Economic appraisal of investments are the main methods of investment appraisal. Abstract: Methods for evaluating investment projects. Initial data for calculating IRR

Net present value
(net present value - Net Present Value, NPV)

Profitability Index (PI)

Internal Rate of Return (IRR)

Modified internal rate of return
(Modified Internal Rate of Return, IRR)

Discounted payback period of investment
(Discounted Payback Period, DPP)

Payback Period (PP)

Investment efficiency ratio (Accounting Rate of Return, ARR)

DYNAMIC METHODS FOR ASSESSING INVESTMENT PROJECTS.

STATIC METHODS FOR ASSESSING INVESTMENT PROJECTS.

02.08.2021

Introduction

Investments - costs Money aimed at reproduction (maintenance and expansion) of fixed assets of the enterprise. Investing (investing money) in land, buildings, production facilities is aimed at continuing and expanding the production activities of the enterprise, generating income and profit in the future.

The need for investment is caused by several reasons.

The main among them are the need to update or replace the existing material and technical base of production, its improvement or modernization due to wear and tear of production equipment, the need to increase and commission fundamentally new production capacities due to an increase in production volumes and the development of new activities.

The main sources of investment are own funds ( authorized capital, depreciation fund, others reserve funds, accumulation fund, retained earnings of the enterprise).

The cheapest source of investment financing is the reinvested profit of the enterprise. Its productive application avoids the additional costs associated with paying interest on borrowed funds or the costs associated with issuing valuable papers. The reinvestment of profits preserves the existing system of control over the activities of the enterprise, since the number of shareholders of the enterprise does not change (in contrast to their inevitable increase in the event of an additional issue of securities).

Investment activity is carried out primarily in conditions of uncertainty. If we are talking about replacing existing production capacities, then the investment decision can be made quite simply, since the company's management clearly understands how much and with what characteristics new fixed assets (machines, machine tools, equipment, etc.) are needed. If we are talking about expanding the core business or diversifying it, then the risk factor begins to play a significant role.

At the time of acquisition of machinery and equipment, other fixed assets, it is impossible to predict with certainty the economic effect of such an operation. Investment decisions are usually made in conditions where there are several alternative projects that differ in the types and volumes of required investments, payback periods and sources of funds raised. Decision-making in such conditions involves the evaluation and selection of one of several projects based on some criteria. It is clear that there may be several criteria, their choice is arbitrary, and the probability that one project will be preferable to others in all respects is very small. Therefore, the risk associated with the adoption of an investment decision is also great.

Making investment decisions is the same art as making any other entrepreneurial (management) decisions. The intuition of the entrepreneur, his experience, and the knowledge of qualified specialists are important here. Certain assistance can be provided by well-known world and domestic practice methods of assessment investment projects.

Methods for evaluating investment projects

Methods used in the analysis investment activity, can be divided into two groups: a) based on discounted estimates; b) based on accounting estimates.

1) Discounting capital and income.

Financial resources, the material basis of which is money, have a temporary value. The time value of financial resources can be considered in two ways. The first aspect is related to purchasing power of money. The second aspect is related to the circulation of funds as capital and the receipt of income from this turnover. Money should make new money as quickly as possible.
Discounting income - bringing income to the time of investment. To determine the accumulated capital and additional income, taking into account discounting, the following formulas are used:

K = K (1 + n) , (1.)

where K is the amount of capital investment by the end of the t-th period of time from the moment the initial amount was deposited, rub.;

K - current estimate of the amount of invested capital, i.e. from the position of the initial period when the initial contribution is made, rub.;

n - discount factor (i.e. rate of return, or interest rate), fractions of a unit;

t is the time factor (number of years or number of capital turnovers).

D \u003d K (1 + n) - K, (2.)
where D - additional income, rub.

Income discounting is used to estimate future cash receipts (profit, interest, dividends) from the position of the current moment. The investor, having made an investment of capital, is guided by the following provisions. First, there is a constant depreciation of money; secondly, it is desirable to periodically receive income on capital, and in an amount not lower than a certain minimum. The investor must evaluate how much income he will receive in the future and what is the maximum possible amount of financial resources that can be invested in this business based on the predicted level of profitability.

This assessment is made according to the formula:

K = (1.5)
(1 + n) (3.)

2) Method for calculating the net present effect.

This method is based on comparing the value of the original investment (IC) with the total discounted net cash flow generated by it over the forecast period. Because cash inflows are spread over time, they are discounted by a factor r set by the analyst himself based on the annual percentage return he wants or can have on his invested capital.

Suppose a forecast is made that an investment (IC) will generate, over n years, annual returns of P1, P2,...,Pn. Total cumulative discounted returns (PV) and net present effect
(NPV) respectively are calculated according to the formulas:

NPV=
Obviously, if: NPV > 0, then the project should be accepted;

NPV< 0, то проект следует отвергнуть;

NPV = 0, then the project is neither profitable nor unprofitable

If the project involves not a one-time investment, but a consistent investment of financial resources over m years, then the formula for calculating NPV is modified as follows:

where i is the projected average inflation rate.

It should be noted that the NPV indicator reflects the predictive assessment of the change in the economic potential of the enterprise in the event that the project under consideration is accepted. This indicator is additive in time, i.e. The NPV of different projects can be summarized. This is a very important property that distinguishes this criterion from the rest and allows it to be used as the main one when analyzing the optimality of an investment portfolio.

3) Method for calculating the index of return on investment.

This method is, in fact, a continuation of the previous one. Profitability Index (PI) is calculated by the formula:

Obviously, if: PI > 1, then the project should be accepted;
PI< 1, то проект следует отвергнуть;
PI = 1, then the project is neither profitable nor unprofitable.

Unlike the net present effect, the profitability index is a relative indicator. Due to this, it is very convenient when choosing one project from a number of alternative ones with approximately the same NPV values, or when completing an investment portfolio with the maximum total NPV value.

4) Method for calculating the rate of return on investment.

The rate of return on investment (IRR) is understood as the value of the discount factor at which the NPV of the project is zero:

IRR = r, where NPV = f(r) = 0.

The meaning of this ratio when analyzing the effectiveness of planned investments is as follows: IRR shows the maximum allowable relative level of expenses that can be associated with a given project. For example, if the project is funded entirely by a loan commercial bank, then the IRR value shows the upper limit of the acceptable level of banking interest rate, exceeding which makes the project unprofitable.

5) Method for determining the payback period of investments.

This method is one of the simplest and most widespread in world practice, it does not imply a temporal ordering of cash receipts. The algorithm for calculating the payback period (RR) depends on the uniformity of the distribution of projected income from the investment. If the income is evenly distributed over the years, then the payback period is calculated by dividing the one-time costs by the amount of annual income due to them. When a fractional number is received, it is rounded up to the nearest whole number. If profits are unevenly distributed, then the payback period is calculated by directly counting the number of years during which the investment will be repaid with cumulative income. The general formula for calculating the PP indicator is as follows:

РР = n, at which Рк > IC.

The indicator of the payback period of investments is very simple in calculations, however, it has a number of disadvantages that must be taken into account in the analysis.
First, it does not take into account the impact of income from recent periods. Second, because this method is based on undiscounted estimates, it does not distinguish between projects with the same amount of cumulative returns but different distributions over the years.

There are a number of situations in which it may be appropriate to apply the payback method. In particular, this is a situation where the company's management is more concerned with solving the problem of liquidity, rather than the profitability of the project - the main thing is that the investment pays off as soon as possible. The method is also good in a situation where investments are associated with a high degree of risk, therefore, the shorter the payback period, the less risky the project is. This situation is typical for industries or activities that are characterized by a high probability of fairly rapid technological change.

6) Method for calculating the investment efficiency ratio.

This method has two characteristic features: it does not involve discounting income indicators; income is characterized by the net profit indicator PN (balance sheet profit minus deductions to the budget). The calculation algorithm predetermines the wide use of this indicator in practice: the investment efficiency ratio (ARR) is calculated by dividing the average annual profit PN by the average investment value (the coefficient is taken as a percentage). The average investment is found by dividing the initial amount of capital investments by two, if it is assumed that after the expiration of the analyzed project, all capital costs will be written off; if residual value (RV) is allowed, its valuation should be excluded.

