Investment projects relate to the future period of time, therefore it is problematic to predict the results of their implementation with confidence: The implementation of an investment project is influenced by many changes in the political, social, commercial and business environment, changes in technology, technology and productivity, the state of the environment, current taxation, inflation rate, legal and other aspects. This predetermines the existence of a known risk in projects.
An investment decision is considered risky or uncertain if it has several possible outcomes. In the "Methodological recommendations ..." the concepts of uncertainty and risk are separated. Under uncertainty refers to the incompleteness and inaccuracy of information about the conditions for the implementation of the investment project. Risk - this is the possibility of the occurrence during the implementation of the project of such conditions that will lead to negative consequences for all or individual participants in the project.
As follows from these definitions, uncertainty is an objective characteristic and equally affects any participant in an investment project (for example, uncertainty about the future price of raw materials). The risk is more subjective, and for individual participants in the project, the same uncertainty may represent different levels of risk (uncertainty of the future price, for example, of gasoline for one participant may be the reason for abandoning the project, and the other risk-knock to implement the project).
According to the "Methodological recommendations ...", the risk is associated with the onset negative consequences (losses, failure to meet the construction deadlines, etc.). An alternative is the interpretation of risk as the possibility of any (positive or negative) deviations of indicators from the values provided for by the project. According to this interpretation, risk is an event (possible danger) that may or may not occur.
If it happens, then the options are:
a) a positive result (profit or other benefit);
b) negative result (loss, damage, loss, etc.);
c) zero result (break-even or non-profit project).
When analyzing the risks of investment projects, the classification of investment risks is of great importance.
Classification of investment risks.
The distribution of risks and their classification should be carried out in the process of preparing the business plan of the project and contract documents. Risk classification is their distribution into separate groups according to certain characteristics in order to achieve the set goals. When classifying risks, it should be taken into account that scientific papers provide various schemes for dividing risks based on certain criteria.
Thus, it is advisable to divide the risks depending on possible outcome impact on investment process:
1. Pure risks- the result of their impact is to obtain a negative or zero result. Typically, this group of risks includes natural (earthquake), natural (fire), environmental (emission of harmful gases), political (regime change) and transport (accidents) risks. This also includes part of the commercial risks - property (theft, sabotage), production (stopping equipment due to breakdown) and trade (delayed payments, untimely delivery of goods).
2. Speculative risks- are characterized by obtaining both positive and negative results. These primarily include financial risks that are part of commercial risks.
Another classification criterion is cause of the risk Depending on what risks are divided into the following types:
a) natural-natural;
b) environmental;
c) political;
d) transport;
e) commercial.
Commercial risk is a common risk exposed to the enterprise or industry in the course of its activities. This includes the above-mentioned property, production and trade risks, as well as financial risks.
The latter determine the solvency of the enterprise associated with the financing of its assets, and are divided into several types:
a) risks associated with the purchasing power of the ruble (inflationary, deflationary, currency risks and liquidity risks);
b) risks associated with investing capital (occurrence of indirect financial damage as a result of failure to carry out any actions - insurance, investment, hedging etc.);
c) return risk (includes interest rate and credit risk);
d) risks of direct financial losses (stock exchange risk, bankruptcy risk. Another way to classify risks is to divide them into external ones:
TO external risks relate:
Risks associated with the instability of the economic situation and economic legislation, investment conditions and the use of profits:
External economic risks - the possibility of introducing restrictions on trade, closing borders, etc.;
The uncertainty of the political situation and the possibility of its deterioration:
Changes in natural and climatic conditions, natural disasters;
Fluctuations in market conditions (prices, exchange rates, GDP etc.).
Internal risks include;
Incompleteness or inaccuracy of project documentation;
Production and technical risks - accidents and equipment failures, manufacturing defects, etc.;
Incorrect selection of the project team;
Uncertainty of goals, interests and behavior of project participants;
The risk of changing priorities in the development of the enterprise and loss of support from the management;
Incompleteness or inaccuracy of information about the financial position and business reputation of the project participants;
Incorrect assessment of demand, competitors and prices for the project products. Risks can also be classified according to their degree of predictability.
TO outwardly unpredictable risks include:
Unexpected government regulatory measures in the field of production, environmental protection, design and production standards, pricing and taxation, land use, etc.;
Natural disasters;
Crimes (intentional disruption of work by open refusal to perform it, threats of reprisals, violence, intimidation, etc.);
Unexpected externalities (environmental and social);
Failures in the creation of the necessary infrastructure due to the bankruptcy of contractors, as well as due to errors in the definition of project goals.
Part outwardly predictable risks include:
Market risk (deterioration of the possibility of obtaining raw materials, an increase in its cost, changes in consumer requirements, increased competition and loss of market positions, etc.);
Operational risks (impossibility to maintain the working state of the project elements, violation of security, deviation from the goals of the project);
Negative environmental and social impacts;
Deviation of the inflation rate from the calculated values;
Possible changes in the taxation system. The uncertainty of project implementation conditions is not given.
As the investment project is implemented, its participants receive additional information about the conditions for implementation, and the previously existing uncertainty is “removed”. In this regard, when implementing an investment project, it is necessary to constantly monitor information about the changing conditions for its implementation and make appropriate adjustments to input and output data, work schedules, and the conditions of relationships between project participants.
To take into account risk factors in evaluating the effectiveness of a project, information about the conditions for its implementation is used, including information that does not have any strict mathematical representation.
In this case, two main methods of risk assessment can be used:
Qualitative risk assessment;
Quantitative risk assessment.
Methods for qualitative risk assessment.
The methodology for such an assessment is descriptive, but, in essence, it should lead project managers to a quantitative result, to a cost assessment of risks, their negative consequences and measures to prevent them. A qualitative analysis of project risks is carried out at the stage of developing a business plan.
Qualitative risk assessment methods include:
a) expert method;
b) method of cost-benefit analysis;
c) the method of analogies.
expert method. It is used at the initial stages of working with the project: if the amount of initial information is insufficient for a quantitative assessment of the effectiveness and risks of the investment project (high error in the results of estimates - over 30%).
The expert risk assessment procedure contains the following steps:
Project managers determine the main types of risks that may be encountered in the implementation of an investment project, and set the maximum level for each type of risk (on a thousand-point scale);
Project managers select competent specialists - experts, after which a differentiated assessment of the level is established on a ten-point scale competence experts (information is confidential);
Each expert is asked to evaluate the risks in terms of the probability of a risk event occurring (in fractions of a unit) and the potential danger of this risk for the successful completion of the project (on a hundred-point scale).
The results obtained for each expert (for example, S. A. Ivanov) are entered in Table. nine.
Table 9.
Risk assessment by expert S. A. Ivanov
The assessments made by experts for each type of risk (for example, untimely delivery of equipment) are summarized by project managers in separate tables. to calculate the integral level of risk (Table 10).
Table 10
Determination of the integral level of risk of untimely delivery of equipment
Based on the data in Table. 5.3 the average value of the integral level of risk is calculated. If we assume that in our case the number of experts is N = 3, then ;
For each type of risk, the values are compared R, and predetermined limit levels of risk, on the basis of which a decision is made on the acceptability of a particular type of risk for project developers.
Other methods of using experts to assess the risks of implementing investment projects are also used.
