Methods for assessing the effectiveness of investment projects. Vasilenok K.V. Commercial efficiency of an investment project Methodology for calculating the commercial efficiency of an investment project

The innovation process is accompanied by an investment process, since investments- monetary costs of enterprises, the results of which are manifested over a long period of time or over a long period. Therefore, the effectiveness of innovation is assessed on the basis of generally accepted market economy approach to assessing the effectiveness of investment projects.

Efficiency mark investment project can be carried out taking into account the socio-economic consequences of its implementation for society as a whole and taking into account the financial consequences only for the entity (operator) implementing the project, on the assumption that it makes all the necessary costs and receives all its results. In the first case, public (socio-economic) is determined, and in the second - commercial viability investment project.

The main principles for assessing the effectiveness of an investment project are:

Review of the project throughout its life cycle;

Modeling the cash flow associated with the implementation of the project:

Taking into account the time factor.

Most often, the estimated period (life cycle) of an investment project is justified:

Depletion of hydrocarbon reserves;

Depreciation of the main (defining) part of fixed assets;

The cessation of market needs for manufactured products.

Monetary flow represents a dependence on time cash receipts and payments upon implementation of the project generating it during the billing period. To form it, a certain time interval is selected (month, quarter, year), for which the balance (difference) of expected inflows and outflows is determined Money, which can be either negative or positive. When assessing investment projects in oil and gas industry due to their large life cycles this interval is usually chosen to be equal to a year. Therefore, cash flow represents a sequence (within an accounting period) of annual balances of cash inflows and outflows.

Cash flow is the initial basis for calculating all performance indicators of an investment project. It usually consists of streams from individual species activities:

Cash flow from investment activities;

Cash flow from operating activities;

Cash flow from financial activities. Cash flow from investing activities mainly

characterized by cash outflows, which include pre-project costs, capital investments, costs of increasing working capital, liquidation costs that can be transformed when modeling cash flow and funds invested in creating a liquidation fund.

Cash flow from operating activities is formed by revenue from sales of manufactured products, production costs and the totality of taxes paid.

Financial activities include transactions with funds external to the investment project being evaluated, i.e. coming for its implementation not at the expense of the project. Cash flow from financial activities is formed by investments equity and raised funds, costs for repayment and servicing of loans and issued debt securities, for the payment of dividends on shares of the enterprise. Cash flows from financial activities are taken into account when it is necessary to assess the effectiveness of the investment project for each of the participants in its implementation.

When modeling cash flow, current and forecast prices can be used. Current (permanent) prices that do not take into account inflation are called. Forecast are the prices expected in the future, taking into account projected inflation. Cash flows expressed in forecast prices must be deflated by dividing by the expected overall underlying inflation index to eliminate the impact of inflation on performance measures.

When assessing the effectiveness of an investment project, along with the concept of cash flow, the concept is used accumulated cash flow. The accumulated cash flow is determined (at each interval of the billing period) as the algebraic sum of the balances of all previous intervals.

Taking into account the time factor (achieving comparability of funds at different times) is carried out using the operation of discounting monetary values.

Discounting a cash flow is the reduction of its interval (annual) cash balance values to their value at a certain point in time, which is called the moment of reduction. The beginning of the first year of the calculation period is most often chosen as the reduction point (when evaluating oil and gas projects).

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

The discount rate used in assessing commercial efficiency reflects the annual interest received on invested capital, below which a potential investor (investors) considers financing an investment project unacceptable. Each business entity individually assesses the required rate of return on invested capital, taking into account the possibilities of alternative use of capital, its financial condition and the risks associated with the implementation of the project.

Discounting the cash flow balance corresponding to year t is carried out by multiplying its value by the discount factor (a), calculated by the formula:

where E n is the discount rate; t- this year billing period.

The main indicators when assessing the commercial effectiveness of an investment project are:

Net present value;

Internal rate of return;

Need for additional funding;

Profitability indices;

Payback period.

The most important indicator of the effectiveness of an investment project is net present value (NPV, NPV). It corresponds to the value of the accumulated discounted cash flow and is defined as the algebraic sum of discounted values of annual balances for the calculation period.

In oil and gas field development projects, the NPV is calculated using the following formula:

where V. is revenue from sales of products in year i;

T - calculation period of assessment;

K - capital investments in field development in year i;

E - operating costs (production) in year i Les depreciation deductions and taxes included in the cost of extracted products;

N. - tax payments in year i;

A. - depreciation deductions in year i.

Net present value is the amount of income reduced to the initial moment of the project, which is expected after reimbursing the invested capital and receiving an annual percentage equal to the discount rate chosen by the investor.

If the NPV value is positive, investment project i is considered profitable, which indicates the feasibility of financing and implementing the project.