ARR=PN.
1/2 (IC - RV)

This indicator is compared with the ratio of return on capital advanced, calculated by dividing the total net profit of the enterprise by the total amount of funds advanced into its activities (the result of the average net balance) .

The adoption of any decision of an investment nature is necessarily associated with an assessment of the economic efficiency of projects. At the same time, the question often arises of which performance parameters, which criteria to give preference to. For example, what is more important: less risk or more efficiency? Therefore, the need for a systematic approach to solving this issue is obvious. We need objective methods for evaluating investment projects that would take into account the economic, industrial, social, environmental and even political situation in each individual case. At the same time, speaking of environmental factors, one should not forget about the time factor as well.

Basic methods of investment appraisal

One of the main requirements for an enterprise in market conditions is its ability to create added value, which includes wage employees, loan interest, profit, minimum obligations to shareholders. If an enterprise does not have such an ability, then, having lost its competitiveness, it is forced out of the market.

The company develops due to the growth of net income, which is formed from net profit (enrichment of the owner) and depreciation. Therefore, as an efficiency criterion, we can consider the value of the ratio of value added and the capital that was spent on its creation, and the more (services or products must be of high quality) the enterprise has profit per unit of costs, the more competitive it will be.

Some methods are based on this efficiency criterion. These include profitable (spectacular) and costly methods:

The cost method is based on an analysis of the costs associated with the project. They make it possible to evaluate the economic annual effect of a given project in comparison with an alternative one.

A profitable, or effective, method is based on an analysis of the results of investments, that is, profits (additional, balance sheet, products, annual economic effect. NPV is a reflection of the absolute result of investments, and PI and IRR (internal rates of return), including efficiency ratio - relative.

Methods for evaluating investment projects that take into account the time factor are divided into two main groups: static and dynamic.

Static costs, payback, profit, profitability) are based on indicators using accounting estimates, for example, efficiency ratio, reduced costs, payback period, economic annual effect.

Dynamic methods (accumulated value, annuity, discounting) use indicators that are based on net present value, the internal rate of the project's payback period, that is, on discounted estimates.

Methods for evaluating investment projects are also differentiated by the number of criteria used in the evaluation. From this position, evaluation models are divided into normative and multifactorial, and single- and multi-criteria methods are singled out in the methods.

With the multicriteria optimality method, in addition to the profitability of the project, there are also such indicators as: stability of capital growth, safety, risk, payback period, social and environmental efficiency. Since in normative models the assessment is carried out only on the basis of financial and economic indicators, multi-criteria method should use multi-factor modeling.

Efficiency can be calculated in predicted or current prices:

at the initial stage of development of an investment project, calculations can be carried out at current prices;

the effectiveness of the entire project as a whole is produced both in forecast and current prices;

forecast prices are used to develop a financing scheme and evaluate the effectiveness of participation in it.

Before assessing the effectiveness of investments, it is important to expertly determine the social significance of the industry in which investments are planned, and the project itself. Socially significant projects are those that affect the environmental, social and economic environment in the country and in the world. Further, the assessment is carried out in two stages (Figure 5.3).

At the first stage, performance indicators as a whole are determined. The purpose of this stage is the aggregated economic evaluation design solutions and the creation of the necessary conditions for the search for investors. If the project turns out to be socially significant, then its commercial effectiveness is evaluated. And with insufficient commercial efficiency of a socially significant project, the possibility of using various forms of its support is considered.

Rice. 5.3. Stages of evaluating the effectiveness of investment projects

The second stage of the assessment is carried out after the development of the financing scheme. At this stage, the composition of participants and the effectiveness of participation in the project of individual enterprises and shareholders are specified. The effectiveness of investments can be expressed in accounting for costs and results both in natural-material and in value (cash) form. The cost indicators of the economic efficiency of investments, despite their shortcomings, are currently the main indicators of the justification of programs and projects.

According to the type of generalizing indicator, investment calculation methods are divided into:

Absolute (in which absolute values of the difference between capital investments and current costs of the project implementation and the monetary value of its results are used as generalizing indicators);

Relative (in which generalizing indicators are defined as the ratio of the valuation of results and total costs);

Temporary (in which the return period (payback period) of investments is estimated).

The methods used in the analysis of investment activity can be divided into two groups depending on the consideration of the time parameter:

Based on discounted estimates;

Based on accounting estimates.

1. based on discounted estimates ("dynamic" methods):

Net Present Value - NPV(Net Present Value);

Return on investment index - PI(Profitability Index);

Internal rate of return - IRR(Internal Rate of Return);

Modified internal rate of return- MIRR(Modified Internal Rate of Return);

Discounted payback period of investment - DPP(Discounted Payback Period).

2. based on accounting estimates (“statistical” methods):

Payback period of investments - PP(Payback period);

Investment efficiency ratio - ARR(Accounted Rate of Return).

Net present value. (NPV). This method is based on comparing the value of the original investment (IC) with the total discounted net cash flow generated by it over the forecast period. Since cash inflows are spread over time, they are discounted by a factor r set by the analyst (investor) on their own based on the annual percentage return that they want or can have on their capital invested.

Suppose a forecast is made that an investment (IC) will generate, over n years, annual returns of P 1 , P 2 , ..., P n . The total accumulated value of discounted income (PV) and the net present effect (NPV) are respectively calculated by the formulas:

, (5.1)

. (5.2)

Obviously, if: NPV > 0, then the project should be accepted;

NPV< 0, то проект следует отвергнуть;

NPV = 0, then the project is neither profitable nor unprofitable.

When forecasting income by years, it is necessary to take into account, if possible, all types of income, both industrial and non-productive, that may be associated with this project. So, if at the end of the project implementation period it is planned to receive funds in the form of the salvage value of equipment or the release of part of working capital, they should be taken into account as income of the corresponding periods.

If the project involves not a one-time investment, but a consistent investment of financial resources over m years, then the formula for calculating NPV is modified as follows:

, (5.3)

where i is the projected average inflation rate.

Manual calculation using the above formulas is quite laborious, therefore, for the convenience of using this and other methods based on discounted estimates, special statistical tables have been developed in which the values of compound interest, discount factors, and discounted value are tabulated monetary unit etc. depending on the time interval and the value of the discount factor.

It should be noted that the NPV indicator reflects the predictive assessment of the change in the economic potential of the enterprise in the event that the project under consideration is accepted. This indicator is additive in terms of time, i.e. NPV of various projects can be summed up. This is a very important property that distinguishes this criterion from all the others and allows it to be used as the main one when analyzing the optimality of an investment portfolio.

Return on investment index. (PI). This method is essentially a consequence of the net present value method. Profitability Index (PI) is calculated by the formula:

. (5.4)

Obviously, if: PI > 1, then the project should be accepted;

PI< 1, то проект следует отвергнуть;

PI = 1, then the project is neither profitable nor unprofitable.

The logic of the PI criterion is as follows: it characterizes income per unit of costs; it is this criterion that is most preferable when it is necessary to streamline independent projects in order to create an optimal portfolio in the case of a limited amount of investment from above.

Unlike the net present effect, the profitability index is a relative indicator. Due to this, it is very convenient when choosing one project from a number of alternative ones that have approximately the same NPV values. or when completing an investment portfolio with the maximum total NPV value.

Internal rate of return of investment. (IRR). The second standard method for evaluating the effectiveness of investment projects is the method of determining internal norm project profitability (internal rate of return, IRR), i.e. the discount rate at which the net present value is zero.

IRR = r, where NPV = f(r) = 0.

The meaning of calculating this ratio when analyzing the effectiveness of planned investments is as follows: IRR shows the maximum allowable relative level of expenses that can be associated with a given project. For example, if the project is fully financed by a loan from a commercial bank, then the IRR value shows the upper limit of the acceptable level of the bank interest rate, the excess of which makes the project unprofitable.