The main thing advantage The method of expert assessments lies in the possibility of using the experience of experts in the process of analyzing the project and taking into account the influence of various factors. The advantages of the method include the absence of the need for accurate data and software products, the ability to conduct a risk assessment before calculating the integral indicators of the effectiveness of an investment project, and the simplicity of calculations.
However, this method is associated with certain shortcomings, the main of which are the difficulties in attracting highly qualified specialists and the subjectivity of the assessments.
A variation of the expert method is the so-called Delphi method. It is characterized by a strict procedure for organizing risk assessment: experts are deprived of the opportunity to jointly discuss the answers to the questions posed, which makes it possible to ensure the anonymity of the assessments, to avoid group decision-making and the dominance of the leader's opinion. The processed and generalized results are communicated to each expert through controlled feedback. The main purpose of this is to allow you to get acquainted with the assessments of other members of the expert commission, without being subjected to pressure from authoritative specialists. This method allows you to increase the level of objectivity of expert assessments.
Cost appropriateness analysis method.
This method is focused on identifying potential risk areas and is used by the investor to minimize the risk that threatens capital.
It is assumed that cost overruns can be caused by one of four main factors (or a combination of them):
Initial underestimation of the cost of the project as a whole or its individual stages and components;
Changing the design boundaries due to unforeseen circumstances;
Deviation of the performance of the equipment used in the project from the design values;
Impact on the cost of the project inflation, changes in tax legislation and interest rates.
These factors can be disaggregated and a detailed checklist of possible itemized cost increases for each project option or project element is drawn up on the basis of a generic list. The process of financing a project is divided into stages, which should be interconnected with the stages of project implementation and take into account additional information about the project that comes as it is being implemented. The phased disbursement of funds allows the investor, at the first sign that the risk of investments is growing, to either stop financing the project, or start looking for measures to reduce costs.
analogy method consists in the analysis of the available data concerning the implementation by the firm of similar projects in the past, in order to calculate the probability of losses. You can also use the data on project risks of completed projects, the analysis of which is carried out, for example, by the World Bank. Insurance companies also have useful information.
The analogy method is most widely used in risk assessment; frequently recurring projects, particularly in construction. If a construction firm is embarking on a project similar to an already completed one, then it is possible to statistically process the available data on completed projects and build risk distribution curves.
When using the analogy method, some caution should be exercised, since the failures of a number of projects may not provide a reliable choice of possible scenarios for the failure of a future project.
The reasons for the discrepancies may be different:
The resulting complications often overlap, as they often appear over a long period;
They are qualitatively different from each other;
The impact effect is manifested as a result of their complex interaction.
Methods for quantitative risk assessment.
Let us consider some methods of such an assessment, which are often used in practice.
Project sensitivity analysis. The methods considered earlier will evaluate the effectiveness of the investment project (NPV, IRR, RVR, RT) are based on the use of cash flows, which in themselves are estimates and represent the forecast of project managers. It is clear that many variables that determine cash flows are not known for sure and are most likely random values.
If some key variable, for example, production costs, changes, then integral performance indicators also undergo changes. Sensitivity analysis - this is a method that accurately shows how the integral performance indicators will change (NPV or IRR) when one of the input variables changes, if all other variables do not change.
Sensitivity analysis begins with the construction of a base case developed on the basis of the expected values of the input quantities. Let us choose as such an option the example of the implementation of an investment project by the Orion company considered in the previous chapter. For this project, the value was calculated NPV = +1760 thousand roubles.
Then several key input parameters are set that have a significant impact on the value NPV- for example, the volume of revenue, production costs and becoming a discount. After that, each variable is repeatedly changed, decreasing or increasing it in a certain proportion, leaving other factors unchanged. Values are calculated each time NPV, and based on them, a dependency graph is built NPV mutable variable.
Let's analyze the sensitivity of the Orion project, for which, based on the tables of cash flows for the project used in the previous chapter, we calculate the NPV values \u200b\u200bfor various deviations of the three selected variables from the baseline and summarize the data in Table. eleven.
Table 11
Project Sensitivity Analysis
| Deviations from the baseline, % | Net present value (thousand rubles) when changing: | ||
| revenue volumes | variable costs | discount rates | |
| -5 | -796 | +3493 | +2000 |
| -2 | +806 | +2473 | +1856 |
| +1760 | +1760 | +1760 | |
| +2 | +2714 | +1049 | +1668 |
| +5 | +4153 | -21 | +1528 |
Rice. 9. Sensitivity analysis NPV project
a) reflected the impact on NPV the project of changes in revenue, b) - changes in variable costs and in fig. in)— changes in discount rates. Since NPV is a non-linear function, in each of the figures, the actually calculated NPV values deviate slightly from straight lines.
As can be seen from fig. 9., the project under study is most sensitive to changes in the amount of revenue, less sensitive to fluctuations in variable costs and poorly responsive to changes in the discount rate. When analyzing a project with steeper sensitivity curves, it is considered more risky, since even relatively small deviations of the estimated variable from the baseline (for example, revenue) give a large error in the predicted value NPV project. This allows you to understand the essence of the risks of the project.
Scenario analysis. Sensitivity analysis of the project provides an opportunity to imagine how significant the impact of a particular indicator is on NPV project. However, the fact that the project we are considering is most sensitive to changes in revenue does not answer another important question - how likely are such changes in revenue? In other words, the risk of the project should be determined by the interaction of two factors: first, the sensitivity of its NPV to changes in key parameters, and secondly, by the range of probable values of these parameters, which is reflected in their probability distributions.
The scenario analysis method is based on a comparison of these two factors.
Let us turn again to the Orion project and consider three options for the development of the situation:
a) pessimistic - revenue will decrease by 5 %, costs will increase by 5% and the discount rate will also increase by 5%;
b) the most expected - corresponds to the initial data of the project;
c) optimistic - revenue will increase by 5 %, costs will be reduced by 5% and the discount rate will decrease by 5%.
Let us estimate the value NPV project in each of the three options. At the same time, we will assume that, according to the project managers, the probability of a pessimistic option is 30%, an expected one is 50%, and an optimistic one is 20%. We summarize the results in Table. 12.
Table 12 Project risk assessment using scenario analysis
Expected (arithmetic mean) value NPV find by formula
where P t is the probability of each option, N is the number of options.
We find the standard deviation from the expression:
Comparison of values E(NPV) and allows you to assess the risk of the project.
Scenario analysis expands the boundaries of project risk assessment, but this method is limited to considering only a few discrete project outcomes, while in reality there are infinitely many options for changing project parameters.
Simulation Modeling by the Monte Carlo Method. This method combines sensitivity analysis and probability distribution analysis of input variables. It requires the use of special software.
Using the method involves several steps. First, the probability distribution of the initial variables is set, let's say, revenue, costs and discount rates, as in our case. As a rule, continuous distributions are used, completely specified by a small number of parameters, for example, the arithmetic mean and standard deviation, as in the case of a normal distribution, or the upper and lower limits, as well as the most probable value in the case of a triangular distribution, etc. P.
After that, the simulation program randomly selects the value of each initial variable, taking into account its probability distribution, and calculates NPV project for this option. Project managers specify the number of options to be evaluated (for example, 500 times). This will give 500 random values NPV, on the basis of which it is possible to calculate the expected values E (NPV), standard deviation and, as a general rule, estimate the probability of finding the values NPV projects within certain boundaries.