When choosing the most effective project option (among alternatives), preference is given to the option characterized by the highest NPV value.

To others important indicator the effectiveness of an investment project is internal rate of return (profitability) (VND, VNR). The value of this indicator corresponds annual interest, which is expected to be received for the capital invested in the project. In the most common cases (cash flow is characterized by one investment cycle), this is the value of the variable discount rate at which the net present value goes to zero. IRR is determined based on solving the following equation:

To solve such an equation, iterative methods are used.

With a number of assumptions, it is assumed that the value of the IRR corresponds to the annual interest rate of the loan for the full financing of the investment project, at which the enterprise - the borrower and is able to pay the lender, but its profit is equal to zero.

To assess the effectiveness of an investment project, IRR is compared with the discount rate. If the IRR value is greater than the discount rate, the NPV is positive and the investment project is effective. If the value of IRR is less than the discount rate, the NPV is negative, and the investment project is ineffective,

Payback period call the duration of the period from the initial moment of project implementation to the moment of payback. The payback point is the earliest point in time in the calculation period, after which the accumulated discounted cash flow becomes positive and subsequently remains non-negative (payback period taking into account discounting).

The payback period (T*) can be determined from the following equality:

Need for additional funding- maximum value the absolute value of the negative accumulated discounted cash flow balance of the investment project. This value shows the minimum discounted amount of project financing required for its financial feasibility. This indicator is sometimes called capital-1Ш risk.

Return Indices (PI) characterize the “return of the project” on the money invested in it. Return is measured by quantity monetary units received for each invested monetary unit for the billing period of the project with discounting accounting.

Discounted cost profitability index- the ratio of the sum of discounted cash inflows to the sum of discounted cash outflows.

The discounted cost return index (R) is calculated using the following formula:

Where E.- operating costs in year i, taking into account depreciation and taxes included in the cost of production;

H*i - taxes in year i, not included in the cost of extracted products.

Investment projects can be assessed according to many criteria - in terms of their social significance, the scale of their impact on the environment, the degree of involvement of labor resources, etc. However, efficiency is central to these assessments.

Under efficiency in general case understand the correspondence of the results obtained from the project - both economic (in particular profit) and non-economic (relief of social tension in the region) - and the costs of the project.

The effectiveness of an investment project is a category that reflects the compliance of the project generating this IP with the goals and interests of the project participants, which are understood as subjects of investment activity (discussed above) and society as a whole. Therefore, the term “effectiveness of an investment project” is understood as the effectiveness of the project. The same applies to performance indicators.

Among the basic principles and approaches that have developed in world practice to assessing the effectiveness of investment projects, adapted for the conditions of transition to a market economy, the following can be distinguished:

modeling of flows of products, resources and funds;
taking into account the results of market analysis, the financial condition of the enterprise applying for the implementation of the project, the degree of trust in the project managers, the impact of the project on the environment, etc.;
determining the effect by comparing upcoming results and costs with a focus on achieving the required rate of return on capital and other criteria;
bringing forthcoming expenses and income at different times to the conditions of their commensurability in terms of economic value in the initial period;
taking into account the impact of inflation, delays in payments and other factors on the value of the funds used;
taking into account the uncertainty and risks associated with the implementation of the project.

It is proposed to evaluate the following types of effectiveness:

1) the effectiveness of the project as a whole;

2) effectiveness of participation in the project.

The effectiveness of the project as a whole. It is assessed in order to determine the potential attractiveness of the project and the feasibility of its adoption for possible participants. It shows the objective acceptability of the IP, regardless of financial opportunities its participants. This efficiency, in turn, includes:

Public (socio-economic) effectiveness of the project;

Commercial effectiveness of the project.

Social efficiency takes into account the socio-economic consequences of the implementation of an investment project for society as a whole, including both the direct costs of the project and the results of the project, as well as “external effects” - social, environmental and other effects.

Commercial viability investment project shows financial consequences its implementation for the individual entrepreneur, assuming that he independently makes all the necessary costs for the project and benefits from all its results. In other words, when assessing commercial efficiency, one should abstract from the capabilities of project participants to finance IP costs, conditionally assuming that the necessary funds are available.

Effectiveness of participation in the project. It is determined in order to verify the financial feasibility of the project and the interest of all its participants in it. This efficiency includes:

The effectiveness of enterprises’ participation in the project (its effectiveness for enterprises participating in the investment project);

Efficiency of investing in enterprise shares (efficiency for JSC shareholders - participants in the investment project);

The effectiveness of structures' participation in the project is more high level in relation to enterprises participating in the IP (national economic, regional, sectoral and other efficiency);

Budgetary efficiency of individual entrepreneurs (the effectiveness of state participation in the project in terms of expenses and revenues of budgets of all levels).

