Irr should be. What is the IRR of an investment project, how to calculate it correctly and why is it so important? Data analysis

Internal rate of return (other names - IRR, internal discount rate, internal rate of return, internal efficiency ratio, Internal Rate of Return, IRR).

In the most common case of investment projects that start with (investment) costs and have positive net cash receipts, the internal rate of return is a positive number of units if:

At the discount rate E = EB, the net present value of the project becomes 0,
is the only number.

In a more general case, the internal rate of return is such a positive number of EB that at the discount rate E = EB the net present value of the project turns to 0, for all large values of E it is negative, for all smaller values of E it is positive. If at least one of these conditions is not met, it is considered that the GNI does not exist.

In order to make it easier to understand the category of GNI, we will agree that for now we will talk about such investment projects, during the implementation of which:

It is necessary first to carry out the costs of funds (to allow an outflow of funds) and only then can one count on cash receipts (inflows of funds);
- cash receipts are cumulative in nature, and their sign changes only once (i.e. at first they can be negative, but, becoming then positive, they will remain so throughout the entire billing period).

IRR stands for Internal Rate of Return, which translates into Russian as "internal rate of return". This is the name of one of the two main methods for evaluating investment projects. There are many articles on the Internet that are a summary of this topic in financial analysis textbooks. Their common disadvantage is that they have too much math and too little explanation.

IRR or internal rate of return is the rate of interest at which the present value of all cash flows of an investment project (i.e. NPV) is zero. This means that at this rate of interest, the investor will be able to recover his initial investment, but no more.

Internal rate of return

The Internal Rate of Return (IRR) is the discount rate at which the Net Present Value (NPV) equals zero. In other words, this indicator reflects the break-even rate of return of the project.

In practice, the IRR value is calculated:

1. Graphically - the most popular method, it also offers the opportunity to demonstratively analyze various options for applying the discount rate in the project.
2. With the help of specialized programs, for example, in Microsoft Excel, the function = VSD is used to calculate the IRR value.

The internal rate of return (IRR) is equal to the maximum interest rate of a bank loan for the full financing of an investment project, in the implementation of which the profit of the enterprise is equal to zero. At the same time, credit funds should be provided by the bank and be repayable at the time and in the amount corresponding to the dynamics of investments and net cash receipts in the project under consideration.

The internal rate of return (yield, profitability) can be interpreted as annual net cash receipts (profit or income in financial terms) created on capital not realized during a certain period, or, in other words, it can be interpreted as the highest annuity rate after tax (annual debt repayment rate), at which the project can increase funds - provided that the annual cash flows are more or less constant.

The internal rate of return is defined as the rate of interest at which the value of the initial investment is equal to the value of the present value of future additional income. The advantage of the internal rate of return method is that it takes into account the time value of money. Its disadvantage is the complexity of the calculations.

The internal rate of return is defined as a discount factor that brings multi-temporal balance values to the beginning of the project.

The internal rate of return is equal to the value of r for which this equation is true.

Internal rate of return (IRR) It allows you to determine the economic viability of the project differently than reduction to current values.

Internal rate of return - characterizes the level of profitability of the project, expressed as a discount rate, at which the future value of the net cash flow from investments will be equal to the present value of investments.

The internal rate of return is the limit beyond which the project becomes ineffective. This indicator gives the investor the opportunity to compare the profitability of the project with the level of profitability of existing assets, with the average rate of return on investments, with the% rates at which loans are issued, with WACC, as well as with the amount of risk.

The internal rate of return is the discount value at which the NPV for the billing period is zero. The project's IRR reflects the expected annual interest on capital investment in the development of the field. IRR cannot be calculated in the following situations: all annual cash flows are negative, all annual cash flows are positive, and the amount of undiscounted profit is less than the amount of costs.

The Internal Rate of Return, IRR, is the discount rate at which the net present value of an investment is zero. The internal rate of return of an investment project should not be less than a certain minimum that the company has determined for itself.

The internal rate of return of an investment project corresponds to the discount rate at which the NPV of the project is equal to zero.

The project internal rate of return (IRR) method allows you to determine the minimum acceptable level of profitability of the project or the discount rate at which the net present value will be equal to zero. Of several projects, the one whose internal rate of return is higher is selected.

What does the internal rate of return show.

This is an internal rate of return measure in which reinvested earnings are accounted for at a predetermined discount rate that differs from the rate used to discount lease payments.

The index of profitability, the internal rate of return in the economic assessment were not considered, because. hydraulic fracturing is associated with an increase in operating costs and does not require large capital investments.

The higher the values of the internal rate of return and the greater the difference between its value and the chosen discount rate, the greater the safety margin of this project.