Despite the certain clarity of sensitivity analysis, the method of scenarios, as well as simulation modeling, it should be borne in mind that after the completion of all computational procedures, these methods do not provide clear criteria for making a decision on the project. The analysis ends with the calculation of the expected values E (NPV) project and getting the distribution of random values NPV around the expected value. However, the methods do not provide a mechanism by which it was possible to determine how adequate the return of the project is, the measure of which is E (NPV), investment risk, estimated by the value. In other words, having received quantitative assessments of the risks of the project, the investor must ultimately make his own decision on the advisability of accepting the project.
Decision tree analysis. Risk assessment of an investment project is an integral part of the investment decision-making process. However, despite the importance measurements risk of an investment project, no less foamy for project developers is the task decrease investment risk. To the greatest extent, the need to solve such a problem is manifested when the investment costs of the project do not occur at one moment, but in stages. This allows project managers to evaluate the results obtained at the end of each stage and draw a conclusion about the expediency of further capital expenditures. It is in such cases that a project risk assessment can be carried out using decision tree.
Let us turn again to Orion and assume that the capital costs of the project do not occur in the course of one zero step, but are distributed over the stages as follows.
Stage 1: at the initial time t0 it is planned to spend 300 thousand rubles. to obtain the necessary documents and conduct initial research on the potential of the market and the possible niche of the company in it.
Stage 2: if it is established that the Orion company is able to ensure the sale of the planned products, then six months later, at the time t y , it is planned to carry out capital investments in the amount of 1 million rubles. for the production of prototype products.
Stage 3: if prototypes arouse the interest of consumers, then in another six months the remaining 8,700 thousand rubles will be invested in the project. As before, the subsequent production cycle will contain five half-years, and at the sixth step the project will be liquidated. At the same time, according to managers' estimates, a pessimistic, most probable and optimistic scenario for the further implementation of the project is possible.
Project managers evaluate the probability of possible options at each stage: for example, it is assumed that at the end of the first, estimated stage, there is a probability equal to 0.85 that the company will decide on the organization of a pilot production and a probability of 0.15 of refusing further continuation of the project. Upon completion of the second stage, the probability of deploying the entire project is estimated at 0.7; accordingly, the probability of completing the project at this stage will be 0.3.
Finally, the probabilities of the pessimistic most probable and optimistic options for the implementation of the project are taken by the corresponding data in Table. 11. For ease of assessment, we will assume that when implementing each of the three options, the total cash flows from investment and operating activities are annuities, the net present value of which corresponds to the data in Table. eleven.
All emerging opportunities and options for the implementation of the project can be reflected in the form of a decision tree.
Rice. 10. Decision tree analysis
Expected value NPV= +608
As can be seen from fig. 10, if the Orion company, after preliminary estimates of pilot production, decides to invest 8,700 thousand rubles. in the implementation of the project, then three options for further development of events are possible:
Optimistic, with probability 0.2 and magnitude NPV= + 6953; the resulting cash flows by calculation steps are conditionally taken equal to the equivalent of annual income +1550, NPV which is equal to +6953;
The most probable, with a probability of 0.5 and NPV project = + 1760;
Pessimistic, with a probability of 0.3 and NPV project = -2061. Cumulative probabilities are obtained by multiplying all probabilities on specific branches of the tree and show the final probability of each possible outcome. In the last column of Fig. 5.6 are the values NPV project, multiplied by the final probabilities of the branches of the decision tree. The sum of the data in this column gives the value of the expected JVPV of the project (+ 608 thousand rubles). Since the expected value E (NPV)>0, then we can conclude e acceptability of such a project.
Analysis of the limiting level of stability. Limit indicators characterize the degree of stability of the project in relation to possible changes in the conditions for its implementation. One of the most important indicators of this type is break even, the meaning of which is to determine the minimum (critical) level of output at which the project (a specific project participant) does not yet incur losses, i.e. revenue is equal to the total cost of production. In other words, 1 for the break-even point, it is characteristic that the volume of sales is equal to the volume of production, and the proceeds from the sale of products coincide with the total production costs.
When calculating the break-even point, it is assumed that production costs can be divided into conditionally constant (not changing when the volume of production changes) and conditionally variable, associated with a direct relationship with the volume of production.
The break-even point is determined by the formula:
Where In EP- point of break-even production; FC - fixed costs; P is the price of the product; TC - variable costs.
A project is considered sustainable if BFP< 0,6-0,7 после освоения проект-ных мощностей. Если In EP—>1, it is considered that the project has insufficient resistance to fluctuations in demand at this stage. But a satisfactory In EP does not yet guarantee a positive value NPV the project being evaluated.
Break-even analysis allows you to determine the required volume of sales, providing coverage of costs and obtaining the necessary profit, as well as to assess the dependence of the company's profit on price changes, variable and fixed costs. The break-even analysis method is usually used when introducing new products into production, upgrading production facilities, creating a new enterprise.
The advantages of this method should primarily include ease of use and visibility in planning profits. However, it should be noted that this method has significant limitations.
In particular, it must be assumed that:
1. The volume of production is equal to the volume of sales.
2. Fixed costs are the same for any volume of production.
3. Variable costs change in proportion to the volume of production.
4. The price does not change during the period for which the break-even point is determined.
5. The price of a unit of production and the cost of a unit of resources remain constant.
6. In the case of calculating the break-even point for several types of products, the ratio between the volumes of products produced must remain unchanged.
The calculation of the break-even point becomes more complicated when evaluating a project that results in the release of several types of products: it must be taken into account that they have different prices and variable costs and, therefore, their shares of contributions to cover the total costs differ. In this case, the breakeven point depends on the share of each product in the mixed sales volume.
The method of calculating the break-even point becomes much more complicated if, with a change in production volumes, the value of costs changes non-linearly.
Measures to reduce investment risk. After all the risks in the investment project have been identified and an analysis has been carried out, it is necessary to give recommendations on how to reduce risks by project stages. The main principle of the mechanism for reducing investment risk is the complexity of its impact and economic expediency.
To the main measures on reduction of investment risk in conditions of uncertainty of the economic result include the following:
1. Redistribution of risk between the participants of the investment project.
2. Creation of reserve funds (for each stage of the investment project) to cover unforeseen expenses.
3. Reducing risks in financing an investment project - achieving a positive balance of accumulated money at each calculation step
4. Collateral for invested financial resources.
5. Insurance - the transfer of certain risks to an insurance company.
6. System of guarantees - obtaining guarantees from the state, bank, investment company, etc.
7. Getting more information.
Analysis of emerging investment risks and skillful use of risk mitigation methods allow project participants to achieve their goals.
When implementing any investment project, it is necessary to conduct a comprehensive analysis or risk assessment in order to provide potential partners with the necessary data to make decisions on the advisability of participating in the project and develop anti-risk measures to protect against possible financial losses.
All methods used to analyze project risks can be conditionally divided into qualitative and quantitative.
The main task of a qualitative analysis of investment risks is to identify and identify possible types of risks of the investment project under consideration, as well as to identify and describe the sources and factors that affect this type of risk. In addition, a qualitative analysis involves a description of the possible damage, its cost estimate and measures to reduce or prevent the risk.