General scheme for assessing the effectiveness of an investment project. First of all, the social significance of the project is determined, and then the effectiveness of the IP is assessed in two stages. At the first stage, performance indicators of the project as a whole are calculated. Wherein:

if the project is not socially significant (local project), then only its commercial effectiveness is assessed;
for socially significant projects, their social effectiveness is first assessed (methods of such assessment in general outline set out in " Methodical recommendations»).

If such efficiency is unsatisfactory, then the project is not recommended for implementation and cannot qualify for state support. If social efficiency is acceptable, then commercial efficiency is assessed. If the commercial effectiveness of a socially significant individual entrepreneur is insufficient, it is necessary to consider various options its support, which would improve the commercial efficiency of the individual entrepreneur to an acceptable level. If the conditions and sources of financing for socially significant projects are already known, then their commercial effectiveness need not be assessed.

The second stage of assessment is carried out after the development of a financing scheme. At this stage, the composition of participants is clarified and the financial feasibility and effectiveness of participation in the project of each of them is determined. We can formulate the main tasks that have to be solved when assessing the effectiveness of investment projects:

1. Assessing the feasibility of the project - checking that it satisfies all actually existing restrictions of a technical, environmental, financial and other nature. Typically, all restrictions, except financial feasibility, are checked in the early stages of project formation. The financial feasibility of an investment project is ensuring such a structure of cash flows in which at each step of the calculation there is a sufficient amount of money to implement the project that generates this IP. Accordingly, the cash flows of an investment project are understood as the cash flows of the project associated with this individual entrepreneur.

2. Assessing the potential feasibility of implementing the project, its absolute effectiveness, that is, checking the condition according to which the total results of the project are no less valuable than the required costs of all types.

3. Assessment of the comparative effectiveness of the project, which is understood as an assessment of the advantages of the project under consideration compared to the alternative.

4. Evaluation of the most effective set of projects from their entire set. Essentially, this is an investment project optimization problem, and it generalizes the previous three problems. As part of solving this problem, it is possible to rank projects, that is, select the optimal project.

Basic methods for assessing the effectiveness of investment projects

There are two groups of methods for evaluating investment projects:

1. simple or static methods;

2. discounting methods.

Simple or static methods are based on the assumption of equal importance of income and expenses in investment activities and do not take into account the time value of money.

Simple ones include: a) calculation of the payback period; b) calculation of the rate of return.

The rate of return shows how much of the investment costs are recovered as profits. It is calculated as the ratio of net profit to investment costs:

Rate of return = Net profit / Investment costs.

Discounted methods for assessing the effectiveness of an investment project are characterized by the fact that they take into account the time value of money.

At economic assessment the effectiveness of an investment project uses indicators widely known in world practice:

Present value (PV);

Net Present Value (NPV);

Payback period (PBP);

Internal rate of return (IRR);

Profitability Index (PI).

Present value (PV). The task of any investor is to find a real asset that would ultimately bring income that exceeds the cost of its acquisition. In this case, a complex problem arises: money must be spent today (at the moment t = 0) to purchase a real asset, but the investment usually does not give a return immediately, but after a certain period of time (at the moment t = 1). Consequently, to solve the problem, it is necessary to determine the cost of a real asset, taking into account the remoteness in time of future receipts (income) from its use.

In general, to find the present value PV of any asset (real or financial) used during a certain holding (investment) period, it is necessary to multiply the expected income stream from this asset (C) by the value 1/(1 + r):

PV = C * (1/(1+r)) ,

where r determines the return on the best alternative financial instrument with the same holding period and similar level of risk.

The value 1/(1+r) is called the discount factor (discount factor). The return on an alternative financial instrument r is called the discount rate. The discount rate determines the opportunity cost of capital, since it characterizes what benefits the company missed by investing money in real assets, rather than the best alternative financial means.

To determine the feasibility of purchasing a real asset worth C0 rubles, you must:

a) estimate what cash flow C1 expects from the real asset for the entire holding period;

b) find out which security with the same holding period has the same level of risk as the planned project;

c) determine the yield r of this security at the present time;

d) calculate the present value PV of the planned cash flow C1 by discounting the future income stream:

PV = C1 / (1+r) ;

e) compare investment costs C0 with the present value PV:

if PV > C0, then the real product can be purchased;

if PV = C0, then you can either buy or not buy a real asset (that is, from an economic point of view, investing in a real asset has no advantage compared to investing money in securities or to other objects).

If an investment project is designed for several steps (in particular, n years), then to find the present value of future income from the project it is necessary to discount all amounts Ct that the project must provide:

PV = Σ Ct / (1+r)^t .

