The efficiency of investments is assessed by a fairly large number of indicators. They are used by specialists -. A few of them are usually enough for investors to make an investment decision. Below is this necessary list.

This indicator gives the investor information about what the absolute amount of money he will receive for the whole.

To calculate it, you need to know the nature of the cash flows that investments will cause, and how they will change over time.

In the chart below, we can see how the total cash flow changes. The first phase of the investment, designated on the graph as "Pre-production period", can be considered a one-time investment if it is made within one year. Or maybe as a process in time from a year or more. In this case, the calculation of the net present value of investments should take into account the changing value of investments in the investment project, that is, it should be calculated discounted at the discount rate r, which is determined based on the criteria chosen by the investor. The main criteria for choosing a discount rate can be named:

• the cost of capital of the invested object;
• the lending rate of banks in the financial environment;
• average industry return on capital for the invested object;
• profitability of financial instruments on the stock market;
• internal rate of return.

Cash inflows to the invested object in the form of cash receipts NV are calculated as follows:

• CIt - investments for the entire life cycle of the project;
• CFt - cash receipts for the entire life cycle of the project;
• n is the life cycle of the investment.

Here is the cash flow for the entire investment cycle does not include cash flows from operating activities and financing activities They are taken into account in the implementation of the investment process.

To calculate the net present value, the cash flows are discounted at the rate r.

The calculation of the net present value of the project at the preliminary stage of investment is carried out according to the formula:

• ICt - in the period from i = 0 to T;
• CFt is the cash flow from investments in the t-year;
• n is the duration of the investment life cycle;
• r is the discount rate.

If investments are made at the same time, then the formula takes the form:

where ICo is the initial investment.

To simplify calculations of NPV, the quotient of division

are called the discount factor and, their values, for different r, are brought together in special tables, where you can easily determine the necessary factor for the given conditions. These tabulated values ​​are easy to find on the internet.

Indicator at the preliminary stage of investment:

• serves as a criterion for the expediency of investing in a given investment object,
• an estimated indicator when choosing options;
• an absolute indicator of the future return on investment.

At the same time, the indicator, if it is equal to 0, shows the marginal level of profitability at the lower boundary, reflected by the selected discount rate r. If, they do not pay off, but if, the investment will bring the investor an increase in his capital. It is obvious that the choice of the discount rate affects the final result when deciding on investments.

The higher the efficiency of the active capital in which investments are directed, the lower the capital gain will be, other things being equal. In other words, it is advisable to make highly efficient investment projects in highly efficient production.

For example:

• 1 investment object with a capital cost of 25%;
• 2 investment object at the level of 15%;
• The investment life is 3 years;
• The size of the initial investment is 60 million rubles;
• The industry average profitability of enterprises in this industry is 14%.

Investment income receipts:

1. For 1 object:
2. For 2 object: 1 year - 27 million rubles; 2 years - 33 million rubles; 3 year 35 million rubles.

For 1 object, the discount rate of 14% is unacceptable, since the investment project will reduce the cost of its capital, so it can be at least 25%. Let's calculate NPV at this discount rate: NPV = -60 + 27 / 1.25 + 33 / 1.5625 + 35 / 1.953 = -60 + 21.6 + 21.12 + 18.14 = 0.86.

For object 2: NPV = -60 + 27 / 1.15 + 33 / 1.322 + 35 / 1.52 = -60 + 23.47 + 24.96 + 23.02 = 11.45.

The example shows that the same project for enterprises with different discount rates can be low-profit and profitable. To eliminate the ambiguity of such assessments, the relative indicators of the effectiveness of investment projects come to the rescue.

Discounted profitability index of an investment project

The discounted profitability index is the ratio of all investment income discounted at the rate of raising capital in investments during the life cycle of the project to the size of all investments, also discounted in terms of the time of these investments. The profitability index is designated as DPI (Discounted Profitability Index) and the formula for its calculation looks like this:

It is also obvious that the discounted investment return index should be greater than 0.

Return on investment index

For small investment properties with implementation periods of about a year or more, a simplified formula for the return on investment index is used, which looks like this:

where ICo is the initial investment.

So for the previous example, we get:

For 1 object = 60.86 / 60 = 1.014.

For 2 objects = 71.45 / 60 = 1.19.