Qualitative analysis serves as the basis for quantitative analysis, since before proceeding to an accurate assessment of the risk value, it is necessary to find out what risks the investor will face and what factors affect them, what are the possible consequences of their implementation. Accordingly, without a qualitative analysis it is impossible to conduct a quantitative analysis.
A qualitative analysis of project risks is carried out at the stage of developing a business plan, and a mandatory examination of an investment project allows you to prepare complete information for analyzing its risks.
The main risk factors for investment projects include:
Mistakes in design estimates
Insufficient qualification of specialists
force majeure circumstances
Violation of terms of deliveries, terms of contracts
Poor quality of raw materials
Also, in the course of a qualitative analysis, the boundary values (minimum and maximum) of a possible change in all factors or project variables that are checked for risks are determined.
Among the qualitative methods for assessing investment risk, the following are most often used:
cost-benefit analysis
the analogy method
method of expert assessments
Let's consider the first qualitative method for evaluating an investment project - an analysis of the appropriateness of costs. Based on this method, cost overruns can be associated primarily with the following factors:
Initial underestimation of the cost of the project as a whole or its individual phases and components
change in design boundaries due to unforeseen circumstances
the difference between the performance of machines and mechanisms from the performance provided by the project
increase in the cost of the project compared to the original due to inflation or changes in tax legislation
During the qualitative analysis, all these factors are detailed, as well as a checklist of possible increase in cost items for each project option or its elements.
When using this method, project financing is divided into stages or stages, which allows you to gradually monitor the level of risk, and at the right time, if the risk exceeds an acceptable value, suspend financing, or find ways to reduce the costs of implementing this project.
The next qualitative method for assessing investment risks is the analogy method. The essence of this method is the analysis of all available data related to the implementation of similar projects by the company in the past to calculate the probabilities of losses, as well as the study of all available information on analogous projects. Based on various publications or practical experience of other enterprises, financial managers evaluate the likelihood of certain events, obtaining a specific financial result, and the degree of financial risk.
The disadvantage of this method of assessing investment risks is that it is difficult to choose the right analogue that is as similar as possible to the proposed investment project. Also, the disadvantages include the difficulty in assessing the accuracy with which the level of risk of a similar project can be taken as the risk of the one under consideration.
Thus, it can be concluded that the cost appropriateness method and the analogy method are not designed to accurately assess the risk of an investment project. They are more suitable for describing possible risky situations.
Another qualitative method for assessing investment risks is the method of expert assessments. This method involves the use of the experience of experts in the management of investment projects, that is, a selected group of experts evaluates the project according to the degree of risk. If large discrepancies are found between the opinions of experts, they are discussed by all experts in order to develop a more consistent position. In order to obtain a more objective assessment, the specialists conducting the examination should have a full range of information about the project being assessed.
Expert evaluation methods include a set of logical and mathematical-statistical methods and procedures related to the activities of an expert in processing the information necessary for analysis and decision-making.
The main methods of expert assessments can be considered:
Questionnaires
· SWOT-analysis. The method gives an assessment of the strengths and weaknesses, opportunities and threatening dangers associated with a particular area of activity.
· The Delphi method is a tool that allows taking into account the independent opinion of all members of the expert group on the issue under discussion by consistently combining ideas, conclusions and proposals and reaching an agreement. This method is based on multiple anonymous group interviews.
The main problem that arises when using the method of expert assessments is related to the subjectivity and inaccuracy of the results obtained. This may be due to factors such as:
Poor selection of experts
Possibility of group discussion
Dominance of any opinion (opinion of "authoritative leader")
Let us consider quantitative methods for assessing investment risks. The main task of the quantitative approach is to numerically measure the influence of risk factors on the behavior of the investment project efficiency criteria.
To carry out a quantitative analysis, the main condition is to conduct a full-fledged qualitative analysis of the risks of this investment project.
The main methods used in the quantitative analysis of investment risks are:
· Statistical method. This method is most widely used in the quantitative analysis of investment risks. The statistical method consists in studying the statistics of losses and profits that have taken place in a given or similar enterprise in order to determine the likelihood of an event, to establish the magnitude of the risk.
When assessing investment risks, the average expected values of any indicators that have a significant impact on the implementation of an investment project are calculated. For example, one of these indicators may be the expected profit from the implementation of this project. In order to be able to calculate these average expected values, statistical indicators are most often used:
b Calculate the average expected value using the weighted arithmetic mean:
where x is the average expected value
xi - expected value for each case
ni - number of observation cases (frequency)
But the calculation of the average expected value does not allow making a decision on investing in this project with full accuracy. To do this, you can use indicators such as variance and standard deviation. These indicators allow you to determine the variability of a possible result.
If the investor is faced with such a situation that the degree of expected income in both investment projects is the same, then it would be advisable to choose the project with a smaller standard deviation.
And if a situation arises in which the expected returns will be different, then when choosing the right decision regarding the investment of funds, it will be necessary to focus not on the standard deviation, but on the coefficient of variation, which estimates the amount of risk by the amount of return. Preference is given to those investment projects for which the value of the coefficient is lower, which indicates a better ratio of income and risk.
The main advantage of the statistical method is that this method allows you to evaluate not only the risk of an investment project, but the entire risk of the enterprise as a whole.
The disadvantage of this method is that the statistical method involves the use of a large amount of information over a long period for analysis, which complicates its application.
· Sensitivity analysis. When using this method, risk is considered as the degree of sensitivity of the resulting indicators of project implementation to changes in operating conditions (changes in tax payments, price changes, changes in average variable costs, etc.). As the resulting indicators of the project implementation can be: performance indicators (NPV, IRR, PI, payback period), annual project indicators (net profit, accumulated profit).
The technique of sensitivity analysis is to change the selected parameters within certain limits, provided that the other parameters remain unchanged. The larger the range of parameter variation, in which NPV or the rate of return remains positive, the more stable the project.
Thus, this type of analysis allows you to determine the most critical variables that can most affect the feasibility and effectiveness of an investment project.
When using this method, the value of the resulting indicator, such as, for example, NPV, is first calculated. Then it is calculated how much the resulting indicator will change, deviate when one of the operating conditions changes, taking into account that all other conditions remain unchanged.
For sensitivity analysis, the calculation of the elasticity index is often used, which is quite informative. This indicator is the ratio of the percentage change in the resulting indicator to the change in the value of the parameter by one percent:
where x1 is the base value of the variable parameter,
x2 - changed value of the variable parameter
The higher the value of elasticity for some factor, the more risky the investment project is, since this project is more sensitive to changes in this factor.
After all calculations, a “sensitivity matrix” is built, which allows you to combine all risk factors and rank them in order of importance, and accordingly, this allows you to highlight the most and least risky factors for the project.
The main disadvantage of sensitivity analysis is that the influence of a factor on the resulting indicator occurs in isolation, and in fact in real life all factors are interconnected, and, accordingly, studying the influence of one factor without considering the others will not be very accurate and possible.
· Stability test method. The degree of stability of the project in relation to possible changes in the conditions for its implementation is characterized by indicators of the limiting level. The main indicator of this group is the break-even point - such a level of production and sales of products at which the net present value of the project (NPV) is zero, i.e. the project does not bring any profit or loss. The lower this level is, the more likely that this project will be viable in the face of reduced demand, and the lower the investor's risk.