For example, for an investment project designed for three years, the present value is estimated as follows:

PV = Ct / (1+r) + Ct / (1+r)^2 + Ct / (1+r)^3 .

Some funds can provide a continuous stream of income indefinitely. The present value of such a facility at a given and constant discount rate r is:

PV = Ct / (1+r) + Ct / (1+r)^2 + Ct / (1+r)^3 + ... = C / r .

The present value of an annuity that provides an income stream C for n periods (years) at a constant discount rate r is calculated using the formula:

PVannuity = C * Fannuity,

where F annuity is the annuity factor, which is determined as follows:

Annuity F = 1/r - 1/(1+r)^n .

Net Present Value (NPV)

The feasibility of acquiring a real asset can be assessed using net present value (NPV), which is understood as the net increase in the potential assets of the company due to the implementation of the project. In other words, NPV is defined as the difference between the present value of the PV of the asset and the amount of initial investment C0:

NPV = Σ Ct / (1+r)^n - C0 .

Payback period (PVR)

The payback period of a project is the period over which the initial investment costs are recovered, or the number of periods (calculation steps, for example, years) during which the accumulated amount of estimated future income streams will be equal to the amount of the initial investment. As a rule, the company itself sets an acceptable completion date for the investment project, for example, k steps. This period is determined by the company on the basis of its own strategic and tactical guidelines: for example, the company’s management rejects any projects lasting more than 5 years, since after 5 years the company is planned to be repurposed to produce other products.

When the completion date k of alternative projects is determined, then the payback period of the project under evaluation can be found by calculating how many calculation steps m the sum of cash flows C1+C2+...+Cm will be equal to or begin to exceed the value of the initial investment C0. In other words, to determine the payback period of a project, it is necessary to consistently compare the accumulated amounts of income with the initial investment. According to the payback period rule, a project can be accepted if the following condition is met: m

Internal rate of return (IRR)

The internal rate of return is settlement rate discounting, at which the net present value of the project is zero.

It is found by solving the following equation:

NPV = C0 + C1/(1+IRR) + C2/(1+IRR)^2 + C3/(1+IRR)^3 + ... + Cn/(1+IRR)^n = 0 .

This equation is solved by iteration. To calculate IRR, you can use specially programmed calculators or computer programs. Rule of internal rate of return: it is necessary to accept those projects whose discount rate (that is, the opportunity cost of capital) is less than the internal rate of return of the project (r

The profitability index (PI) is understood as a value equal to the ratio of the present value of the expected cash flows from the project to the initial cost of investment:

The profitability index shows how much an investor receives per invested ruble. The rule of the profitability index is as follows: it is necessary to accept only those projects whose profitability index value exceeds one. When evaluating two or more projects that have a positive profitability index, you should choose the one that has a higher profitability index.

The effectiveness of the IP is assessed during the calculation period - the investment horizon from the start of the project to its liquidation. The start of a project is usually associated with the start date of investment in design and survey work. Billing period are divided into calculation steps, which are time periods within which data is aggregated to estimate cash flows and discounted cash flows are carried out.

Calculation steps are usually numbered (step 0, step 1, step 2, etc.). The duration of calculation steps is measured in years or fractions of a year, their sequence is counted from a fixed moment t0 = 0, taken as the base one. For reasons of convenience, the moment of the beginning or end of the zero step is usually taken as the base one. If several projects are being compared, it is recommended to choose the same base point for them. When the base moment coincides with the beginning of the zero step, the moment of the beginning of step number m is denoted by tm, but if the base moment coincides with the end of step 0, then tm denotes the end of the calculation step m. The duration of different steps may vary.

Source - Maksimova V.F. Investment management: Educational and practical manual. – M.: Publishing house. EAOI center. 2007. – M., 2007. – 214 p.

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Ministry of Education and Science of Ukraine

Kherson National Technical University

Faculty of Genetics

Department of Economics and Entrepreneurship.

ABSTRACT

discipline: "Investing"

on the topic: “Assessing the commercial effectiveness of investment projects”

Completed by: student 3zGB

Checked by: assistant

Genichesk, 2007

1. general characteristics effectiveness assessment methods

Work by definition economic efficiency investment project is one of the most critical stages of pre-investment research. It includes a detailed analysis and integral assessment of the entire technical, economic and financial information, collected and prepared for analysis as a result of work at previous stages of pre-investment research.