The economic meaning of this indicator is as follows: an enterprise can make any decisions of an investment nature, the level of profitability of which is not lower than the current value of the CC indicator (or the price of the source of funds for this project, if it has target source). It is with him that the IRR indicator calculated for a specific project is compared, while the relationship between them is as follows.

If: IRR > CC. then the project should be accepted;

IRR< CC, то проект следует отвергнуть;

IRR = CC, then the project is neither profitable nor unprofitable.

Practical use This method is complicated if the analyst does not have a specialized financial calculator at his disposal. In this case, the method of successive iterations is applied using tabulated values of discount factors. To do this, using tables, two values of the discount factor r 1

, (5.5)

where r 1 is the value of the tabulated discount factor at which f(r 1)>0 (f(r 1)<0);

r 2 - the value of the tabulated discount factor at which f(r 2)<О (f(r 2)>0).

The calculation accuracy is inversely proportional to the length of the interval (r 1 ,r 2), and the best approximation using tabulated values is achieved when the length of the interval is minimal (equal to 1%), i.e. r 1 and r 2 - the nearest to each other values of the discount coefficient that satisfy the conditions (in case of changing the sign of the function from "+" to "-"):

r 1 - the value of the tabulated discount factor, minimizing the positive value of the NPV indicator, i.e. f(r 1)=min r (f(r)>0);

r 2 - the value of the tabulated discount factor, maximizing the negative value of the NPV indicator, i.e. f(r 2)=max r (f(r)<0}.

By mutual replacement of the coefficients r 1 and r 2, similar conditions are written for the situation when the function changes sign from "-" to "+".

Payback period of investment.(PP). This method is one of the simplest and most widespread in world practice, it does not imply a temporal ordering of cash receipts. The algorithm for calculating the payback period (RR) depends on the uniformity of the distribution of projected income from the investment. If the income is evenly distributed over the years, then the payback period is calculated by dividing the one-time costs by the amount of annual income due to them. When a fractional number is received, it is rounded up to the nearest whole number. If profits are unevenly distributed, then the payback period is calculated by directly counting the number of years during which the investment will be repaid with cumulative income. The general formula for calculating the PP indicator is as follows:

РР = n, at which Рк > IC.

The indicator of the payback period of investments is very simple in calculations, however, it has a number of disadvantages that must be taken into account in the analysis.

First, it does not take into account the impact of income from recent periods. Second, because this method is based on undiscounted estimates, it does not distinguish between projects with the same amount of cumulative returns but different distributions over the years.

Investment efficiency ratio. (ARR). This method has two characteristic features: it does not involve discounting income indicators; income is characterized by the net profit indicator PN (balance sheet profit minus deductions to the budget). The calculation algorithm is extremely simple, which predetermines the widespread use of this indicator in practice: the investment efficiency ratio (ARR) is calculated by dividing the average annual profit PN by the average investment value (the coefficient is taken as a percentage). The average investment is found by dividing the initial amount of capital investments by two, if it is assumed that after the expiration of the analyzed project, all capital costs will be written off; if residual value (RV) is allowed, its valuation should be excluded.

(5.6)

Example:

The company is faced with a choice between two investment projects characterized by the following data:

Projects	IC	C1	C2
BUT	-4000
B	-2000

Rank projects according to IRR, PP, NPV criteria if r = 10%.

Solution.

1) net present value

for project A:

= = $752.07

for project B:

= = $330.58

2) payback period of the project:

for project A:

1 year + = 1.5 years or 1 year and 6 months

for project B:

1 year + = 1.53 years or 1 year and 6 months

3) the internal rate of return of the project is calculated by the formula:

, where

r 1 is the value of the discount factor at which NPV > 0 (NPV<0);

r 2 - the value of the discount factor at which NPV<0 (NPV > 0);

IRR is calculated using a linear approximation.

For project A:

NPV 1 (r=10%) = = $752.07

NPV 2 (r=25%) = = -80 USD

= 23,56%.

For project B:

NPV 1 (r=10%) = = $330.58

NPV 2 (r=25%) = = -80 USD

= 22,08%.

Comparison of two projects according to the calculated criteria indicates that preference should be given to project A, since its net present value and internal rate of return are higher than those of project B. Therefore, project A is more expedient than project B.

SUMMARY

Investments are, first of all, cash, securities, other property, including property rights having a monetary value, invested in objects of entrepreneurial and (or) other activities in order to make a profit and (or) achieve another beneficial effect. Distinguish, first of all, real and financial investments.

Any organization can face the problem of alternative implementation of real or financial investments. At the same time, it is recommended to optimize the ratio of the volumes of real and financial investment in the process of developing the appropriate policy of the enterprise based on a number of factors: the functional orientation of the enterprise, the stage of the life cycle of the enterprise, the size of the enterprise, the nature of strategic changes in the operating activities of the enterprise, the predicted interest rate in the financial market, projected rate of inflation.

An investment project is a planned and ongoing set of measures to invest capital in various industries and sectors of the economy in order to increase it. In form, it is a set of documents to justify the economic feasibility, volume and timing of capital investments, including the necessary design and estimate documentation developed in accordance with the legislation of the Russian Federation and duly approved standards (norms and rules), as well as a description practical actions for the implementation of investments (business plan).

All financial sources of investment are divided into own (internal) and external. To own funds of enterprises and organizations implementing investment projects, include: depreciation charges on existing funds (for their renovation); profit from production and economic activities directed to production development; amounts received from insurance companies in the form of compensation for damage as a result of natural disasters and accidents; funds from the sale of unnecessary surplus fixed assets and the immobilization of surplus working capital; funds from the sale of intangible assets (government securities, securities of other enterprises, patents, ownership of industrial product designs, production methods, etc.). The own sources of investment of enterprises and organizations also include funds attracted by them from other sources: funds received as a result of the issue and sale of shares and other securities by the investor; funds of other enterprises and organizations involved in the investment project as partners and on the relevant terms of participation in the distribution of dividends; funds allocated by superior holding and joint-stock companies, industrial and financial groups on an irrevocable basis; state subsidies, various kinds of monetary contributions and donations from regional and local budgets, entrepreneurship support funds, etc., provided free of charge. To external sources of investment include various forms of borrowed funds, as well as: allocations from the federal, regional and local budgets, various funds to support entrepreneurship, provided free of charge; foreign investments provided in the form of financial or other tangible and intangible participation in the authorized capital of joint ventures.

The investment strategy is a part of the overall financial strategy of the enterprise, the main purpose of which is a profitable investment of funds and the timely and complete renewal of the non-current assets of the enterprise. The initial prerequisite for the formation of an investment strategy is the general strategy for the economic development of the company (firm). In relation to it, the investment strategy is subordinate and must be consistent with it in terms of goals and stages of implementation. At the same time, the investment strategy is considered as one of the main factors for ensuring the effective development of the company in accordance with the general economic strategy chosen by it.

The classification of investment strategies of enterprises involves the allocation of so-called "pure" (if there is only one motive) and "mixed" investment strategies (if more than one motive is indicated). All "pure" strategies are typical, and among the mixed ones - motivated as "maintaining capacities with intensification" and "modernization of production", "expansion of production with product renewal" (note that they are used even somewhat more often than "pure" investment strategies, corresponding to the second motive), "intensification and modernization of production with its expansion" and "maintenance of capacities with the renewal of products."

If we rank the motives of investment activity according to their "progressiveness", from relatively conservative "capacity maintenance" to "release of new products", then the types of "pure" investment strategies can be defined as: conservative (the corresponding motive for investment activity is "capacity maintenance"); extensive ("expansion of existing production"); intensive (“intensification and modernization of production”); progressive ("release of new products"). The "mixed" types of strategies include: conservative-intensive ("capacity maintenance with intensification and modernization of production"); extensively progressive (“expansion of production with the renewal of products”); extensive-intensive (“expansion of production with its intensification and modernization”); conservative-progressive (“maintaining capacities with product renewal”).

The methods used in the evaluation of investment projects can be divided into two groups depending on the time parameter: those based on discounted valuations (net present value, return on investment index, internal rate of return, modified internal rate of return, discounted payback period of investments) and those based on accounting estimates (payback period, investment efficiency ratio).