To confirm the sustainability of the project, it is necessary that the value of the break-even point be less than the values of the nominal volumes of production and sales. The farther from them the value of the break-even point, the more stable the project. The project is usually recognized as sustainable if the break-even point does not exceed 75% of the nominal production volume. The closeness of the break-even point to 100%, as a rule, indicates the insufficient stability of the project to fluctuations in demand for products.
The break-even point is calculated by the formula:
where Зc - fixed costs, the level of which is not directly related to the volume of production
Zv - variable costs, the value of which changes with a change in the volume of production
C - the price of a unit of production.
The disadvantage of this method of investment risk analysis is that even satisfactory values of the break-even point at each step do not guarantee the effectiveness of the project, because when determining the break-even point, the amount of costs usually does not include payments to compensate for investment costs, interest on loans, etc. d. In addition, this method does not make it possible to conduct a comprehensive risk analysis for all interrelated parameters, since each indicator of the limit level characterizes the degree of sustainability, depending only on a specific project parameter.
Scenario method. This method implies the development of various scenarios for the implementation of an investment project, their detailed description in various adverse situations and conditions. For each scenario, it is investigated how the project implementation process will proceed, what will be the income, losses and performance indicators for individual participants, the state and the population.
A project is considered sustainable and effective if, in all situations considered:
b NPV will be > 0
ь the necessary reserve of financial feasibility of the project is provided
This method just allows you to take into account all the changing factors affecting the implementation of the investment project, in interconnection, that is, to conduct a comprehensive analysis. But this method allows us to consider only a few possible outcomes for the project, although in reality the number of possible outcomes is not limited. Also, if it is not possible to determine the probability of a particular scenario, then one has to rely on making a decision to invest only on assumptions, judgments or personal experience, so the problem of the reliability of probabilistic estimates arises.
· Decision tree method. A decision tree is a graphic representation of a sequence of decisions and environment states indicating the corresponding probabilities and payoffs for any combination of alternatives and environment states. This method can be used when decisions that need to be made at the moment are dependent on previous decisions, and, accordingly, leave an imprint on future decisions.
Thus, this method involves a step-by-step branching of the project implementation process with an assessment of risks, costs, damages and benefits.
When evaluating an investment project using a decision tree, this process is usually divided into 5 stages:
v formulation of the problem, i.e. determining the possibilities for collecting information, compiling a list of events that with a certain probability can occur, establishing a temporary order of events and those actions that can be taken
l building a decision tree
e estimation of the probabilities of occurrence of any event
the formation of wins or losses
problem solving
The limitation of the practical use of this method is the initial premise that the project must have a reasonable number of development options so as not to clutter up the analysis of the investment project.
· Monte Carlo method. This method is a combination of sensitivity analysis and scenario analysis based on probability theory. It involves the use of modern information technology due to the complexity and large number of calculations. Thus, the computer generates hundreds of possible combinations of parameters, factors of the project, taking into account their probabilistic distribution. Each combination gives its own NPV value, and in the aggregate, the analyst receives a probability distribution of the possible outcomes of the project.
Simulation modeling, which is used in Monte Carlo estimation, is built according to the following scheme:
l formulates the parameters, factors affecting the cash flows of the project
b a probability distribution is constructed for each parameter, factor
b the computer randomly selects the value of each risk factor based on its probability distribution;
These risk factor values are combined with parameters that are not expected to change (for example, the tax rate or depreciation rate) and a net cash flow value is calculated for each year. Based on net cash flows, the value of net present value (NPV) is calculated;
l the above actions are repeated many times (usually about 500 simulations), which allows you to build a probability distribution of NPV;
The results of the simulation are supplemented by probabilistic and statistical analysis.
The Monte Carlo method is a very effective tool for analyzing investment risks, allowing you to take into account the maximum possible number of environmental factors.
The main advantages of building simulation models are the transparency of all calculations, the ease of perception and evaluation of the results of the project analysis by all participants in the planning process. One of the serious disadvantages of this method is the significant cost of calculations associated with a large amount of output information. It can also be considered a disadvantage that when developing real models, it may be necessary to involve specialists or scientific consultants from outside. This method entails that the study of the model is possible only with the availability of computer technology and special software packages.
Almost all enterprises are connected with investments to some extent. Any investment program is accompanied by numerous risks. The risks of an investment project is a rather complex concept associated with investment activities. Under the risks in investment activities are meant possible deviations from the expected profit and the occurrence of losses that lead to the loss of capital.
Assessment methods and analysis
Management of the development of an investment project should be accompanied by the collection and processing of information about changes in the market and the correction of the project implementation program, this will determine the degree of danger. There are two main risks of investment projects - qualitative and quantitative.
A qualitative assessment always leads to a quantitative result. In this way, researchers can determine the degree of risk, possible negative situations and the amount of costs associated with them. Qualitative analysis is always carried out when creating the initial business plan. A comprehensive examination is also carried out, on the basis of which information is prepared for the analysis of all risks under the investment program. Qualitative analysis can be carried out:
- analogy method;
- expert method;
- method of analyzing the threat to capital.
For recurring investment projects, risk analysis is most often carried out using the analogy method. It is mandatory to pay attention to the opinion of large banks on already implemented projects, and use information on the level of danger of similar projects. All the information received is carefully processed, which makes it possible to identify potential dangers in the implementation of new programs.
The expert method consists in studying the assessments made by experts separately for each type of risk. One of the methods of expert risk assessment of an investment project is the Delphi Method. In this case, the experts cannot share the results of the research and their own opinion among themselves, which makes it possible to obtain the most objective final assessment. The positive qualities of this method include:
- no need to use special software and computer technology;
- precise information is not required;
- all calculations are carried out very simply.
Of course, there are also negative aspects - it is the difficulty to find highly qualified experts and subjective results.
The investment risk analysis method is used by investors to identify the risk of overspending their own funds due to inappropriate costs. This phenomenon can be caused by the following factors:
- Initially, the participants in the investment process underestimated the total cost of the project;
- unforeseen circumstances led to a change in design boundaries;
- the performance indicated in the business plan does not correspond to reality;
- project costs have risen sharply due to inflation or changes in tax legislation.
Each of the above factors can be detailed. Experts can make a detailed list of all the points that contribute to increasing the level of planned funding. Approval of appropriations in this case can be divided into certain stages. It is necessary that all stages be based on additional information that comes in as the project develops, and are associated with all stages of its implementation. 
In this case, investors allocate funds in parts for each of the stages and can take timely measures that will reduce costs or stop financing altogether.
Quantitative risk assessment of an investment project includes:
- analysis of possible scenarios for the development of the enterprise;
- detection of sensitivity;
- imitation of various risk situations;
- determination of the limiting level of stability.
Analysis of possible scenarios for the development of the enterprise is carried out using special software and simulation models. As a rule, the following main scenarios are considered:
- the most optimal (medium);
- the best (optimistic);
- worst (pessimistic).
It is based on identifying possible changes in the efficiency of the enterprise's performance due to fluctuations in any indicator initially specified in the business plan, for example, sales volume. This approach involves the recalculation of all performance indicators of the enterprise, taking into account deviations from the initial data of one variable, for example, the discount rate. 