Methods for assessing the effectiveness of investment projects are based primarily on comparing the effectiveness (profitability) of investments in various projects. At the same time, an alternative to investing in the production in question is financial investments to other production facilities, premises financial resources to the bank at interest or their conversion into securities. From the position of financial analysis, the implementation of an investment project can be presented as two interrelated processes: the process of investment in the creation production facility(or accumulation of capital) and the process of obtaining income from investments. These two processes occur sequentially (with or without a gap between them) or over a certain period of time in parallel. In the latter case, it is assumed that the return on investment begins even before the investment is completed. Both processes have different intensity distributions over time, which largely determines the efficiency of investment.

The direct object of financial analysis is cash flow, which characterizes both of these processes in the form of one combined sequence. In the case of industrial investments, the intensity of the resulting flow of payments is formed as the difference between the intensity (expenses per unit of time) of investments and the intensity of net income from the project.

Net income means income received in each time interval from production activities, minus all payments associated with its receipt (current costs of labor, raw materials, energy, taxes, etc.). In this case, repayment of depreciation does not apply to current costs.

Efficiency assessment is carried out by calculating a system of indicators or criteria for the effectiveness of an investment project.

They all have one important feature. Expenses and income are spread over time and are reduced to one (base) point in time. The base point in time is usually the date of implementation of the project, the date of commencement of production, or a conventional date close to the time of calculations of the effectiveness of the project.

The procedure of bringing payments at different times to the base date is called discounting. Economic sense This procedure is as follows. Let a certain loan interest rate r and a flow of payments (negative or positive t), the beginning of which coincides with the base moment of reduction time, be given. Then the discounted value of the payment P(t), made at a time distant from the base one by t intervals (months, years), is equal to a certain value Pd(t), which, being issued at a loan interest rate r, will give at the time t the value P (t). Thus, Pd(t) (1+r)t = P(t) , or the discounted payment value P(t) is equal to:

The value of the loan interest r is called the discount rate (reduction) and, in addition to the above meaning, is interpreted in economic literature as the rate (or degree) of preference for income received at the moment over income that will be received in the future.

When choosing a discount rate, they are guided by the existing or expected average level of loan interest. In practice, specific benchmarks are chosen (the yield of certain types of securities, banking operations etc.) taking into account the activities of relevant enterprises and investors.

For example, in the USA the largest oil companies When analyzing efficiency, three rate options are used: the average return on shares, existing loan rates (medium and long-term), and subjective assessments based on the experience of firms. The discount rate used in a market economy largely depends on economic conditions, prospects economic development countries, the world economy, is the subject of serious research and forecasts.

To others important factor, which influences the assessment of the effectiveness of an investment project, is a risk factor. Since risk in the investment process, regardless of its specific forms, ultimately appears in the form of a possible decrease in the real return on capital compared to the expected one, to take into account the risk, an adjustment is often introduced to the level of the interest rate, which characterizes the return on risk-free investments (for example, compared with bank deposits or short-term government securities).

The inclusion of a risk premium in the discount rate is a common, but not the only, means of accounting for risk. Another method for solving this problem is to analyze the sensitivity or stability of an investment project to changes in external factors and parameters of the project itself.

External factors include: future inflation levels, changes in demand and prices for products planned for production, possible changes in prices for raw materials, changes in interest rates, tax rates etc. The internal parameters of the project include: changes in the timing and cost of construction, the pace of development of production, the need for various types of raw materials and supplies, sales costs, etc.

Since the implementation of an investment project includes processes capital construction, development and expansion of production, its functioning in a changing economic environment, is dynamic, then dynamic simulation models implemented with the help of computer technology are used to describe it. The variables used in these models are techno-economic and financial indicators investment project, as well as parameters characterizing the external economic environment (characteristics of product markets, inflation, interest rates on loans, etc.). Based on these models, the flows of expenses and income are determined, the efficiency indicators of the investment project are calculated, annual balances of the results of production activities are constructed, and the influence of various factors and internal parameters of the investment project on the results of production activities and the effectiveness of the project is analyzed.

2. Indicators of economic efficiency of an investment project

Most methods for determining the economic efficiency of investment projects in a market economy are based on the calculation of net present value. Net present value (NPV) is the difference between the results of income and capital investment at one point in time (usually the year the project began).

To assess the effectiveness of industrial investments, the following indicators are mainly used: net present value, internal rate of return, payback period capital investments, project profitability and break-even point.

Variable indicators are the results of comparisons of income distributed over time with investments and production costs.

Let's consider the definition, semantic content and algorithm for calculating the above indicators of an investment project.

Net present value NPV is calculated at a given discount rate (reduction) according to the formula

where t is the years of implementation of the investment project including the construction stage (t = 0, 1, 2, 3, ..., T); Pt is the net flow of payments (cash) in year t; d - discount rate.

The net flow of payments includes as income profit from production activities and depreciation charges, and as expenses - investments in capital construction, reproduction of fixed assets retired during the production period, as well as the creation and accumulation of working capital.