In this case, the profitability index confirms that object 2 is more profitable than object 1. The investor will prefer object 2, although the cost of capital of the investment object for 1 object is significantly higher and financial stability is also higher.

Internal rate of return of an investment project

The internal rate of return is widely used in evaluating investment projects and in their analysis; it is designated IRR (Internal rate of return). The mathematical expression for the internal rate of return looks like this:

IRR = r, with NPV = 0, or in more detail:

• CFt - cash flow from investments in the t -th year;
• ICt - investment flow in year t;
• n is the lifetime of the project.

That is, if income and investment are equal, the resulting rate is the lower bound of the rate of return at which investment is not advisable. If the obtained IRR is lower than the weighted average return on capital of the invested object, the project must be abandoned.

In addition, the resulting internal rate of return can serve as the rate of discounting of cash flows when calculating indicators for evaluating investment projects.

When comparing several investment options, IRR serves as a criterion for selecting the most efficient option. IRR is expressed as a percentage, therefore, as a relative indicator, it is used to compare even projects of different sizes and with different life cycles.

The indicator is calculated by the method of successive approximation. NPV (r) is non-linear because the denominator in the above equation has a power function. Therefore, r, close to the indicator NPV = 0, are determined, and in this range r is selected, at which the equation NPV = 0 is fulfilled.

The graph below shows what it looks like:

Find the value NPV≥0 on the graph and the value NPV≤0 on the graph.

This calculation shows for option 1 25.88%, which means that the project must provide such an average rate of return for the entire life of the project and since IRR> r, which we have taken equal to 25%, the project is being implemented.

For option 2, 18%, the weighted average cost of capital is 14%, and the industry average profitability of enterprises in the industry is 15%. and can be offered to the investor for implementation.

The modified internal rate of return is necessary when calculating the efficiency of investment projects, in which the profit from it is reinvested annually at the rate of the total capital value of the invested object. In this case, the formula takes the form:

where:

• MIRR - modified internal rate of return;
• d is the weighted average cost of capital;
• r is the discount rate for cash inflows;
• CFt - cash inflows in the t-th year of the project's life;
• ICt - investment cash flows in the t-th year of the project's life;
• n is the life cycle of the project.

Both indicators have a common disadvantage: cash inflows from investment activities must be relevant, i.e. incremental throughout the process. In the event of flows of different signs, the calculation of indicators will not reflect the real picture.

Indicators for evaluating investment projects include several simple and visual indicators that are widely used by investors, and the most common among them is the payback period.

Payback period of initial investment

This indicator tells the investor about the period of return of the initial investment.

The general formula for calculating the payback period is as follows:

Where:

• PP is the payback period of the investment;
• Io - initial investment in the project;
• t is the period for calculating the payback period.

If it is possible to determine the average annual or average monthly income from invested funds, then: where CFcr is the average annual return on investment.

This indicator is simple and clear, but does not take into account the factor of the change in the value of money over time.

If this factor is included in the calculation of the payback indicator, then it will be called the payback period of the initial investment, calculated taking into account discounted cash flows (DPP):

• CFt - cash flow from investments in the t-th year;
• r is the rate of discounting of cash receipts.

From a comparison of these formulas, it is obvious that DPP> PP is always.

There is another drawback of these indicators: outside the payback period, cash flows can change at different rates and, with the same payback periods, the amount of accumulated cash flow may be different.

In other words, one cannot be guided by this indicator in the case of comparing investment options; a mandatory absolute assessment of the accumulated cash flow over the life cycle of the project is required.

If you look closely at the formula for calculating the investment ratio, it is easy to see that it is, by definition, the reciprocal of the payback period:

If is the residual (liquidation) value of investments in the project, determined by the sale of property and equipment after its completion.

CFcr is the average annual cash flow from the project over the life of the project. This is especially evident when If = 0, then there is no need to take it into account in the formula, and it takes the form:

РР - the payback period of the project.

All these indicators characterize investments from an economic point of view. The investor is also interested in indicators characterizing the degree of risk of an investment project. These indicators include probabilistic assessments of the achievement of the parameters laid down in the investment project. Risk indicators are characterized by the mathematical expectation of risk events in a given range. Risk events are determined by analyzing the characteristics of the invested object, such as the profitability of its capital, the financial stability of the invested object, the turnover of its assets and the liquidity of capital. Cost-effectiveness metrics, coupled with risk metrics, form project metrics. On their basis, the investor decides on the advisability of investing in a particular project.