Determining the marginal degree of project sustainability is based on identifying the so-called break-even point, that is, the moment when the volume of output produced by the enterprise will be at such a level that the profit will be equal to production costs. Thus, it is possible to obtain a break-even indicator, which is very important when:
- equipment upgrades;
- implementation of programs to organize a new type of activity;
- release of new types of products.
After all the investment project has been identified and all analyzes have been carried out, a number of specific measures can be taken that will reduce the level of danger at all stages of the project. Sometimes all participants distribute possible risks among themselves and create reserve funds from which it will be possible to cover unforeseen expenses. You can also contact the insurance company and take out insurance against certain risks.
The uncertainty of the conditions for the implementation of the investment project is not given. As the project progresses, the participants receive additional information about the implementation conditions, and the previously existing uncertainty is “removed”.
With this in mind, the management system for the implementation of an investment project should provide for the collection and processing of information about the changing conditions for its implementation and the appropriate adjustment of the project, schedules for joint actions of participants, and the terms of contracts between them.
To take into account risk factors in evaluating the effectiveness of a project, all available information about the conditions for its implementation is used, including information that is not expressed in the form of any probabilistic distribution laws. In this case, the following two types of methods can be used:
– methods of qualitative risk assessment,
– methods for quantitative risk assessment.
Qualitative assessment methods . The methodology for a qualitative assessment of project risks should lead the analyst-researcher to a quantitative result, to a cost assessment of the identified risks, their negative consequences and “stabilization” measures.
A qualitative analysis of project risks is carried out at the stage of developing a business plan, and a mandatory comprehensive examination of an investment project allows preparing extensive information for analyzing its risks.
Qualitative assessment can be divided into the following methods:
- expert method,
– method of cost appropriateness analysis,
- analogy method.
expert method represents the processing of expert assessments for each type of risk and the determination of the integral level of risk.
Its variety is:
Delphi Method- a method in which experts are deprived of the opportunity to discuss the answers together, take into account the opinion of the leader. This method allows to increase the level of objectivity of expert assessments.
Positive aspects: simplicity of calculations, no need for accurate information and the use of computers. Negative sides: subjectivity of assessments, difficulty in applying highly qualified experts.
Cost Appropriateness Analysis Method is focused on identifying potential risk areas and is used by the person making the investment decision to minimize the risk that threatens capital. It is assumed that cost overruns can be caused by one of four main factors or their combinations:
Initial underestimation of the cost of the project as a whole or its individual phases and components;
Change of design boundaries due to unforeseen circumstances;
Difference in performance (difference in performance from that envisaged by the project);
An increase in the cost of the project compared to the original due to inflation or changes in tax legislation.
These factors can be detailed. Based on the template, a detailed checklist of possible itemized cost increases can be developed for each project option or project element. The appropriation approval process is broken down into stages.
Approval stages should be linked to project phases and based on additional information about the project as it develops. At each stage of approval, having received information about the high risk that is ripe for the required funds, the investor can decide to stop investing.
The phased allocation of funds allows the investor, at the first sign that the risk of investments is growing, either to stop financing the project, or to start looking for measures to reduce costs.
analogy method- this method involves the analysis of analytical projects to identify the potential risk of the project being evaluated. Most applicable in risk assessment of recurring projects. The analogy method is most often used when other methods of risk assessment are unacceptable, and is associated with the use of a risk database of similar projects. An important phenomenon in the analysis of project risks using the analogy method is the evaluation of projects after their completion, practiced by a number of well-known banks, such as the World Bank. The data obtained as a result of such surveys is processed to identify dependencies in completed projects, this allows you to identify potential risks in the implementation of a new investment project.
Quantification methods involve numerical determination of the risk of an investment project. They include:
– determination of the maximum level of project sustainability;
– project sensitivity analysis;
– analysis of project development scenarios;
- Simulation of risks using the Monte Carlo method.
Analysis of the limit level of stability the project involves identifying the level of output, at which the proceeds are equal to the total production costs, i.e. finding a break-even level (“break-even point”).
The indicator of the break-even level of production is used when:
a) introduction of new products into production,
b) the creation of a new enterprise,
c) modernization of the enterprise.
The indicator of break-even production is determined by:
VER- break-even point of production;
FC- fixed costs;
R– product price;
VC- variable costs.
A project is considered sustainable if VER≤ 0.6÷0.7 after the development of design capacities. If VER→ 1, then the project has insufficient resistance to fluctuations in demand at this stage.
Sensitivity analysis project involves determining the change in variable indicators of project effectiveness as a result of fluctuations in the initial data.
With this approach, each project performance indicator is sequentially recalculated (for example, NPV, IRR, PI) when a single variable changes (for example, the discount rate or sales volume).
The project sensitivity indicator is calculated as the ratio of the percentage change in the performance indicator to the change in the value of the variable by one percent.
Scenario analysis project development involves assessing the impact of a simultaneous change in all the main parameters of the project on project performance indicators.
In this type of analysis, special computer programs, software products and simulation models are used.
Three scenarios are usually considered:
a) pessimistic
b) optimistic,
c) the most probable (average).
Simplified Method risk assessment (proposed by the Ministry of Economics of the Russian Federation) is that an adjustment is made to project indicators for risk or an adjustment to the discount rate. Correction factor " P» is selected from the proposed standards.
For example, the adjustment factor is 3-5% when investing in reliable equipment, and this corresponds to a low level of risk. A high level of risk is observed when investing money in the production and promotion of a new product to the market, while the adjustment factor is 13-15%.
Measures to reduce the risk of an investment project. After all the risks in the investment project have been identified and an analysis has been carried out, it is necessary to give recommendations on how to reduce risks by project stages.
The main principle of operation of the mechanism to reduce investment risk is the complexity of the nature of its impact and economic feasibility.
The main measures to reduce investment risk in the face of uncertainty in the economic result include the following:
1. Redistribution of risk between the participants of the investment project.
2. Creation of reserve funds (for each stage of the investment project) to cover unforeseen expenses.
3. Reducing risks in financing an investment project - achieving a positive balance of accumulated money at each calculation step.
4. Collateral for invested financial resources.
5. Insurance - the transfer of certain risks to an insurance company.
6. System of guarantees - obtaining guarantees from the state, bank, investment company, etc.
7. Obtaining additional information.
An obligatory component of evaluating the effectiveness of an investment project is an analysis of project risks, the purpose of which is to provide potential investors with the necessary data to make a decision on the feasibility of participating in the project and determine measures to protect against possible financial losses.
The project planning process should qualitative and quantitative analysis risks. If, based on the results of the assessment, a decision is made to implement the project, then the organization faces the task of managing the identified risks. The statistics accumulated based on the results of the implementation of the investment project makes it possible to more accurately identify risks and work with them in the future. If, at the stage of project risk analysis, a high degree of uncertainty inherent in the project is revealed, then this project can be sent for revision, after which the risks are assessed again. The procedure for managing project risks, as well as collecting and using statistical information in a particular situation, depends on the specifics of the company and the project being implemented.
At the initial stage, analysis of strengths, weaknesses, opportunities and threats (strengths, weaknesses, opportunities and threats analysis, or SWOT analysis). It is a method of gathering information in which the project is studied in terms of each of its strengths, weaknesses, opportunities and threats, which allows to increase the coverage of risks considered within risk management.