The influence of investment costs and income from them on NPV can be presented in a more visual form by writing formula (1) in the form

where tn is the year of commencement of production;

tc - year of completion of capital construction;

KVt - investment expenses (capital investments) in year t.

It should be noted that instead of an annual interval, these formulas can also use smaller time intervals - a month, a quarter, a half-year. The year of commencement of production of tn products may not coincide with the year of completion of construction.

The case tn > tc means a temporary delay in production after completion of construction, and the case tn< tc означает запуск продукции до завершения строительства.

Internal rate of return (IRR) investment project is the estimated interest rate at which the net present value corresponding to this project is zero. The economic meaning of this indicator is expressed in the following: as an alternative to investing financial resources in an investment project, placing the same funds (also distributed over the time of investment) at a certain bank interest is considered. The income distributed over time is placed in a deposit account in a bank at the same interest rate.

At a loan interest rate equal to the internal rate of return, investing financial resources in a project will ultimately yield the same total income as placing them in a bank deposit account. Thus, at this interest rate, the investment alternatives are economically equivalent. If the real interest rate is less than the internal rate of return of the project, then investing in it is profitable, and vice versa. Therefore, IRR is the marginal interest rate separating efficient and inefficient projects.

The IRR level is completely determined by the internal data characterizing the investment project. No assumptions are made regarding the use of net proceeds outside the project. Abroad, the calculation of the internal rate of return is often used as the first step in financial analysis investment project. For further analysis, those investment projects are selected that have an IRR of at least threshold value(usually 15 - 20% per annum).

The methodology for determining the internal rate of return depends on the specific features of the distribution of income from investments and the investments themselves. In general, when an investment and its return are given as a stream of payments, the IRR is defined as the solution of the following equation for the unknown quantity d*:

where d* = IRR is the internal rate of return corresponding to the payment flow Pt.

It can be obtained from formula (1) if its left side is equal to zero. Equation (2) is equivalent to an algebraic equation of degree T and is usually solved by iteration. There are numerous PC programs that solve such equations.

Very often in practice, more complex cases can occur when equation (2) has several positive roots. This can, for example, happen when, after the initial investment in production, there is a need for a radical modernization or replacement of equipment in an existing production facility. In this case, you should be guided by the smallest value of the solutions obtained.

Payback period (payback method)- this is one of the most used indicators, especially for preliminary assessment of the effectiveness of investments. The payback period is defined as the period of time during which the investment will be returned from the income received from the implementation of the investment project. More precisely, the payback period refers to the length of the period during which the amount of net income discounted at the time of completion of the investment is equal to the amount of the investment.

To determine the payback period, you can use formula (1*), modifying it accordingly. We equate the left side of this formula to zero and assume that all investments are made at the time of completion of construction. The known value h of the period from the moment of completion of construction, satisfying these conditions, will be the payback period for the investment.

The equation for determining the payback period can be written as:

where h is the payback period; KV is the total investment in the investment project.

It should be noted that in the equation t=0 corresponds to the moment of completion of construction. The value h is determined by sequentially summing the terms of the discounted income series until an amount equal to or greater than the volume of investment is obtained.

Let us denote, and Sm< KV < Sm + 1.

Then the payback period is approximately equal to:

It is obvious that the payback period, in addition to the intensity of income receipt, is significantly influenced by the income discount rate used. Naturally, the shortest payback period corresponds to the absence of discounting of income, increasing monotonically as the interest rate increases.

In practice, there may be cases when the payback period for investments does not exist (or is equal to infinity). In the absence of discounting, this situation arises only if the payback period is longer than the period of receipt of income from production activities. When discounting income, the payback period may simply not exist (tend to infinity) for certain relationships between investments, income and the discount rate.

Let us assume that in formula (3) Pt is a constant value equal to P.

Then the sum is the sum of the terms of a geometric progression. For h a this sum is equal to S = 1+d /d.

For any finite h Sh< S . Отсюда следует, что необходимым условием существования конечного срока окупаемости h является выполнение равенства:

P (1+d / d) = KV,

which is equivalent:

P / KV = d / 1+d. (5)

It should be noted that when determining the payback period, investments were not discounted, but simply summed up. Sometimes it is useful to determine the payback period of investments, bringing them to the end of the construction period, along with income at the same interest rate.

In this case, with a discount rate equal to the internal rate of return, the payback period for investments is equal to the production period during which income from production activities is positive. Thus, IRR is the marginal discount rate at which the payback period exists. It can also be a guideline when assessing the limiting value of the discount rate corresponding to the existence of the payback period even in the absence of discounting of investments.