Test questions

1. What are investments and what are their main types?

2. What characterizes the investment activity of the enterprise?

3. What criterion underlies the division of investments into direct and portfolio ones? How do these forms of investment compare with real and financial investments?

4. What factors should be considered when choosing investment projects?

5. What criteria for evaluating investment projects do you know? Give a brief description and evaluate the scope of each investment criterion.

6. How does the inflation rate affect the performance of investment projects?

7. Should a 15-year project requiring an investment of $150,000 be accepted if no income is expected in the first 5 years and an annual income of $50,000 in the next 10 years?

LEARNING SITUATION

Canadian company Agrimax Inc. undertook to invest 168 million dollars. in the development of technologies based on the Russian "discovery" - an autonomous energy source based on materials such as quartz sand. The contract providing for these investments was signed in February 200X in the presence of the Russian prime minister and his Canadian counterpart. They hardly guessed that official science considers the “discovery” of pure water to be charlatanism.

The authors of the project - specialists from the Volgograd research and production center "GRUS" - could not clearly explain the essence of their discovery at a special press conference. In addition, there were no scientific publications on the declared topic at all. Meanwhile, the authors of the project will receive royalties from the construction of two new plants (one each in Russia and Canada) for the implementation of "alternative energy technology." In general, the business of Katsabanis, the owner of Agrimax Inc., has nothing to do with high technologies.

Questions:

1. What type of investments are included in the described project?

2. How promising is this investment project?

3. What risks are inherent in the implementation of this investment project?

1. Baranov V.V. Financial management / V.V. Baranov. – M.: Delo, 2002.

2. Melkumov Ya.S. Economic assessment of the effectiveness of investments and financing of investment projects / Ya.S. Melkumov. - M.: Finance and statistics, 1997.

3. Limitovsky M.A. Fundamentals of evaluation of investment and financial decisions / M.A. Limitovsky. – M.: DeKA, 1997.

4. Chetyrkin E.M. Financial analysis of industrial investments / E.M. Chetyrkin. – M.: Delo, 1998.

5. Grechishkina M.V. The choice of the optimal investment option (optimization approach) / M.V. Grechishkina, D.E. Ivakhnik // Financial management. - 2006. - No. 3. - S. 82-96.

6. Kovalev V.V. Methods for evaluating investment projects / V.V. Kovalev. - M., 2004.

7. The main criteria for the effectiveness of an investment project and methods for their evaluation

7. 1. General characteristics of methods for evaluating effectiveness

The international practice of assessing the effectiveness of investments is essentially based on the concept of the time value of money and is based on the following principles:

Evaluation of the effectiveness of the use of invested capital is carried out by comparing cash flow(cash flow), which is formed during the implementation of the investment project and the initial investment. The project is recognized as effective if the return of the initial investment amount and the required return for the investors who provided the capital are ensured.
Invested capital as well as cash flow are adjusted to the present time or to a certain settlement year (which usually precedes the start of the project).
The process of discounting capital investments and cash flows is carried out at various discount rates, which are determined depending on the characteristics of investment projects. When determining the discount rate, the structure of investments and the cost of individual components of capital are taken into account.

The essence of all assessment methods is based on the following simple scheme: The initial investment in the implementation of any project generates cash flow CF 1 , CF 2 , ... , CF n . Investments are recognized as effective if this flow is sufficient for

return of the initial amount of capital investments and

ensuring the required return on invested capital.

The most common indicators of the effectiveness of capital investments are:

discounted payback period (DPB).
net present value of the investment project (NPV),
internal rate of return (profitability, profitability) (IRR),

These indicators, as well as the corresponding methods, are used in two versions:

to determine the effectiveness of independent investment projects (the so-called absolute efficiency), when it is concluded whether to accept the project or reject it,
to determine the effectiveness of mutually exclusive projects (comparative efficiency), when a conclusion is made about which project to accept from several alternative ones.

7. 2. Discounted payback method

Let's consider this method on a specific example of the analysis of two mutually exclusive projects.

Example 1 . Let both projects involve the same investment of $1,000 and are designed for four years.

Project A generates the following cash flows: for years 500, 400, 300, 100, and project B - 100, 300, 400, 600. The project capital cost is estimated at 10%. Calculation discounted term carried out using the following tables.

Table 7.1.
Project A

The third line of the table contains the discounted values of the company's cash income as a result of the implementation of the investment project. In this case, it is appropriate to consider the following interpretation of discounting: reduction sum of money to the present time corresponds to the allocation of this amount of that part of it, which corresponds to the income of the investor, which is provided to him for the fact that he provided his capital. Thus, the remaining part of the cash flow is designed to cover the original investment. The fourth row of the table contains the values of the uncovered part of the original investment. Over time, the size of the uncovered part decreases. So, by the end of the second year, only $214 remains uncovered, and since the discounted value of the cash flow in the third year is $225, it becomes clear that the investment coverage period is two full years and some part of the year. More specifically for the project, we get:

Similarly, for the second project, the calculation table and the calculation of the discounted payback period are as follows.

Table 7.2.
Project V.

Based on the calculation results, it is concluded that project A is better because it has a shorter discounted payback period.

A significant disadvantage of the discounted payback period method is that it takes into account only the initial cash flows, namely those flows that fit into the payback period. All subsequent cash flows are not taken into account in the calculation scheme. So, if in the framework of the second project in the last year the flow was, for example, $1000, then the result of calculating the discounted payback period would not change, although it is quite obvious that the project would become much more attractive in this case.

7. 3. Method of pure modern value (NPV - method)

This method is based on the concept of Net Present Value.

where CF i- Net cash flow,
r- the cost of capital raised for an investment project.

The term “pure” has the following meaning: each amount of money is defined as the algebraic sum of input (positive) and output (negative) flows. For example, if in the second year of the investment project the capital investment is $15,000 and the cash income in the same year is $12,000, then the net cash in the second year is ($3,000).

In accordance with the essence of the method, the current value of all input cash flows is compared with the current value of output flows due to capital investments for the project. The difference between the first and the second is a pure modern value, the magnitude of which determines the decision rule.

method procedure.

Step 1. The current value of each cash flow, input and output, is determined.

Step 2. All discounted values of cash flow elements are summed up and the NPV criterion is determined.

Step 3. A decision is made:

for a single project: if NPV is greater than or equal to zero, then the project is accepted;
for several alternative projects: the project with the highest NPV is accepted, provided it is positive.

Example 2 . The management of the enterprise is going to introduce a new machine that performs operations that are currently performed manually. The machine is worth $5,000 with a 5 year lifespan and zero salvage value. According to the financial department of the enterprise, the introduction of the machine by saving manual labor will provide an additional input stream of $1,800. In the fourth year of operation, the machine will require repairs costing $300.

Is it economically feasible to introduce a new machine if the enterprise's cost of capital is 20%.

Solution. Let us present the conditions of the problem in the form of concise initial data.

We will calculate using the following table.

Table 7.3.
Calculation of the NPV value

Name of cash flow	Monetary	Discounting multiplier 20% *	The present the value of money
Initial investment
Input cash flow
Car repairs
Present Net Value (NPV)

* The discount multiplier is determined using financial tables.

As a result of the calculations, NPV = $239 > 0, and therefore, from a financial point of view, the project should be accepted.

Now it is appropriate to dwell on the interpretation of the value of NPV. It is obvious that the amount of $239 represents some “margin of safety” designed to compensate for a possible error in forecasting cash flows. American financial managers they say - this is money set aside for a “rainy day”.

Let us now consider the question of the dependence of the indicator and, consequently, the conclusion made on its basis, on the rate of return on investment. In other words, within the framework of this example, we will answer the question, what if the rate of return on investment (the cost of capital of the enterprise) becomes greater. How should the NPV value change?