The study of the factors of the external and internal environment of the organization ( enterprise environmental factors), affecting the success of the project. Environmental factors are formed by each of the organizations participating in the project. These factors include corporate culture, organizational structure, infrastructure, existing resources, commercial databases, market conditions, and project management software.
Project risk analysis should combine qualitative and quantitative methods.
Holding qualitative risk analysis (perform qualitative risk analysis) – the process of prioritizing risks for further analysis or action by evaluating and comparing them.
When conducting a qualitative analysis, mathematical calculations are not used. At this stage, general scientific (induction, deduction, systematization, generalization (synthesis), abstraction, comparison, etc.) and heuristic methods (inversion method, idealization method, brainstorming, conference of ideas, collective notebook method, control questions method, method of focal objects, method of morphological analysis, etc.).
Consider some methods of qualitative analysis.
Expert judgments - judgments provided on the basis of competence in the application area, area of expertise, field of activity, industry, etc., relevant to the operation being performed. An expert opinion can be given by both groups and individuals with special education, knowledge, skills, experience or training.
Brainstorm (brainstorming) is a general method of gathering information, ideas and suggesting solutions that can be used to identify risks, ideas or problem solving by a group of team members or experts.
Delphi technique - a method of gathering information used to reach expert consensus on a matter. In this method, experts participate on condition of anonymity. The organizer, using a questionnaire, asks for opinions on important points of the project related to this issue. The answers are summarized and returned to the experts for comments. Consensus can be reached in several cycles of this process. The Delphi method helps to overcome data bias and eliminates the excessive influence of individuals on the outcome of the discussion.
Qualitative methods are usually used at the initial and final stages of the analysis. Qualitative methods at the initial stages of quantitative research are used to form the purpose and objectives of the study, to verbally describe the object, to identify problem areas of the organization. At the final stage of economic analysis, qualitative methods make it possible to generalize, systematize the accumulated analytical information, analyze it at a qualitative level, make comparisons, form research conclusions, and give recommendations that will be the basis for making managerial decisions.
To describe the risks of the project, it is convenient to use specially designed logical maps - a list of questions that help identify existing risks.
Based on the results of a qualitative risk analysis, a description is given of the uncertainties inherent in the investment project, the reasons that cause them, and a list of risks to which this project is exposed is formed.
After the list of risks inherent in the project is formed, it is necessary to rank them according to the probability of a risk event and the magnitude of possible losses, for which a matrix of probabilities and consequences is compiled.
Probability and impact matrix– the generally accepted approach for classifying a risk as high, medium or low by comparing two parameters of risk: the likelihood and the impact on the scope of the project if it occurs.
After the risks inherent in the project are identified and ranked in terms of significance, a quantitative assessment of the main project risks is carried out.
Perform quantitative risk analysis) - the process of numerical analysis of the impact of identified risks on the goals of the project as a whole. The result of a quantitative risk analysis is an assessment of the influence of the most risky factors on the performance indicators of an investment project. Quantitative risk analysis involves the use of statistical analysis and probabilistic concepts, which is in line with modern international standards. However, in some cases, when evaluating small investment projects, one can confine oneself to simpler approaches that are associated with the use of sensitivity analysis and scenario analysis.
As a rule, in investment design, at the first stage, sensitivity and scenario analysis is carried out, and if a large investment project with a large amount of financing is considered, the next stage is risk assessment using probabilistic and statistical methods.
Sensitivity analysis is a quantitative risk analysis and modeling method used to identify risks with the greatest possible impact on a project. Sensitivity analysis allows managers to assess how project performance indicators respond to changes in the variables that are used to calculate it. When conducting a sensitivity analysis, one of the variables selected for analysis is varied while fixing the remaining variables at the level of baseline values. As variable factors, the price and volume of sales of products (works, services), operating costs, initial investments, cost of capital, and the project implementation period are usually chosen. The use of sensitivity analysis allows you to identify the variables that are the most critical in terms of impact on the effectiveness of the project, and at what change in variables the project will become ineffective. The display of sensitivity analysis results can be represented as a tornado chart.
To build this diagram, you need to take several sequential steps:
- 1) select the main parameters in relation to which the sensitivity analysis will be carried out NPV(sales volume, expenses, discount rate, etc.);
- 2) in an expert way to assess in what range these parameters can actually be: what are their maximum and minimum values;
- 3) for the maximum and minimum values of each of the selected parameters, find the corresponding change NPV, assuming all other parameters to be constant, i.e. fixing them at the level of projected values;
- 4) build a vertical chart on which to display these changes NPV for each of the selected options. Factor changes NPV arranged so that the parameters for which the change NPV maximum, were in the upper part of the diagram, and for which the minimum was in the lower part.
The diagram will take on a funnel shape and will indeed resemble a tornado in appearance (Figure 5.1). At the top of the diagram will be those parameters and risk factors that most strongly affect NPV project.
Example
Definition NPV project (base case) is presented in Table. 5.1. The weighted average cost of capital is 14.7%.
table 5.1
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Indicator |
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Investments, thousand rubles |
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Sales volume, thousand units |
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Unit price, rub. |
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Revenue, thousand rubles |
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Variable unit costs products, rub. |
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Variable production costs, thousand rubles |
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Fixed costs (without depreciation), thousand rubles |
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Depreciation |
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Operating profit, thousand rubles |
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Post-tax operating profit, thousand rubles |
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Residual value of equipment, thousand rubles |
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Release of working capital, thousand rubles |
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CF, thousand roubles. |
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dcf, thousand roubles. |
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NPV. thousand roubles |
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The first step is to select the parameters against which the sensitivity analysis will be performed (Table 5.2).
table 5.2
The next step is to evaluate the ranges of variation of the parameters selected for analysis; further, within these ranges, the corresponding increases in the net present value of the project are determined (Table 5.3).
table 5.3
The final step is to build a diagram (Fig. 5.1).
Rice. 5.1. Tornado Diagram
Obviously, the most significant project risk is the operational (cost) risk. In second place is market risk, in third place is the risk associated with the pre-operational period and the volume of capital investments. Closes the list of interest rate risk.
When performing sensitivity analysis, you can also use the classical method. In this case, we consider the base case, which uses the most probable values of each initial variable. The effectiveness of the project implemented in the base case is evaluated (see Table 5.1).
Next, situations are considered in which the values of the input variables deviate from the base case, and it is assessed what impact this will have on the effectiveness of the project. To do this, a key indicator of the project is selected, the sensitivity of which to changes in input parameters will be studied. Usually, the net present value is chosen as such an indicator ( NPV) or internal rate of return (IRR). In this example, the net present value of the project is selected as the key parameter.
Then the factors whose influence on the key performance indicator of the project will be studied are determined. These should be factors about which there is no unambiguous judgment (in the example under consideration, we will choose sales volume, capital costs, variable costs per unit of output, cost of capital as such factors).
In sensitivity analysis, each input variable changes by a few percent up and down from the expected value (assumed in the base case); it is assumed that the other variables remain unchanged. A new key indicator value is calculated, provided that the new values are used. For example, if we want to estimate the sensitivity of the net present value to such an indicator as sales, then the sales value of the base case is taken as 100%. Meaning NPV in this case already defined. We then calculate NPV for variants in which all input parameters, except for the volume of sales, correspond to the base case. We vary the value of the sales volume by changing it, for example, by ±5%, ±10% of the value adopted in the base case.