The disadvantage of the payback period as an indicator of the efficiency of capital investments is that this indicator does not take into account the entire period of operation of production and, therefore, it is not affected by income that will be received outside the payback period. In particular, such a measure as the payback period should not be used as a criterion for choosing an investment project, but only as a limitation when making a decision. This means that if the payback period is greater than a certain accepted limit value, then the investment project is excluded from those under consideration.

Profitability (benefit - cost ratio), or profitability index of an investment project, is the ratio of present income to investment expenses given at the same date.

Using the same notation as in formula (1*), we obtain the profitability formula (R) in the form:

As can be seen from this formula, it compares two parts of the given net income - income and investment. If, at a certain discount rate d*, the profitability of the project is equal to one, this means that present income is equal to investment expenses and net present income is zero.

Therefore, d* is the internal rate of return of the project. When the discount rate is less than IRR, the profitability is greater than 1. Thus, the excess of the project's profitability over one unit means some of its additional profitability at the interest rate under consideration. The case when the profitability of a project is less than one means that it is ineffective at a given interest rate.

All considered indicators of the investment project are closely related to each other. This can be explained by the fact that they are all based on discounting the flow of payments. Therefore, often an investment project that is preferable in one respect will also be preferable in other respects.

However, this is not always the case, since the prerequisites and features of the calculation of each indicator differ.

As an example, consider the correspondence between net present value and profitability. Using formulas (1*) and (6), we can write the expression for profitability in the following form:

, (6*)where is the discounted amount of investment.

From this formula it is clear that higher profitability values can be obtained with lower NPV values if investments decrease to a greater extent than the net present value. Due to differences in the assessment of an investment project, which can be observed when using various performance indicators, the question arises about the preference of certain performance indicators. A 1983 survey of 103 major US oil and gas companies found that 98% of firms used at least one formal performance measure as a primary or secondary measure, and many used several. The table shows data on the frequency of use of various investment performance indicators.

As follows from the table, the most commonly used indicator of investment performance is the internal rate of return, and the second most frequently used is net present value. All other investment performance indicators are used much less frequently. It should be noted that it is advisable to use both of the above indicators simultaneously, since the internal rate of return can be considered as a qualitative indicator characterizing the profitability of a unit of invested capital, and net present value is absolute indicator, reflecting the scale of the investment project and the income received. In addition to formal criteria for assessing effectiveness, when deciding on the advisability of financing an investment project, various restrictions and informal criteria are taken into account. Limitations may include the payback period, security requirements environment, personnel safety, etc. Informal criteria may include: penetration into a promising product market, ousting competing companies from the market, political motives, etc.

3. Net cash flow

From the above it follows that the basis for calculating all indicators of the effectiveness of investment projects is the calculation pure flow payments. As already noted, the net flow of payments is defined as the difference between current income and expenses associated with the implementation of an investment project and measured by the number of monetary units per unit of time (rub/day; million rubles/year; USD/year, etc.).

From a financial point of view, the flows of current income and expenses, as well as the net flow of payments, fully characterize the investment project. Therefore, calculating this characteristic of an investment project is extremely important. This part presents the basic formulas for calculating the net flow of payments.

The net flow of payments Pt in time interval t (year) is equal to

Pt = PPt + At + FIt - KVt - POKt, (7)

where t = 0, 1, 2, ...,T; ChPt - net profit; At - depreciation charges; FIt - financial costs (interest on loan); KVt - capital investments.

Let us consider the terms Pt in general form: PPt = Дt - Пt - Нt, (8)

where Дt is the total sales volume of the t-th year (minus VAT); IPt - production costs in t-th year; Нt - tax on non-taxable profit in the t-th year.

Дt = ДВt + ДЭt , (9)

where ДВt is income from sales on the domestic market in the t-th year; DEt is income from export sales in the t-th year.

All income is determined net of VAT.

DVt= CVjt Q DEt = CEjt Qj gt, (11)

where j = 1, 2, ..., N - type of product; CVjt - price jth units products on the domestic market in the t-th year in local currency; Qjt - quantity jth products, sold in the t-th year on the domestic market; CEjt is the price of a unit of j-th product on the foreign market in the t-th year in foreign currency; Qjt- jth quantity products sold in the t-th year on the foreign market; gt - average annual conversion factor foreign currency to the local one.

Ipt = Ct+Mt+KIt+Et+RSt+RMt+ZCht+ZNRt+ANPt+SBt+At+FIt, (12)

where Ct is the cost of raw materials; Mt - costs of materials; Kit - costs for the purchase of components; Et - operating costs; РСt - expenses for paying production personnel, including contributions for social needs (social insurance, Pension Fund, medical insurance, employment fund); РМt - costs of equipment maintenance and repair (without wages); ZCht - costs for spare parts for repair of main and auxiliary equipment; ЗНРt - factory overhead costs; ANPt - administrative overhead costs; СБt - sales and distribution costs; At - depreciation charges; FIt - financial costs (interest on the loan).