In calculating the effectiveness of investment projects, it is recommended to take into account uncertainty , i.e. incompleteness and inaccuracy of information on the conditions for the implementation of the project, and risk, those. the occurrence of such conditions that will lead to negative consequences for all or individual project participants.

A project is considered sustainable if, under all scenarios, it proves to be efficient and financially feasible.

In order to assess the sustainability and effectiveness of a project in conditions of uncertainty, it is recommended to use the following methods (each next method is more accurate, albeit more laborious, and therefore the use of each of them makes it unnecessary to apply the previous ones):

1) aggregate sustainability assessment;

2) calculation of break-even levels;

3) method of variation of parameters;

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

All methods, except for the first one, provide for the development of project implementation scenarios.

Aggregated assessment of the sustainability of the investment project as a whole

A project is generally considered sustainable if it has a positive expected net present value if the following conditions are met:

Use of moderately pessimistic forecasts of the technical and economic parameters of the project, prices, tax rates, etc .;

Providing reserves of funds for unforeseen expenses;

Increase in the discount rate by the amount of the risk adjustment;

Aggregated assessment of the sustainability of the project from the point of view of its participants

In an aggregate sustainability assessment, a project is considered sustainable if:

The value of the internal rate of return (IRR) is 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 exceeding IRR are not expected;

The discounted investment profitability index exceeds 1.2;

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

Break-even level UB m at step m is the ratio of the sales volume corresponding to the "break-even point" (Vcr m) to the project (V m) at this step. The "break-even point" refers to the volume of sales at which the net profit becomes zero.

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

Parameter variation method. Limit values ​​of parameters

The output of the project can change significantly if some parameters change unfavorably.

Investment costs;

Production volume;

Production and distribution costs;

Interest on a loan;

Inflation indices;

Delays in payments;

The duration of the billing period;

Other parameters.

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

TTS is positive;

The necessary reserve of financial feasibility of the project is provided.

Resilience can also be assessed by determining limit values ​​of project parameters.

It is recommended to calculate the limiting integral levels of these parameters, i.e. such coefficients (constant for all calculation steps) to the values ​​of these parameters, when applied, the net present value of the project (or participant) becomes zero.

If there is more detailed information about 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 for each of the scenarios, when assessing the effectiveness of the project, a more accurate method can be used. taking into account the quantitative characteristics of the uncertainty. It allows you to directly calculate the generalizing indicator of the project's effectiveness - the expected integral effect (expected net present value).

Estimation of the expected project efficiency, taking into account the uncertainty, is carried out in the presence of detailed information about various scenarios of the project implementation, the probabilities of their implementation and the values ​​of the main technical and economic indicators of the project for each of the scenarios.

Previous

The stability of an investment project under possible changes in the conditions of implementation can be assessed based on the results of calculations of commercial efficiency for the baseline scenario of its implementation by analyzing cash flows. Included cash flows are calculated for all types of activities, taking into account the terms of the provision and repayment of loans. For an integrated assessment of the sustainability of a project, indicators of the internal rate of return and the index of profitability of discounted costs are often used.

A project is considered sustainable if the IRR is large enough (at least 25-30%), with a discount rate of no more than 15%, no loans are expected at real rates (exceeding IRR), and the discounted cost profitability index exceeds 1.2. The condition for the stability of the project: at each step of the billing period, the sum of the accumulated balance of cash flow from all types of activities (accumulated effect) and financial reserves must be a positive number. It is advisable that it be at least 5% of the sum of net operating costs and investment costs at a particular calculation step. The degree of project stability to possible fluctuations in the implementation conditions can be assessed using indicators of break-even boundaries and limit values ​​of such project parameters as production volume, price of manufactured products, etc. Such indicators are used only to characterize the impact of a possible change in project indicators on its efficiency and financial feasibility. The break-even boundary of the project parameter for a certain calculation step is set using the coefficient to the value of this parameter at this step, when using which the net profit in the project (at this step) is equal to zero. The break-even level (break-even critical point) is determined for the project as a whole.