The calculation shows that at r= 24% we get NPV = ($186), that is, the criterion is negative and the project should be rejected. The interpretation of this phenomenon can be carried out as follows. What does a negative NPV mean? The fact that the initial investment does not pay off, i.e. the positive cash flows generated by this investment are not sufficient to offset, given the time value of money, the original capital investment. Recall that the cost of a company's equity is the rate of return on alternative investments of its capital that the company can make. At r= 20% of the company is more profitable to invest in its own equipment, which, due to savings, generates a cash flow of $1,800 over the next five years; and each of these amounts, in turn, is invested at 20% per annum. At r= 24% of the company, it is more profitable to immediately invest its $5,000 at 24% per annum than to invest in equipment that, due to savings, will “bring” a cash income of $1,800, which in turn will be invested at 24% per annum.

The general conclusion is as follows: with an increase in the rate of return on investments (the cost of capital of an investment project), the value of the NPV criterion decreases.

To complete the presentation of the information necessary for calculating NPV, we present typical cash flows.

Typical input cash flows:

additional sales volume and increase in the price of goods;
reduction of gross costs (reduction of the cost of goods);
residual value of equipment cost at the end last year investment project (since the equipment may be sold or used for another project);
release of working capital at the end of the last year of the investment project (closing of accounts receivable, sale of inventory balances, sale of shares and bonds of other enterprises).

Typical output streams:

initial investment in the first year(s) of the investment project;
increase in the need for working capital in the first year(s) of the investment project (increase in accounts receivable to attract new customers, purchase of raw materials and components to start production);
repair and maintenance of equipment;
additional non-production costs (social, environmental, etc.).

It was previously noted that the resulting net cash flows are designed to provide a return on the amount of money invested and a return for investors. Let's see how each sum of money is divided into these two parts using the following illustrative example.

Example 3 The company plans to invest in a new fixture that costs $3,170 and has a life of 4 years with zero residual value. Implementation of the fixture is estimated to provide an input cash flow of $1,000 each year. The management of the enterprise allows to make investments only in the case when this leads to a return of at least 10% per year.

Solution . Let's do the usual net present value calculation first.

Table 7.4.
Traditional NPV calculation

Thus, NPV=0 and the project is accepted.

Further analysis consists of splitting the $1,000 input stream into two parts:

return of some part of the original investment,
return on the use of the investment (return to the investor).

Table 7.5.
Cash flow distribution calculation

Investment in relation to the current year	Return on investment	investments	uncovered investment at the end of the year

7. 4. Influence of inflation on the evaluation of investment efficiency

An analysis of the impact of inflation can be made for two options

the inflation rate is different for individual components of resources (input and output),
the rate of inflation is the same for various components of costs and expenses.

As part of the first approach, which is more representative of the real situation, especially in countries with unstable economies, the net present value method is used in its standard form, but all components of expenses and income, as well as discount indicators are adjusted in accordance with the expected inflation rate for years. It is important to note that it is extremely difficult and practically impossible to make a consistent forecast of different inflation rates for different types of resources.

As part of the second approach the influence of inflation is peculiar: inflation affects the numbers (intermediate values) obtained in the calculations, but does not affect the final result and the conclusion regarding the fate of the project. Let's consider this phenomenon on a concrete example.

Example 4 . The company plans to purchase new equipment at a cost of $36,000 that provides $20,000 in cost savings (in cash inflow) per year over the next three years. During this period, the equipment will undergo complete wear and tear. The enterprise's cost of capital is 16% and the expected inflation rate is 10% per year.

First, let's evaluate the project without taking inflation into account. The solution is presented in table. 7.6.

Table 7.6.
Inflation-Free Solution

From the calculations, the conclusion is obvious: the project should be accepted, noting a high margin of safety.

Now we will take into account the effect of inflation in the calculation scheme. First of all, it is necessary to take into account the effect of inflation on the required value of the return index. For this, we recall the following simple reasoning. Let the enterprise plan the real profitability of its investments in accordance with the interest rate of 16%. This means that if you invest $36,000, in a year it should receive $36,000 x (1+0.16) = $41,760. If the inflation rate is 10%, then you need to adjust this amount according to the rate: $41,760 x (1+0.10) = $45,936. The total calculation can be written as follows

$36,000 x (1+0.16) x (1+0.10) = $45,936.

In general, if r p is the real interest rate of return, and T- inflation rate, then the nominal (contract) rate of return will be written using the formula

For the example under consideration, the calculation of the reduced cost of capital is as follows:

Let us calculate the value of the NPV criterion taking into account inflation, i.e. Let's recalculate all cash flows and discount them with a discount rate of 27.6%.

Table 7.7.
Inflation-adjusted solution

The answers of both solutions are exactly the same. The results were the same, since we adjusted for inflation both the input cash flow and the rate of return.

For this reason, most Western firms do not take into account inflation when calculating the effectiveness of capital investments.

7. 5. Internal rate of return (IRR)

By definition, the internal rate of return (sometimes called returns) ( IRR) is the value of the discount rate at which the current value of the investment is equal to the current value of cash flows from investments, or the value of the discount rate at which zero value net present value of the investment.

The economic meaning of the internal rate of return is that it is such a rate of return on investment at which it is equally efficient for an enterprise to invest its capital at IRR percent in any financial instruments or make real investments that generate cash flow, each element of which is in turn invested at IRR percent.

The mathematical definition of the internal rate of return involves solving the following equation

where: CF j- input cash flow in the j-th period,
INV- the value of the investment.

Solving this equation, we find the value IRR. The decision scheme based on the method of internal rate of return has the form:

if the IRR value is higher than or equal to the cost of capital, then the project is accepted,

if the IRR value is less than the cost of capital, then the project is rejected.

Thus, IRR is like a “barrier indicator”: if the cost of capital is higher than the IRR value, then the “capacity” of the project is not enough to provide the necessary return and return on money, and therefore the project should be rejected.

In the general case, the equation for determining the IRR cannot be solved in the final form, although there are a number of special cases when this is possible. Consider an example explaining the essence of the solution.

Example 5. It takes $16,950 to buy a car. The machine will save $3,000 annually over 10 years. The residual value of the car is zero. We need to find the IRR.

Let us find the ratio of the required value of the investment to the annual inflow of money, which will coincide with the multiplier of some (still unknown) discount factor

The resulting value appears in the formula for determining the current value of the annuity

And, therefore, with the help of the financial table. 4 app. we find that for n=10 the discount rate is 12%. Let's check:

Cash flow

12% coefficient.

recalculation

The present

meaning

annual economy

Initial investment

Thus, we have found and confirmed that IRR=12%. The success of the solution was ensured by the coincidence of the ratio of the initial investment amount to the amount of cash flow with a specific value of the discount multiplier from the financial table. In general, interpolation should be used.

Example 6. You want to estimate the value of the internal rate of return of an investment of $6,000 that generates a cash flow of $1,500 over 10 years.

Following the previous scheme, we calculate the discount factor:

According to the table 4 app. for n=10 years we find

So the IRR value is between 20% and 24%.

Using linear interpolation we find

There are more accurate methods for determining IRR, which involve the use of a special financial calculator or an EXCEL electronic processor.

7. 6. Comparison of NPV and IRR methods

Unfortunately NPV and IRR methods can conflict with each other. Let's consider this phenomenon on a concrete example. Let's evaluate the comparative efficiency of two projects with the same initial investment, but with different input cash flows. The initial data for calculating the efficiency are placed in the following table.

Table 7.8
Cash flows of alternative projects

For further analysis, we use the so-called NPV profile, which by definition represents the dependence of the NPV indicator on the cost of project capital.

Let's calculate NPV for different values of the cost of capital.

Table 7.9
NPV indicators for alternative projects

Graphs of NPV profiles for projects will have the form shown in fig. 7.1.

Solving the equations that determine the internal rate of return, we get:

for project A IRR=14.5%,
for project B IRR=11.8%.

Thus, according to the criterion of internal rate of return, preference should be given to project A, as it has a higher IRR value. At the same time, the NPV method gives an ambiguous conclusion in favor of project A.

Rice. 7.1. NPV profiles of alternative projects

After analyzing the ratio of NPV-profiles that have an intersection at the point , which in this case is 7.2%, we come to the following conclusion:

, methods conflict - NPV method accepts project B, IRR method accepts project A.