Sometimes, from production costs, two more groups of costs are singled out for further analysis and calculations - factory costs and operating costs:

Зt = Сt + Мt + КИt + РМt+ Эt + ЗЧt + ЗНРt, (13)

where Zit is factory costs.

EZt = ZIt + ANPt + SBt, (14)

where EZt is operating costs.

4. Need for working capital

Along with investments in fixed capital (buildings, machinery, etc.), in financial analysis, much attention is paid to determining the working capital needs of the created production and its changes in connection with changes in the scale of production and other factors. The amount of working capital is influenced by the duration of the production cycle, the established practice of paying bills to suppliers and consumers, planned reserves of raw materials, materials, finished products etc.

Basic calculation formulas to estimate the amount of working capital required to implement an investment project:

The amount of net working capital in year t

OKt = AKt - POSTt, (15)

where t = 0,1,2, ... , T; OKt - the amount of net working capital; АКt - current assets; POST - invoices payable.

In turn, current assets are equal to

AKt= DZt+ZSZt+ZMt+ZKIt+ZEt+ZZCht+NPt+GPt+KNt, (16)

where DZt is accounts receivable; ZСt,ЗМt,ЗКИt,ЗЭt,ЗЗЧt - cost of stocks of raw materials, components, fuel and spare parts; NPt - cost of work in progress; GPt is the cost of finished goods inventories; КНt - cash in hand.

In calculating the working capital requirement, the minimum number of days of inventory plays a significant role. The minimum number of days of supply of the corresponding element is calculated according to standards, set from practice or by expert opinion. The number of annual turnovers of the corresponding type of inventory is calculated using the formula

Пj = 360 / ДНj, (17)

where Pj is the number of revolutions of the jth type of inventory; DNj - the minimum number of days of inventory of the jth type.

Volume accounts receivable is determined by the formula

DZt = EZt / Pd.z. (18)

where EZt is the annual operating costs, calculated using formula (14); Pd.z. - the number of receivables turnover for the year.

The cost of stocks of raw materials, materials, fuel and energy is determined by the formula ZСt = Сt / Ps, (19)

ZMt = Mt / Pm (20)

ZMt = KIt / Pk.i. (21)

ZEt = Et / Pe, (22)

ZZCht = ZCht / Pz.ch., (23)

where Ct, Mt, KIt, Et, ZCht are the corresponding annual costs; Ps, Pm, Pk.i., Pe, Pz.ch. - the number of turnovers of the corresponding inventories per year.

The value of work in progress is

ZNPt = ZIT / Mon, (24)

where Zit is the annual volume of factory costs, calculated according to formula (13); Mon - number of product production cycles per year.

Cost of finished goods inventory

GPt = (Zit + ANPt) / Pp.g., (25)

where ANPt is administrative overhead; Pp.g. - number of finished product turnovers per year.

The volume of cash on hand is estimated using the formula

KNt = (RSt + Kz + ZNRt + Ka + ANRt) / Pk, (26)

where PCt is the cost of paying production personnel (including deductions); Kz and Ka - shares wages in factory and administrative overheads.

Payable invoices (accounts payable) are determined by the formula POST = EZt / POS, (27)

where Po.s. - number of revolutions accounts payable in a year.

The given formulas serve for a preliminary assessment of the amount of working capital, which must be clarified as a result of design work for an investment project.

5. Initial information for determining economic

efficiency of the investment project

Calculation of net payment flow and determination of others financial characteristics investment project requires sufficient knowledge large quantity initial data about the project.

In accordance with accepted practice, an investment project is usually studied over a period covering the capital construction phase (lasting 3-5 years) and the production phase and until its winding down (lasting up to 10-15 years). The initial data should reflect the time dynamics of the project implementation. It is not enough, for example, to know the total capital investments or the annual volume of production, but it is necessary to have a plan for capital construction, development of production and changes in its scale over time.

It is also necessary to have an understanding of the economic situation directly related to the production and marketing of products.

It is necessary to take into account probabilistic scenarios of general economic development, which are expressed in inflation, trends in changes in bank interest rates for various types of loans, the exchange rate of the hryvnia against the dollar and other indicators.

Background information is usually provided in the following sections:

· sales market, sales volume and prices;

· data and proposals on inflation processes, interest rates bank loan, exchange rates currencies;

· data and proposals on taxes and fees;

· construction and investment project program;

· production costs.

Basic methods for assessing the effectiveness of investment projects

Net Present Value (NPV)

Payback period (PVR)

Internal rate of return (IRR)

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