Estimation of the expected effect of the project, taking into account the quantitative parameters of uncertainty, is carried out in the presence of more detailed information about various scenarios of its implementation. In this case, the probabilities of the scenarios and the values ​​of key indicators for each of the scenarios should be known. In such conditions, it is possible to calculate a generalizing indicator of the project's effectiveness - the expected integral effect (expected discounted income, NPV). Such an assessment can be made both with and without taking into account the project financing scheme. The purpose of the project financing scheme is to assess the possible parameters of the project's financial support. It is designed to ensure the financial feasibility of the project and the effectiveness (positive NPV) of participation in it.

For the chosen scenario, for each step of the calculation period, real inflows and outflows of funds and generalized performance indicators are determined. According to the scenarios characterizing emergency situations, the additional costs arising from this are taken into account. When calculating NPV for each scenario, the discount rate is assumed to be risk-free. The initial information about the uncertainty factors is again presented in the form of the probabilities of individual scenarios or intervals of variation of these probabilities. Thus, an approximate list of admissible (arising from the available information) probability distributions of project performance indicators is established.

Violation of the conditions for the feasibility of the project is considered as a necessary prerequisite for the termination of the project. In this case, the losses and incomes of the project participants associated with the termination of its implementation are taken into account. The risk of unrealizability of a project is expressed through the total probability of scenarios in which the conditions of its financial feasibility are violated.

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Monte Carlo simulation

This method combines sensitivity analysis and probability distribution analysis of the input variables. It requires the use of special software.

The use of the method involves several stages. First, we set the probability distribution of the initial variables, put the revenue, cost and discount rate, as in our case. As a rule, continuous distributions are used, completely defined 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.

After that, the simulator randomly selects the value of each initial variable, taking into account the distribution of its probabilities, and calculates NPV project for this option. Project managers set the number of options to be evaluated (for example, 500 times). This will give 500 random values. NPV, on the basis of which the expected values ​​can be calculated E(NPV), standard deviation σNPV and, as a general rule, estimate the probability of finding the values NPV project within certain boundaries.

Despite a certain clarity of sensitivity analysis, the scenario method, as well as simulation, 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) of the project and obtaining 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 on the project is, the measure of which is E(NPV), investment risk, estimated by the value σ ΝΡV. In other words, having received quantitative assessments of the project's risks, the investor must ultimately independently decide on the feasibility of implementing the project.

Analysis of the limiting level of stability

Indicators of the maximum level characterize the degree of stability of the project in relation to possible changes in the conditions of 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 the volume of products at which the project (a specific project participant) still does not incur losses, i.e. revenue is equal to total production costs. In other words, it is typical for the break-even point that the volume of sales is equal to the volume of production, and the proceeds from the sale of products coincide with the total costs of production.

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, directly related to the volume of production. The break-even point is determined by the formula

where V EP - breakeven point; AFC- average fixed costs per unit of production; R- product price; AVC - average variable costs per unit of output.

The project is considered sustainable if V EP< 0,7 после освоения проектных мощностей. Если VЕР → 1, then it is considered that the project has insufficient resistance to fluctuations in demand at this stage.

If you investigate addiction V EP from values AFC and AVC, then you can see that as the share of average fixed costs increases AFC in the price of products the value V EP rises at a damping rate. This means that with an increase in fixed costs (rent, utility bills, salaries of top managers, etc.), the sustainability of the project decreases.

But a satisfactory value V EP does not yet guarantee a positive value NPV of the project being assessed.

The break-even analysis allows you to determine the required sales volume that provides coverage of costs and obtaining the required 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, modernizing production facilities, creating a new enterprise.

The advantages of this method include, first of all, ease of use and clarity in planning profit. However, it should be borne in mind that this method has significant limitations. In particular, it must be assumed that:

• the volume of production is equal to the volume of sales;
• fixed costs are the same for any production volume;
• variable costs change in proportion to the volume of production;
• the price does not change during the period for which the break-even point is determined;
• unit price and resource unit cost remain constant;
• in the case of calculating a break-even point for several product names, the ratio between the volumes of products produced should remain unchanged.

The calculation of the break-even point is complicated when evaluating a project that results in the release of several types of products: it must be borne in mind that they have different prices and variable costs and, therefore, their shares of contributions to cover the total costs differ. In this case, the break-even point depends on the share of each product in the blended sales volume.

The method for calculating the break-even point becomes much more complicated if, with a change in the volume of production, the value of costs changes nonlinearly.