It should be noted that this conflict occurs only in the analysis of mutually exclusive projects. For individual projects, both methods give the same result, a positive NPV always corresponds to a situation where the internal rate of return exceeds the cost of capital.

7. 7. Making a decision on the criterion of the least cost

There are investment projects in which it is difficult or impossible to calculate the cash income. Projects of this kind arise at an enterprise when it is going to modify technological or transport equipment that takes part in many diverse technological cycles and it is impossible to estimate the resulting cash flow. In this case, the cost of operation acts as a criterion for deciding on the feasibility of investments.

Example 7. The tractor is involved in many production processes. You need to decide whether to use the old one or buy a new one. The initial data for making a decision are as follows.

We calculate all the costs that the company will incur by accepting each of the alternatives. To make a final decision, we bring these costs to the present moment of time (we discount the costs) and choose the alternative that corresponds to the lower value of the discounted costs.

Table 7.10
Calculation of discounted costs when buying a new car

	Monetary flow	Coeff. recalculation for 10%	Real value
Initial investment
residual value old tractor
annual cost exploitation
residual value new tractor
The real value of monetary losses

Table 7.11
Calculation of discounted costs for the operation of the old machine

The current value of discounted costs speaks in favor of buying a new car. In this case, the loss will be $10,950 less .

7. 8. Assumptions made in performance evaluation

In conclusion, we note one important circumstance for understanding investment technologies: what assumptions are made when calculating performance indicators and to what extent they correspond to real practice.

For all methods, the following two assumptions were essentially used.

Cash flows are attributed to the end of the accounting period. In fact, they can appear at any time during the year in question. In the framework of the investment technologies discussed above, we conditionally bring all the cash income of the enterprise by the end of the corresponding year.
Cash flows that are generated by investments are immediately invested in some other project to provide additional income for these investments. It is assumed that the return rate of the second project will be at least the same as the discount rate of the analyzed project.

The assumptions used, of course, do not fully correspond to the real state of affairs, however, given the long duration of projects in general, they do not lead to serious errors in the assessment of effectiveness.

Control questions and tasks

Formulate the basic principles of international practice for evaluating the effectiveness of investments.
What is the main scheme for evaluating the effectiveness of capital investments, taking into account the value of money over time?
List the main indicators of the effectiveness of investment projects.
What is the essence of the discounted payback period method?
How is the discounted payback method applied to the relative effectiveness of alternative capital investments?
State the basic principle of the pure modern value method.
What criterion is used in the analysis of the comparative effectiveness of capital investments using the net present value method?
What is the interpretation of the net present value of the investment project?
How does the net present value change as the discount rate increases?
What economic essence has a discount rate in the net present value method?
List typical input and output cash flows that should be taken into account when calculating the net present value of an investment project.
How is the annual cash income of the enterprise, which is obtained through capital investment, distributed?
What two approaches are used to take into account inflation in the process of evaluating the effectiveness of capital investments?
How is inflation taken into account when estimating the discount rate?
What is the definition of the internal rate of return of an investment project?
Formulate the essence of the method of internal rate of return.
Is it possible to calculate the exact value of the internal rate of return in the general case?
What methods of calculating the internal rate of return do you know?
How to use the internal rate of return method for comparative analysis efficiency of capital investments?
What approach should be used in the comparative evaluation of the effectiveness of capital investments, when it is difficult or impossible to assess the cash income from capital investments?

1. Enterprise requires at least 14 percent return on investment own funds. The company currently has the option to purchase new equipment worth $84,900. The use of this equipment will increase production output, which will ultimately result in $15,000 in additional annual cash income over the 15 years of use of the equipment. Calculate the net present value of the project, assuming zero residual value of the equipment in 15 years.

The calculation will be carried out using the table, finding the discount factor using financial tables.

Name of cash flow	Monetary	Discount multiplier	The present the value of money
Initial investment
Input cash flow
Pure modern value

The net present-day value was found to be positive, suggesting acceptance of the project.

2. The company is planning new capital investments over two years: $120,000 in the first year and $70,000 in the second. The investment project is designed for 8 years with the full development of newly commissioned capacities only in the fifth year, when the planned annual net cash income will be $62,000. The increase in net annual cash income in the first four years according to the plan will be 30%, 50%, 70%, 90%, respectively, for years from the first to the fourth. The enterprise requires at least 16 percent return on investment of cash.

Need to define

1. Determine the net annual cash income in the process of implementing the investment project:

in the first year - $62,000 0.3 = $18,600;

in the second year - $62,000 0.5 = $31,000;

in the third year - $62,000 0.7 = $43,400;

in the fourth year - $62,000 0.9 = $55,800;

in all remaining years - $62,000.

2. We will calculate the net present value of the investment project using the table.

Name of cash flow	Monetary flow	Discount multiplier	The present the value of money
Investment
Investment
cash income
cash income
cash income
cash income
cash income
cash income
cash income
cash income
Net present value of the investment project

3. To determine the discounted payback period, we calculate the net cash flows for the years of the project. To do this, you just need to find the algebraic sum of the two cash flows in the first year of the project. It will be ($60,347) + $16,035 = ($44,312). The rest of the values in the last column of the previous table are pure values.

4. We will calculate the discounted payback period using a table in which we will calculate the accumulated discounted cash flow for the years of the project.

	Discounted cash flow	Accumulated cash flow

The table shows that the number of full years of the project payback is 7. The discounted payback period is therefore

of the year.

3. The company has two options for investing its $100,000. In the first option, the company invests in fixed assets by purchasing new equipment, which after 6 years (the term of the investment project) can be sold for $8,000; the net annual cash income from such an investment is estimated at $21,000.

Under the second option, the company can invest money in working capital (inventory, increase accounts receivable) and this will generate $16,000 in annual net cash income over the same six years. It should be noted that at the end of this period, working capital is released (inventories are sold, accounts receivable are closed).

Which option should be preferred if the company expects a 12% return on the money it invests? Use the pure modern value method.

1. Let us represent the initial data of the problem in a compact form.


Investments in fixed assets ...............................
Investing in working capital...................................
Annual cash income ...............................................
Residual value of the equipment ..........
Release of working capital...................................
Project time .............................................................. ....

Note again that the working capital and equipment are planned to be sold only after 6 years.

2. Calculate the net present value for the first project.

Name cash flow	Monetary flow	Discount multiplier	The present the value of money
Investment
cash income
Sale of equipment.
Pure modern value

3. We will carry out similar calculations for the second project

Name cash flow	Monetary flow	Discount multiplier	The present the value of money
Investment
cash income
Release
Pure modern value

4. Based on the calculation results, the following conclusions can be drawn:

the second project should be recognized as the best;
the first draft should be rejected altogether, even without regard to the available alternative.

4. The company is planning a major investment project involving the acquisition of fixed assets and overhaul equipment, as well as investments in working capital according to the following scheme:

$130,000 - initial investment before the start of the project;
$25,000 - in the first year;
$20,000 - investment in working capital in the second year;
$15,000 - additional investment in equipment in the fifth year;
$10,000 - Year 6 capital repairs.

At the end of the investment project, the company expects to sell the remaining fixed assets at their book value of $25,000 and release part of the current assets worth $35,000.

The scheme for solving the problem remains the same. We compile a table of calculated data and determine the discounted values of all cash flows.

The project should be accepted because its net present value is essentially positive.

Name of cash flow	Monetary flow	Discount multiplier	The present the value of money
Acquisition of fixed assets
Investing in working capital
Cash income in the first year
Investing in working capital
Cash income in the second year
Cash income in the third year
Cash income in the fourth year
Acquisition of fixed assets
Cash income in the fifth year
Repair of equipment
Cash income in the sixth year
Cash income in the seventh year
Cash income in the eighth year
Sale of equipment
Release of working capital
Pure modern value

5. The company requires at least 18 percent return on investment of its own funds. Currently, the company has the opportunity to buy new equipment worth $84,500. The use of this equipment will increase the output, which will ultimately result in $17,000 in additional annual cash income over the 15 years of use of the equipment. Calculate the net present value of the project, assuming that the equipment can be sold at a residual value of $2,500 after the project ends.