Therefore, the value of the internal rate of return is 26%, which is the best estimate of the internal rate of return.

The economic content of the normally calculated internal rate of return (IRR) with the considered forms of cash flow changes significantly. This is where a formal element appears in the IRR calculation scheme, which is in no way consistent with real economic conditions: in order to preserve the economic meaning of the internal rate of return (the maximum allowable percentage of a loan for full financing of a project), it turns out that the condition for the possibility of reinvesting the funds received with an efficiency equal to the calculated IRR. Naturally, in most cases, this is unrealistic.

From the point of view of theory, the use of the internal rate of return of the marginal accepted or marginal rejected project is quite justified, but the disadvantage of the method is that in practice it is quite difficult to determine this value and, in addition, the percentages for the marginal accepted project and the marginal rejected project will be different.

From the point of view of theory, the use of the internal rate of return of the marginal accepted or marginal rejected project is quite justified, but the disadvantage of the method is that in practice it is rather difficult to determine this value and, in addition, the percentages for the marginal accepted and marginal rejected projects will be different.

Another interpretation of this indicator: the internal rate of return is the highest rate of interest that an investor can pay without losing money if all funds to finance an investment project are borrowed and the total amount (principal plus interest) must be paid out of income from the investment project after they are received. The most important advantage of this criterion is that it is not necessary to know exactly the discount rate. In addition, many managers are accustomed to thinking in terms of percentages, and therefore the internal rate of return, expressed as a percentage, is psychologically well perceived. In addition, in some cases (if the sign of cash flows changes more than once), the same investment project has several internal rates of return, which excludes the possibility of using this criterion as the main one.

When evaluating an investment, the concept of internal rate of return is additionally introduced. This is the return as a percentage of the investment, calculated at the net present value and often referred to as the return.

The opportunity cost of money is usually understood as the internal rate of return of the marginal accepted or marginal rejected project.

This rate of return r is also called the internal rate of return.

This definition can be applied to calculate the internal rate of return on investment. This indicator is typical when using the trial and error method. If incomes and investments are properly valued, taking into account the time value of money, then the return on investment in each year will be equal to the internal rate of return on investment.

The second criterion widely used in project analysis is the internal rate of return (income) (IRR or IRR) of the project, i.e. discount rate that equalizes the sum of the discounted benefits with the sum of the discounted costs. In other words, at a discount rate equal to IRR, the net present value is zero. This indicator, often used in financial and economic analysis as the main criterion, gives investors the opportunity to compare the profitability of the project (RRR) with the alternative i for this project.

Financial results of the implementation of the plan (net present value, internal rate of return, discount (dynamic) of the project.

The second widely used criterion in project analysis is the internal rate of return (income) (IRR or IRR (English name - IRR - internal rate of return)) of the project, i.e. the discount rate that equalizes the discounted benefits with the discounted costs. This is equivalent to saying that at a discount rate equal to IRR, the net present value is zero. This indicator, often used in financial and economic analysis as an important criterion, gives investors the opportunity to compare the profitability of the project with the opportunity cost of capital E for this project.

The calculation of the project efficiency is determined by the indicators of the payback period and the internal rate of return.

The priority of this or that investment program is determined by the estimated value of the internal rate of return of the project, which is compared with the profitability of alternative projects and the rate of return in the capital markets.

Some people prefer to use a percentage, often referred to as the internal rate of return. Other names are also used for this indicator: discounted cash flow, return on investment, profitability index, present value.

Internal rate of return (IRR, internal discount rate, internal rate of return, Internal Rate of Return, IRR) is such a positive number Eb that at the discount rate E Eb the net discounted income of the project turns to 0, for all large values of E it is negative, for all smaller values of E - positive.

The fundamental condition for the effectiveness of the project is the provision that the internal rate of return should not be less than the accepted interest rate on long-term loans.

Therefore, the graph shows the sequence of implementation of projects based on their internal rate of return. At the same time, it was assumed that the projects have approximately the same level of risk, average for a given company. In addition, all considered projects are classified as independent.

Kiyosaki: Then I do the math, come up with an IRR, internal rate of return, and decide if the game is worth the candle.

What are the basic formulas for calculating the net present value and internal rate of return of a project.

Thus, the enterprise can take as the discount rate the internal rate of return of the marginal accepted project or the internal rate of return of the marginal project not accepted.

By permutation we calculate r and get r 26.5. Thus, the internal rate of return for this investment is 26.5% per year.

