flows on a loan, the lender and the borrower will use different discount rates.

Existing methodological approaches risk premium can be divided into two groups: cumulative and aggregated. With cumulative methods, the main task is to assess and reflect certain types of risks (risk factors) in the value of the risk premium as accurately as possible. With aggregated methods, no attention is paid to individual risk factors; they are aimed only at establishing a discount rate based on the minimum additional information.

Using cumulative method in the value of the risk premium, in the general case, three types of risks associated with the implementation of an investment project are taken into account:

country risk;

risk of unreliability of project participants;

risk of non-receipt of project revenues.

Country risk usually seen as a possibility:

confiscation of property or loss of property rights when they are bought out at a price below the market price or provided for by the project;

unforeseen legislative changes worsening the financial performance of the project (increasing taxes, tightening requirements for production or manufactured products compared to those provided for in the project);

untimely or incomplete repayment of foreign loans granted to the state or under a state guarantee, as well as actions of the state that prevent the repayment of foreign loans by project participants (for example, the introduction of restrictions on foreign currency conversion);

personnel changes in government bodies interpreting legislation of indirect action.

The level of country risk largely determines its investment climate, and the need to take it into account when evaluating the effectiveness of investment projects is noted by many experts.

Ratings of the countries of the world according to the level of country risk of investing in them are published by the specialized rating company BERI (Germany), the Association of Swiss Banks, and the audit corporation ErnstandYoung. The country risk premium is assessed by experts based on these ratings and, according to world statistics, can be up to 200% of the discount rate calculated taking into account all other factors, except for country risk.

With a more accurate assessment, the country risk is divided into socio-economic, domestic economic and foreign economic. Each of these types of risk is assessed in points by factor. However, the transition from risk scores to a quantitative assessment of the premium for the corresponding risk is made by experts.

The size of the country risk premium decreases when federal (and, to a lesser extent, regional) support is provided to the project, and also when the project is implemented under the terms of a production sharing agreement.

When evaluating the regional and budgetary effectiveness of the project, the country risk is not taken into account. In calculations of public and commercial effectiveness, country risk is taken into account only for projects implemented abroad or with foreign participation. In calculating the efficiency of participation of enterprises in the project and the effectiveness of investing in the shares of the enterprise, country risk must be taken into account.

In a number of cases, the country risk is differentiated within the country by region - while talking about the investment attractiveness or the "investment climate" of the region.

Risk of unreliability of project participants. This type of risk is usually seen in the possibility of an unexpected termination of the project due to:

misappropriation of borrowed funds;

financial instability of the company implementing the project (lack of working capital, 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. This risk is most significant in relation to small enterprises.

The amount of the premium for the risk of unreliability of project participants is determined by each specific project participant, taking into account their functions and obligations, as well as the obligations of other participants to him. Typically, the premium for this type of risk is no more than 75% of the risk-free discount rate, however, its value significantly depends on how detailed the organizational and economic mechanism for implementing the project is, how much the concerns of the project participants are taken into account in it. In particular, the amount of the award:

decreases if one of the participants provides the other with property guarantees for the fulfillment of its obligations;

increases if, regardless of the nature of the project, this participant does not have verified information about the solvency and reliability of other project participants who must pay for the work (products, services) they perform or jointly participate in project financing.

Indexation of payments from one participant to another reduces the risk of the latter, but increases the risk of the payer. Throughout the period of project implementation, the risk of unreliability of participants does not remain stable: at first it is relatively large, then, as the relationship between counterparties strengthens, it decreases. In this regard, at later steps of the calculation period, the corresponding component of the risk premium decreases.

Risk of non-receipt of project revenues (unsystematic risk). This type of risk is primarily due to the technical, technological and organizational decisions of the project, as well as random fluctuations in the volume of production and prices for products and resources. This risk increases if ownership of the facility under construction can be challenged. If the project income is less than projected, it may not be profitable for the project participants to continue it, and with even lower income, their investments in the project turn out to be less profitable compared to alternative areas of investment. On the other hand, in this situation it may not be possible to repay the loans in full and on time. Thus, failure to receive the projected income is associated with risks not only for project participants, but also for creditors who take this risk into account by raising the loan interest rate (and the more, the less liquidity of the assets created under the project).

The premium for this type of risk is determined taking into account the technical feasibility and validity of the project, the detail of the development of design solutions, the availability of the necessary scientific and developmental reserve and the representativeness of marketing research. The value of the premium for non-systematic risk depends on the novelty of the equipment or technology used, the lack of knowledge of any processes or phenomena (from demand for products to mineral reserves).

The premium for this type of risk also tends to decrease during the billing period. Thus, the risk associated with the novelty of the applied technology or the difficulties of its development can be high before the enterprise is put into operation. However, after the enterprise is introduced, this risk is significantly reduced.

The disadvantage of cumulative methods is the inability to adequately reflect the features of the organizational and economic mechanism for the implementation of the project. Therefore, for two project options that differ in organizational and economic mechanism, these methods will give the same risk premium. Meanwhile, if one option provides for property insurance, sanctions for violation of construction deadlines or a reserve of free cash, and the other does not, then the risk for such options is different and the discount rate for the first should be higher.

Table 11.1 - The influence of individual factors on the value of the risk premium

Factors and their gradation	Increase in risk premium, %
1) The need to conduct R&D with previously unknown results by specialized research and / or design organizations: duration of R&D less than 1 year duration of R&D over 1 year: a) R&D is carried out by one specialized organization b) R&D is complex and is carried out by several specialized organizations
2) Characteristics of the applied technology: traditional
3) Uncertainty of demand volumes and prices for manufactured products: existing
4) Instability (cyclicality, seasonality) of production and demand
5) Uncertainty of the external environment during the implementation of the project (mining and geological, climatic and other natural conditions, aggressiveness of the external environment, etc.)
6) The uncertainty of the process of mastering the applied equipment or technology. The participant has the opportunity to ensure compliance with technological discipline