6. The company plans new capital investments over three years: $90,000 in the first year, $70,000 in the second, and $50,000 in the third. The investment project is designed for 10 years with the full development of newly commissioned capacities only in the fifth year, when the planned annual net cash income will be $75,000. The increase in net annual cash income in the first four years according to the plan will be 40%, 50%, 70%, 90%, respectively, for years from the first to the fourth. The enterprise requires at least 18 percent return on investment of cash.

Need to define

net present value of the investment project,
discounted payback period.

How will your idea of the effectiveness of the project change if the required return rate is 20%.

7. The company has two options for investing its $200,000. In the first option, the company invests in fixed assets by purchasing new equipment, which in 6 years (the term of the investment project) can be sold for $14,000; the net annual cash income from such an investment is estimated at $53,000.

According to the second option, the company can invest part of the money ($40,000) in the purchase of new equipment, and the remaining amount in working capital (inventory, increase in receivables). This will generate $34,000 in annual net cash income over the same six years. It should be noted that at the end of this period, working capital is released (inventories are sold, accounts receivable are closed).

Which option should be preferred if the company expects a 14% return on the money it invests? Use the pure modern value method.

8. The enterprise is considering an investment project that provides for the acquisition of fixed assets and overhaul of equipment, as well as investments in working capital according to the following scheme:

$95,000 - initial investment before the start of the project;
$15,000 - investment in working capital in the first year;
$10,000 - investment in working capital in the second year;
$10,000 - investment in working capital in the third year;
$8,000 - additional investment in equipment in the fifth year;
$7,000 - year six capital repairs;

At the end of the investment project, the company expects to sell the remaining fixed assets at their book value of $15,000 and release working capital.

The result of the investment project should be the following net (i.e. after taxes) cash income:

9. The project, which requires an investment of $160,000, is expected to generate an annual income of $30,000 over 15 years. Assess the feasibility of such an investment if the discount factor is 15%.

10. The 15 year project requires an investment of $150,000. In the first 5 years, no income is expected, but in the next 10 years, the annual income will be $50,000. Should this project be accepted if the discount factor is 15%?

11. Projects are analyzed ($):

Rank projects according to IRR, NPV criteria, if r = 10%.

12. For each of the projects below, calculate the NPV and IRR if the discount factor is 20%.

14. Compare two projects according to the NPV, IRR criteria, if the cost of capital is 13%:

15. The amount of required investment for the project is $18,000; estimated income: in the first year - $1500, in the next 8 years - $3600 annually. Assess the feasibility of accepting the project if the cost of capital is 10%.

16. The enterprise is considering the feasibility of acquiring a new production line. There are two models on the market with the following parameters ($)

Which project would you like?

* Calculations use average data for Russia

net discounted income;
net present income;
net present value;
net present value;
overall financial result from the implementation of the project;
current value.

The amount of net present value (NPV) is calculated as the difference between the discounted cash flows of income and expenses incurred in the process of implementing the investment over the forecast period.

The essence of the criterion is to compare the present value of future cash receipts from the implementation of the project with the investment costs required for its implementation.

The application of the method involves the sequential passage of the following stages:

Calculation of the cash flow of the investment project.
Selection of a discount rate that takes into account the return on alternative investments and the risk of the project.
Determination of net present value.

NPV or NPV for a constant discount rate and a one-time initial investment is determined by the following formula:

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where

i - discount rate.

Cash flows must be calculated at current or deflated prices. When forecasting income by year, it is necessary, if possible, to take into account all types of Income, both industrial and non-productive, that may be associated with this project. So, if at the end of the project implementation period it is planned to receive funds in the form of the salvage value of equipment or the release of part of working capital, they should be taken into account as income of the corresponding periods.

This method is based on the premise that the value of money varies over time. The process of converting the future value of the cash flow into the current value is called discounting (from the English. Discont - to reduce).

The rate at which discounting takes place is called the discount rate (discount), and the factor F=1/ (1 + i) t is the discount factor.

If the project involves not a one-time investment, but a consistent investment of financial resources over a number of years, then the formula for calculating NPV is modified as follows:

where
I 0 - the value of the initial investment;
C t - cash note from the sale of investments at time t;
t - calculation step (year, quarter, month, etc.);
i - discount rate.

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The conditions for making an investment decision based on this criterion are as follows:
if NPV > 0, then the project should be accepted;
if NPV< 0, то проект принимать не следует;
if NPV = 0, then the adoption of the project will bring neither profit nor loss.

This method is based on following the main target set by the investor - maximizing its final state or increasing the value of the company. Following this target setting is one of the conditions for a comparative evaluation of investments based on this criterion.

The negative value of the net present value indicates the inexpediency of making decisions on financing and implementing the project, since if NPV< 0, то в случае принятия проекта ценность компании уменьшится, т. е. владельцы компании понесут убыток и основная целевая установка не выполняется.

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A positive value of the net present value indicates the feasibility of making decisions on financing and implementing the project, and when comparing investment options, the option with the highest NPV is considered preferable, because if NPV > 0, then if the project is accepted, the value of the company, and hence the well-being of its owners will increase. If NPV = 0, then the project should be accepted provided that its implementation will increase the flow of income from previously implemented capital investment projects. For example, the extension land plot for the hotel car park will boost the real estate income stream.

The implementation of this method involves a number of assumptions that need to be checked for the degree of their correspondence to reality and for what results possible deviations lead to.

Such assumptions include:

the existence of only one objective function - the cost of capital;
the specified period for the implementation of the project;
data reliability;
belonging of payments to certain points in time;
the existence of a perfect capital market.

When making decisions in the investment sphere, one often has to deal not with one goal, but with several goals. In the case of using the method of determining the cost of capital, these objectives should be taken into account when finding a solution outside the process of calculating the cost of capital. At the same time, methods for making multi-purpose decisions can also be analyzed.

The useful life should be established in the performance analysis before applying the cost of capital method. To this end, methods for determining the optimal service life can be analyzed, unless it is established in advance for technical or legal reasons.

In reality, when making investment decisions, there is no reliable data. Therefore, along with the proposed method for calculating the cost of capital based on predicted data, it is necessary to analyze the degree of uncertainty, at least for the most important investment objects. This purpose is served by methods of investing in conditions of uncertainty.

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When forming and analyzing the method, it is assumed that all payments can be attributed to certain points in time. The time interval between payments is usually one year. In fact, payments can be made at shorter intervals. In this case, you should pay attention to the compliance of the settlement period step (calculation step) with the condition for granting a loan. For the correct application of this method, it is necessary that the calculation step be equal to or a multiple of the term for calculating interest on the loan.

Also problematic is the assumption of a perfect capital market, in which financial resources can be attracted or invested at a single calculated interest rate at any time and in unlimited quantities. In reality, such a market does not exist, and interest rates for investing and borrowing funds tend to differ from each other. As a result, the problem of determining an appropriate interest rate arises. This is especially important as it has a significant impact on the cost of capital.

When calculating NPV, different discount rates can be used over the years. In this case, it is necessary to apply individual discount factors to each cash flow, which will correspond to this calculation step. In addition, it is possible that a project that is acceptable at a constant discount rate may become unacceptable at a variable one.

The net present value indicator takes into account the time value of money, has clear decision criteria and allows you to select projects to maximize the value of the company. In addition, this indicator is an absolute indicator and has the property of additivity, which allows you to add the values of the indicator by various projects and use the total indicator for projects in order to optimize the investment portfolio.

With all its advantages, the method also has significant disadvantages. Due to the difficulty and ambiguity of forecasting and generating cash flow from investments, as well as the problem of choosing a discount rate, there may be a danger of underestimating the risk of a project.

The profitability index (profitability, profitability) is calculated as the ratio of the net present value of cash inflow to the net present value of cash outflow (including initial investment):

where I 0 - investments of the enterprise at time 0;
C t - cash flow of the enterprise at time t;
i - discount rate.
P k - the balance of the accumulated flow.

The conditions for accepting a project under this investment criterion are as follows:

if PI > 1, then the project should be accepted;
if PI< 1, то проект следует отвергнуть;
if PI = 1, the project is neither profitable nor unprofitable.