To test our recommendations, calculations were carried out according to another criterion - the internal rate of return (IRR), which confirms the correctness of the decisions. Namely, with 90 and 80% compensation and distribution of 40 and 60%, respectively, to the investor and the state, the HRR corresponds to from 113 to 106%, which indicates the unacceptability of the decisions. The results of the calculations also show that out of nine possible solutions for further consideration with a view to the practical implementation of design solutions, only five competing conditions of the PSA remain - points 1, 2, 4, 5, 7.

In general, the return on investment (indicators of payback, net present value, internal rate of return, etc.) is planned within the framework of a long-term budget (development budget) for 1-3 years. Within the framework of the short-term (quarterly) budget, the approach to investments is carried out mainly through the prism of development, that is, the expenditure of working capital of the enterprise (mainly cash) for the purposes of capital construction. This means the immobilization of a part of current assets and a decrease in the liquidity of the company's balance sheet.

Using the cost of capital as a discount makes it possible to select for implementation only those projects whose internal rate of return is higher than the cost of capital.

Therefore, the value of the internal rate of return is 26%, which is the best estimate of the internal rate of return.

In the general case, when investments and returns on them are given in the form of a stream of payments, the internal rate of return is determined using the method of successive iterations. To do this, using discount factors (factors) choose two values of the discount factor r TI so that in the interval r - function NPVf (r) changes its value from plus to minus.

In the general case, when investments and returns on them are given in the form of a stream of payments, the internal rate of return is determined using the method of successive iterations. To do this, with the help of discount factors (factors), two values of the discount factor r G2 are chosen so that in the interval r - r the function NPy f (r) changes its value from plus to minus.

As we have already noted, it is very difficult to clearly define the limits of change in the calculated economic indicators of investment efficiency - net present value, internal rate of return and payback period of projects, but, undoubtedly, it is possible to determine satisfactory values or fluctuation limits for these indicators using an expert method.

Project internal rate of return

This is the second most important indicator of the profitability of an investment project, IRR (English internal rate of return). The internal rate of return (recoupment) is the calculated interest rate at which the benefits (revenues) from the project become equal to the costs of the project, i.e. it can be defined as the calculated interest rate at which the net present value is zero. One more definition can be given - this is the maximum percentage that can be paid to mobilize investment in the project.

The calculation of the internal rate of return is feasible only on a computer with a special program or on a special financial calculator. Under normal conditions, the internal rate of return can be determined by a series of attempts in which the NPV is calculated at different discount rates. For example, NPV is positive at a discount rate of 10% and negative at a discount rate of 20%. This means that the internal rate of return lies between 10 and 20%. Let's try again: NPV is still positive at 15%. This means that the internal rate of return lies between 15 and 20%. The following attempts will narrow this range more and more, and, in the end, the discount rate at which NPV = 0 will be found. This calculation method is called the iteration method.

We add that Вt - Сt as an indicator is widely used in assessing the performance of a firm (enterprise) and is called cash receipts (cash flow, English cash flow). It has a broader meaning than the receipt of cash in the cash desk of the firm (enterprise): it is the net monetary result of the commercial activities of the firm.

The profitability of an investment project is the main condition in the investment process. It is determined by static and dynamic indicators, absolute and relative. Absolute indicators tell the investor how much he can earn by investing money in the project, and relative indicators tell him the return on each ruble of his investment.

Among the relative indicators, the indicator of the internal rate of return of an investment project, which shows the average rate of return of investments over their entire life cycle, has the most informative value. At the same time, this indicator tells the investor about the limit of return on investment, below which it is not advisable to invest. In addition, it can serve to select the best investment project, among equal projects, according to other indicators.

In mathematical terms, the IRR of an investment project is the rate of return of the project at which NPV = 0, that is, the costs are equal to the results. In this case, the investor has nothing to lose, but nothing to gain from the investment. The interest rate at which this happens can serve as an acceptable discount rate for cash flows when calculating the economic efficiency of investment projects.

The investment choice among investment options will belong to the option with a higher internal rate of return. And when assessing the feasibility of investing in a single project, the internal rate of return should exceed the weighted average cost of investment resources. That is, any investment decision at a rate of return below the IRR should be rejected by the investor.

This indicator has the form of a non-linear function and is determined in two ways: graphical and iteration method. The iteration method is the selection of a variant of the rate of return at which the investment capital is equal to investment income. The mathematical algorithm for calculating the indicator is quite simple and the computer can easily cope with this task.

Internal rate of return

The internal rate of return (IRR) is the discount rate at which cash inflows equal the current cash outflows, or the rate at which the project's current proceeds equal the current investment and the net present value is zero. The same methodology is used to calculate the VNO as to calculate the NPV. The same types of tables can be used, and instead of discounting the cash flows at a predetermined minimum rate, various discount factors can be used to determine the rate at which the NPV is zero. This coefficient is the VNO, and it shows the profitability of the project.