Measures to reduce the risk of an investment project

After all the risks in the investment project have been identified and their analysis has been carried out, it is necessary to give recommendations on how to reduce risks by stages of the project. The main principle of the mechanism for reducing investment risk is the complexity of its impact and economic feasibility. The main measures to reduce investment risk in conditions of uncertainty in economic results 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 step of the calculation.
• 4. Collateral for the invested funds.
• 5. Insurance - 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.

Analysis of emerging investment risks and skillful use of risk mitigation methods allow project participants to achieve their goals.

Consider, for example, one of the most complex methods that is used to assess the sustainability of an investment project (the method of variation of parameters with the establishment of limit values).

Due to changes that may occur during the implementation of the project, its output indicators may change significantly, i.e. deviate from the design parameters. It is recommended to check the feasibility and evaluate the effectiveness of the project depending on changes in the following parameters:

- investment costs (both in general and by individual components);

- production volume;

- production and marketing costs;

- interest on loans;

- fluctuations in foreign currency;

- inflation index, price index;

- delay in payments;

- the duration of the billing period;

- other parameters provided by the project.

In the case when there is no information about possible changes in the parameters, it is recommended to carry out variant calculations of the scenarios of the feasibility and effectiveness of the project, which are presented in Figure 2.1.

Figure 2.1 - Basic scenarios of the feasibility of the investment project of the project

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

The project is considered resistant to possible changes in parameters in two cases:

- net present value is positive;

- the necessary reserve of financial feasibility of the project is provided.

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

Let's consider the calculation using an example. Suppose the volume of production is equal to the volume of sales, costs are divided into conditionally fixed and conditionally variable, and only material costs are variable. To determine investment sustainability, revenue, conditionally variable costs and taxes proportional to revenue are multiplied at each step by a common factor l, everything else (investment and conditionally fixed production costs, taxes not related to revenue) remains unchanged, after which the multiplier l is selected so that the net present value becomes zero or, equivalently, the internal rate of return becomes equal to the discount rate (10%). The factor λ chosen in this way is the investment stability. The calculation shows that in this example the investment stability is 0.965. The calculation results are illustrated in Table 2.1.

Table 2.1 - Results of calculating the sustainability of an investment project

Index	Step number (m)
Operating activities Proceeds excluding VAT from the project		75,00	125,00	125,00	100,00	175,00	175,00	150,00
limit value		72,36	120,60	120,60	96,48	168,85	168,85	144,72
Production costs excluding VAT for the project		-45,00	-55,00	-55,00	-55,00	-60,00	-60,00	-60,00
limit value		-43,76	-53,44	-53,44	-53,44	-58,43	-58,43	-58,43
Material costs excluding VAT for the project		-35,00	-40,00	-40,00	-40,00	-45,00	-45,00	-45,00
limit value		-33,77	-38,77	-38,77	-38,77	-43,45	-43,45	-43,45
Wage		-7,22	-10,83	-10,83	-10,83	-10,83	-10,83	-10,83

Continuation of table 2.1

Index	Step number (m)
Social contributions		-2,78	-4,17	-4,17	-4,17	-4,17	-4,17	-4,17
Calculations of the Amount of Depreciation		15,00	25,50	25,50	25,50	34,50	34,50	34,50
Gross profit for the project		15,00	44,50	44,50	19,50	80,50	50,50	55,50
limit value		13,90	41,51	41,51	17,39	75,94	75,94	51,81
Property taxes		-1,85	-2,85	-2,34	-1,83	-2,43	-1,74	-1,05
for the road fund		-3,00	-5,00	-5,00	-4,00	-7,00	-7,00	-6,00
limit value		-2,89	-4,83	-4,83	-3,67	-6,89	-6,89	-5,67
Taxable income for the project		10,15	36,68	37,17	13,68	71,08	71,77	48,90
limit value		8,56	34,67	35,87	11,23	69,78	69,97	46,78
Balance of the operating flow for the project		21,60	49,33	49,66	34,39	80,70	81,15	66,00
limit value		20,56	47,32	47,32	32,97	78,32	79,43	64,78
Investment activity Balance	-100	-70			-60
Balance of the total flow for the project	-100	-48,40	49,33	49,66	-25,61	80,70	81,15	66,00	-80
limit value	-100	-49,56	47,56	47,56	-26,89	77,88	78,33	63,73	-80
GNI for the project	11,92%
limit value	10%

The calculation of this example leads to a very small value of the stability margin in terms of revenue of 3.5%.