Finally, a set of key indicator values is plotted to show how sensitive that value is to changes in each of the variables (Figure 5.2).
Addiction NPV from sales volume is presented in table. 5.4.
table 5.4
Addiction NPV from the value of variable costs per unit. products are presented in table. 5.5.
table 5.5
Addiction NPV from the value of capital costs is presented in table. 5.6.
table 5.6
Addiction NPV of the cost of capital is presented in gabl. 5.7.
table 5.7
The results of the analysis performed are shown in Fig. . 5.2.
Rice. 5.2.
The higher the sensitivity of the resulting indicator (in the considered example - NPV) to a change in the factor indicator, the higher the risks associated with the deviation of this variable factor from the predicted value. The sensitivity is determined by the slope of the line on the graph (the greater the slope, the higher the sensitivity). The point of intersection of the line with the abscissa shows by what percentage the variable factor can change before the investment results in a negative value NPV. The constructed schedule allows you to identify high-risk factors that will need to be paid special attention during the implementation of the investment project. Thus, sensitivity analysis can provide useful information about the riskiness of a project.
This graph allows you to draw a conclusion about the most critical factors of the investment project in order to pay special attention to these factors during its implementation.
So, in the considered example, the factor of variable costs turned out to be critical. With an increase in variable costs by 12% NPV project goes to zero. If variable costs increase by more than 12%, the project will become inefficient. Since variable costs proved to be a critical factor, it is advisable to improve the relationship with suppliers by entering into long-term contracts, which may reduce the purchase price of raw materials.
Sensitivity analysis, being a widely used risk assessment technique, has a number of limitations. For example, in a sensitivity analysis, we saw that the net present value of a project is very sensitive to changes in unit variable costs, which indicates that the project is risky. However, if we assume that the company has contracts with suppliers for the supply at a fixed price, then in these conditions the project will be risky, despite its high sensitivity to this variable.
Obviously, sensitivity analysis should be extended to take into account the probability distributions of the original data and be able to change more than one variable at a time to analyze the combined effect of changing several parameters.
This opportunity is provided scenario analysis– a risk analysis technique that, along with the basic set of initial project data, considers a number of other data sets that, in the opinion of the project developers, may take place in the implementation process.
Initially, the base case is considered, in which the most probable values of the input variables are accepted. Further, taking into account the correlation of the input parameters, indicators are selected for the "bad" and for the "good" scenario.
Most often, three scenarios are considered: baseline, best, and worst. In this case, scenario analysis is also called a three-point assessment.
Three-Point Assessment (three point estimate) is an analytical method that uses three estimates of cost or duration, reflecting the optimistic, most likely and pessimistic scenarios. This technique is used to improve the accuracy of cost or duration estimates when the source element of the activity or cost is inaccurate.
Typically, the best and worst scenarios are assigned a probability of 25%, and the base scenario is assigned a probability of 50%. In practice, scenario probabilities may differ from those named, and more than three scenarios may be considered. However, in most cases, they are limited to considering three scenarios, with each of them being assigned the above probability value. For each scenario, performance indicators are calculated, for example NPV. Knowing the meanings NPV for each scenario and the likelihood of the scenarios, you can calculate the expected net present value of the project (mean) using the formula
It is useful to compare the coefficient of variation of the project with the "average" coefficient of the company's projects - this will give an idea of the relative riskiness of the project.
Scenario analysis provides useful information about the offline risk of projects. However, in this case, a limited number of scenarios are considered, usually only three scenarios. If a large investment project is being considered, it is advisable to go beyond sensitivity and scenario analysis in risk assessment, and resort to a more complete method for assessing autonomous risk.
Monte-Carlo method (Monte-Carlo analysias)- a method that repeatedly (iteratively) calculates the cost of a project or project duration using input values arbitrarily taken from possible values of cost or duration, in order to obtain a probability distribution of the total project costs or project completion dates.
Monte Carlo simulation ( Monte-Carlo simulations A process that generates hundreds or thousands of possible outcomes based on probability distributions for cost and time for individual tasks. The results are then used to generate the probability distribution of the project as a whole.
The advantage of the Monte Carlo simulation method is that it makes it possible to create random scenarios, thus providing an additional opportunity in risk assessment.
(5.2)
and coefficient of variation of the project
investment project. This method can only be implemented in a computer environment. A mathematical model is created for determining some effective financial indicator (for example, in the example discussed above, this can be NPV, IRR, WG). For example, the net present value of the project is selected as the performance indicator NPV. Based on the chosen model, in combination with appropriate probabilistic information, testing is carried out. The selected model is subjected to a series of simulation runs.
When using the simulation method, the initial variables, whose values are uncertain and may vary, are assumed to be random variables. The price of products, variable costs, sales volume, etc. can be chosen as such variables. The simulation process should be carried out in such a way as not to violate the existing or expected correlations between the input variables. The computer program starts by selecting the value of each of them randomly from certain probability distributions of the initial variables. For the selected values of variables, the value of the effective indicator is determined (for example, NPV) which must be stored in the computer's memory. The considered process can be repeated several thousand times, i.e. many random scenarios are calculated. Each time one or another combination of values of the initial variables and the corresponding value are obtained NPV investment project. Thus, not one or two values \u200b\u200bwill be obtained NPV, but several thousand, according to the number of runs. The results of simulation runs are combined into a sample and analyzed in order to obtain a probability distribution law NPV. Having determined the probability distribution law, we can find the expected value NPV and spread around this expected value.
The probability distribution law is not always determined. In some cases, they may be limited to the statistical characteristics of the object. Determine the average value NPV according to the obtained sample and variation indicators used for risk assessment. As a measure of risk in investment design, the probability of obtaining a negative value is also used NPV. Simulation runs that resulted in a negative value NPV, can also be combined into a separate sample, from which the average value will be calculated NPV(it will be negative). This value characterizes the expected loss if the project turns out to be ineffective.
The process of risk analysis by simulation can be divided into the following stages:
- 1) a predictive model is built that determines the resulting indicator as a function of variables and parameters. As a basic model for the analysis of investment risk, the indicator calculation model is usually used. NPV;
- 2) the analysis of the selected variables is carried out. Of these, only those are selected whose change significantly affects the result (selection can be made, for example, using sensitivity analysis);
- 3) the probabilistic law of distribution of the selected variables is determined;
- 4) the boundaries of the range of values of variables are set;
- 5) correlations between the selected variables are determined (in fact, the presence of correlation limits the random selection of individual values for correlated variables; two correlated variables are modeled so that when one of them is randomly selected, the other is not chosen freely, but in a range of values that is controlled by the simulated value of the first variable );
- 6) simulation runs are carried out (random scenarios are generated based on a set of assumptions; all the work is done by a computer);
- 7) a statistical analysis of the simulation results is carried out.
Summarizing the above, we note that when using simulation modeling, the result of the project risk analysis is not expressed by any single value NPV, and in the form of a probabilistic distribution of all possible values of this indicator. Thanks to this, the potential investor will be provided with a complete set of data characterizing the risk of the project, and will be able to make an informed decision about participating in the project.