The internal rate of return can be quite interesting to interpret. It represents the highest rate of interest that an investor can pay without losing money if all funds for financing are borrowed and the total amount (principal plus interest) must be paid out of the income of the investment project after they are received.

The internal rate of return method involves the use of the concept of present value. It comes down to finding such a discount rate at which the current value of the expected income from the investment project will be equal to the current value of the required cash investments. The search for such a discount rate is carried out by an iterative (trial and error) method. For example, in the case of traditional investments (that is, those for which there is one or more periods of expenditure followed by one or more periods of cash income), if cash income and expenditure in each of the following years are known, one can start at any discount rate and for this rate, determine the present value of current income and the present value of investments. If the net present value of the cash flows is positive, a higher discount rate should be used to equalize the present value of income and investments.

Internal rate of return (profit) IRR - the rate of return, which, when applied to the proceeds from investments over the life cycle, gives zero net present value.

These criteria (NPV and IRR) can be considered as independent, while the analysis of the internal rate of return and the analysis of net present value leads in most cases to the same decision. Of two independent traditional investment options, it is recommended to approve the one for which the internal rate of return is greater than some minimum acceptable rate, and the net present value of the project is greater than zero at the chosen discount rate.

The method of analytical calculations is based, as a rule, on a combination of the considered evaluation criteria. Priority in each particular case is given to those criteria that currently best reflect the interests of owners or investors. If the profitability of the project is put forward in the first place, then the calculation is based on the index of return on investment or the internal rate of return.

Net internal rate of return

The profitability of capital investments is considered on the basis of a comparison of the return on investment with the market rate of loan interest. The Internal Rate of Return (IRR) is the rate of return on each unit of a firm's investment.

If NPV=0, then the IRR for the project is equal to the loan interest rate (discount rate), at which total income is equal to expenses. That is, IRR is equal to the maximum interest on loans (r) used to invest and operate the project, while operating at break even.

IRR=r.
If IRR>r, hence net internal rate of return NIRR>0
NIRR = IRR - r.

Thus, an investment decision can be made if the internal rate of return IRR3 r or NIRR30, i.e. the demand for borrowed funds is determined by the net internal rate of return NIRR. For the production of 100 kg of products at a discount rate of r=10%, the demand for borrowed funds is formed, because IRR is 16%, hence NIRR = 6%.

For the production of 400 kg of products at the same rate r = 10%, the internal rate of return IRR is 5%, therefore NIRR = -5%, which means that there will be no demand for investment resources.

Internal rate of return or payback The internal rate of return is the calculated interest rate at which the benefits from a project are equal to the costs of the project, i.e. can be defined as the calculated interest rate at which the net present value is zero. Other definition of internal rate of return is that maximum percentage that can be paid to mobilize investment in a project.

The calculation of this indicator is possible only with a special program or using a special computer. Under normal conditions, there are several attempts to determine the internal rate of return, in which the NPV is calculated at different discount rates.

For example, at a discount rate of 10%, the net present value is positive, and at a discount rate of 20%, it is negative.

This shows that the internal rate of return is between 10 and 20%. Let's make further calculations: at a discount rate of 16%, the net present value is also positive, which means that the internal rate of return is between 16 and 20%.

Similar calculations are made until the discount rate at which the net present value is zero is found. This method is called the integration method.

The NRCA is a measure that is widely used in evaluating the performance of a firm and is referred to as cash receipts or cash flow. This indicator has a broader meaning than cash receipts at the cash desk of the enterprise. This is the net monetary result of the commercial activities of the enterprise.

For example, if the internal rate of return of our project is 20%, then what does knowing this indicator give the entrepreneur?

If alternative projects give the firm a lower internal rate of return, then this project is the most profitable one. Conversely, if the internal rate of return is greater than 20%, then this project is less profitable than other projects.

Internal norm method

All revenues and all project costs are adjusted to present value not on the basis of an externally assigned weighted average cost of capital, but on the basis of the internal rate of return of the project itself.

Method Tools:

The internal rate indicator (rate) of project profitability is the discount rate at which the net present value of the project is zero (all costs, taking into account the time value of money, pay off). In other words, this is the discount rate at which the present value of the expected cash costs and the present value of expected cash receipts;
a graphical technique for determining the internal rate of return of a project is based on calculating a series of values of the net present value of the project at various discount rates and involves the following actions:
1. a certain discount rate is set and the net present value of the project is determined, the corresponding point is marked on the graph (the ordinate axis is the discount rate, the abscissa axis is the value of the net present value of the project); 2. a much higher discount rate is set, the net present value of the project is calculated (which decreases sharply compared to the original calculation), the corresponding point is marked on the graph;
3. these two points marked on the graph are connected, if necessary, the line of the net present value of the project is extended until it intersects with the y-axis; this is the point at which the net present value of the project is zero, and corresponds to the value of the internal rate of return.