It is easy to see that when evaluating projects involving the same amount of initial investment, the PI criterion is fully consistent with the NPV criterion.

Thus, the PI criterion has an advantage when choosing one project from a number of projects with approximately the same MPV values, but different amounts of required investments. In this case, the one that provides greater efficiency of investments is more profitable. In this regard, this indicator allows you to rank projects with limited investment resources.

The disadvantages of the method include its ambiguity when discounting cash inflows and outflows separately.

Under the internal rate of return, or internal rate of return, investment (JRR) understand the value of the discount rate at which the NPV of the project is zero:
IRR=i, where NPV= f(i)=0

In practice, any enterprise finances its activities from various sources. As a payment for the use of advances in the activities of the enterprise financial resources it pays interest, dividends, remuneration, etc., i.e., incurs some reasonable expenses for maintaining its economic potential. An indicator that characterizes the relative level of these incomes can be called the price of advanced capital (capital cost - CC). This indicator reflects the minimum return on the capital invested in its activities, its profitability, which has developed at the enterprise, and is calculated using the weighted arithmetic average formula.

The economic meaning of this indicator is as follows: an enterprise can make any decisions of an investment nature, the level of profitability of which is not lower than the current value of the CC indicator (price of the source of funds for this project). It is with him that the IRR indicator calculated for a specific project is compared, while the relationship between them is as follows:

if IRR > СС, then the project should be accepted;
if IRR< СС, то проект следует отвергнуть;
if IRR = CC, then the project is neither profitable nor unprofitable.

Another interpretation is to interpret the internal rate of return as a possible discount rate at which the project is still profitable according to the NPV criterion. The decision is made on the basis of comparing the IRR with the standard profitability; at the same time, the higher the values of the internal rate of return and the greater the difference between its value and the selected discount rate, the greater the safety margin of the project. This criterion is the main guideline in making an investment decision by an investor, which does not detract from the role of other criteria.

To calculate IRR using discount tables, two values of the discount factor i 1 are selected< i 2 таким образом, чтобы в интервале (i 1 ,i 2) функция NPV = f(i) меняла свое значение с "+" на "-" или с "-" на "+".

where i 1 - the value of the discount factor, at which f (i 1) > O (f (i 1)< 0),
r 2 - the value of the discount factor at which f (i 2)< 0 < f(i 2) > 0).

Modified rate of return (MIRR) eliminates a significant drawback of the internal rate of return of the project, which occurs in the case of repeated cash outflows. An example of such repeated outflows is an installment purchase or construction of a property over several years. The main difference of this method is that reinvestment is carried out at a risk-free rate, the value of which is determined on the basis of an analysis of the financial market.

AT Russian practice it can be the profitability of a fixed-term foreign currency deposit offered savings bank Russia. In each case, the analyst determines the risk-free rate individually, but, as a rule, its level is relatively low.

Thus, discounting costs at a risk-free rate makes it possible to calculate their total present value, the value of which allows a more objective assessment of the level of investment return, and is a more correct method in case of making investment decisions with extraordinary cash flows.

The Discounted Payback Period (DPP) eliminates the disadvantage of the static payback period method and takes into account the time value of money, and the corresponding formula for calculating the discounted payback period, DPP, is:
DPP = min n, at which

Obviously, in the case of discounting, the payback period increases, i.e. always DPP > PP.

The simplest calculations show that such a technique under conditions of a low discount rate, characteristic of a stable Western economy, improves the result by an imperceptible amount, but for a much higher discount rate characteristic of the Russian economy, this gives a significant change in the calculated value of the payback period. In other words, a project that is acceptable under the PP criterion may not be acceptable under the DPP criterion.

When using the PP and DPP criteria in the evaluation of investment projects, decisions can be made based on the following conditions:
a) the project is accepted if the payback takes place;
b) the project is accepted only if the payback period does not exceed the deadline set for a particular company.

In general, the definition of the payback period is of an auxiliary nature with respect to the net present value of the project or the internal rate of return. In addition, the disadvantage of such an indicator as the payback period is that it does not take into account subsequent cash inflows, and therefore may serve as an incorrect criterion for the attractiveness of the project.

The most common static indicator for evaluating investment projects is payback period (Payback Period - PP).

The payback period is understood as the period of time from the start of the project until the moment of operation of the facility, in which the income from operation becomes equal to the initial investment (capital costs and operating costs).

This indicator gives an answer to the question: when will the full return on invested capital occur? The economic meaning of the indicator is to determine the period for which the investor can return the invested capital.

To calculate the payback period, the elements of the payment series are summed up on an accrual basis, forming the balance of the accumulated flow, until the amount takes a positive value. The sequence number of the planning interval, in which the accumulated flow balance takes a positive value, indicates the payback period, expressed in planning intervals.

The general formula for calculating the PP indicator is as follows:
РР = min n, at which

where P t - the value of the balance of the accumulated flow;
1 B - the value of the initial investment.

When a fractional number is received, it is rounded up to the nearest whole number. Often, the RR indicator is calculated more accurately, i.e., the fractional part of the interval (billing period) is also considered; at the same time, it is assumed that within one step (calculated period), the balance of accumulated cash flow changes linearly. Then the "distance" from the beginning of the step to the moment of payback (expressed in the duration of the calculation step) is determined by the formula:

where P to - - the negative value of the balance of the accumulated flow at the step until the payback;
P k+ - positive value of the accumulated flow balance at the step after the payback moment.

For projects that have a constant income at regular intervals (for example, an annual income of a constant value - an annuity), you can use the following payback period formula:
PP = I 0 /A

where PP is the payback period in planning intervals;
I 0 - the amount of initial investment;
A is the size of the annuity.

It should be borne in mind that the elements of the payment series in this case must be ordered by sign, i.e., first the outflow of funds (investments) is meant, and then the inflow. Otherwise, the payback period may be calculated incorrectly, since when the sign of the payment series is reversed, the sign of the sum of its elements may also change.

Initial investment

Annual Savings

Annual Savings

Annual Savings

Pure modern value

Another indicator of static financial evaluation project is the investment efficiency ratio (Account Rate of Return or ARR). This ratio is also called the accounting rate of return or the profitability ratio of the project.

There are several algorithms for calculating ARR.

The first calculation option is based on the ratio of the average annual profit (minus deductions to the budget) from the implementation of the project for the period to the average investment:
ARR =P r /(1/2)I cf.0

where R r is the average annual profit (minus deductions to the budget) from the implementation of the project,
I cf.0 - average value initial investment, if it is expected that at the end of the project life all capital costs will be written off.

Sometimes the profitability of the project is calculated based on the initial investment:
ARR = P r /I 0

Calculated on the basis of the initial investment, it can be used for projects that create a stream of uniform income (for example, an annuity) for an indefinite or sufficiently long period.

The second calculation option is based on the ratio of the average annual profit (minus deductions to the budget) from the implementation of the project for the period to the average investment, taking into account the residual or salvage value of the initial investment (for example, taking into account the salvage value of equipment at the end of the project):
ARR= P r /(1/2)*(I 0 -I f),

where P r - the average annual profit (minus deductions to the budget) from the implementation of the project;
I 0 - the average value of the initial investment;
I f is the residual or salvage value of the initial investment.

The advantage of the investment performance indicator is the ease of calculation. At the same time, it also has significant drawbacks. This indicator does not take into account the time value of money and does not imply discounting, respectively, does not take into account the distribution of profits over the years, and, therefore, is applicable only to assess short-term projects with a uniform income. In addition, it is not possible to assess the possible differences in projects associated with different implementation periods.

Since the method is based on the use accounting characteristics investment project - the average annual profit, then the investment efficiency ratio does not quantify the growth of the company's economic potential. However given coefficient provides information on the impact of investments. For the company's financial statements. Indicators financial statements sometimes they are the most important in the analysis by investors and shareholders of the attractiveness of the company.

This material was prepared according to the book "Commercial Investment Appraisal"
Authors: I.A. Buzova, G.A. Makhovikova, V.V. Terekhov. Publishing house "PITER", 2003.

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