The graphical method for determining the internal rate of return of a project does not provide the necessary accuracy, but it can be used in the absence of a special financial calculator or a computer program for investment analysis.

The analytical method for determining the internal rate of return can be implemented in two ways:

With the help of a gradual approximation of the result obtained to its final form in an iterative process, in which all the calculation operations are repeated with each subsequent step, the value of the indicator is corrected, and so on until the desired result is obtained. Such calculations can be continued many times until the desired result is obtained with such accuracy as the investor will need. The accuracy of the calculations in this case is the reciprocal of the length of the interval. The best result is achieved with a minimum interval length of 1%;
by solving the equation when the net present value is equal to zero.

This method assumes that projects with an internal rate of return that exceeds the weighted average cost of capital (taken as the minimum acceptable rate of return) are approved. Of the selected projects, preference is given to the most profitable and the investment portfolio with the highest total net present value is formed if the investment budget is limited. The internal rate of return determines the maximum allowable loan interest rate at which the project is credited without loss, i.e. without using for loan payments a part of the profit received on own invested capital.

The indicator of the internal rate of return is the most suitable for the comparative evaluation of projects within a wide range:

With the level of profitability of all assets in the process of operating the enterprise;
with an average rate of return of similar investment projects;
with the rate of return on alternative investment with a deposit, municipal bonded loan, foreign exchange transactions, etc.).

Advantages of the method:

It is in good agreement with the main goal of financial management - increasing the wealth of shareholders;
guarantees the lower level of profitability of the investment project;
reflects the maximum rate of payment for attracted sources of project financing, at which the latter remains breakeven;
ensures the independence of the results of calculations from the absolute size of investments;
acceptable for a comparative assessment not only within the framework of the investment projects under consideration, but also in a wider range (for example, in comparison with the profitability ratio of operating assets, the return on equity ratio, the level of return on alternative types of investment - deposits, purchase of government bonds, etc.). P.);
takes into account the change in the cost of funds over time (in other words, it allows you to take into account both the magnitude and distribution over time of the expected cash flows in each period of the project), and therefore is recognized as one of the methods that most accurately determine the total income from investment and give an objective assessment of the investment project;
does not require initially setting the value of the internal rate of return.

Disadvantages of the method:

Uses complex calculations, especially when the project life cycle includes several time intervals;
does not reflect the absolute value of net economic benefits;
assumes an unrealistic situation of reinvestment of all intermediate cash receipts from the project at the rate of internal profitability. In fact, part of the funds can be paid out in the form of dividends, and part can be invested in low-yielding but reliable assets (short-term government bonds, etc.).

The VNR criterion also has a number of weaknesses:

Not always a project with a larger IRR is more profitable;
problematic is the establishment of a "threshold IRR", which is the basis for making a decision on the feasibility of investing. This problem is especially significant for unstable environmental conditions;
the possibility of multiple threshold IRR values for different periods during the project implementation is not taken into account.

In addition, the main problem with the internal rate of return is that it often gives unrealistic rates of return. Let's say VNR is defined at the level of 40%. This should not mean that managers should immediately approve the project. GNR=40% assumes that the company can reinvest future cash income at 40%. If experience and economics indicate that 40% is an unrealistic rate for future reinvestment, then IRR is suspect. To put it simply, a GNR of 40% is too high to be true. Thus, if the calculated value of IRR does not give a moderate rate of reinvestment of future cash flows, it should not be accepted.

Internal rules of the organization

The internal environment of the organization contains the potential that enables it to function, and, therefore, to exist, survive and develop in a certain period of time. But this environment can also be a source of problems and even the death of the organization if it does not provide the necessary functioning of the organization.

The internal environment of the organization is a combination of the following components:

- goals and objectives of the organization;
- the structure of the organization (for example, "supply - production - finance - personnel department - sales of products");
- intra-organizational processes (management structure);
– technology (production processes, level of automation);
- personnel (division of labor);
– organizational culture (communications).

In addition, management manages the functional processes that take place in the organization. Consider the components of the internal environment of the organization in more detail.

The goals and objectives of the organization depend on different circumstances. These can be: the sale of goods and profit; production of goods and increase in labor productivity; training of specialists in various specialties and scientific level education, etc. Its structure depends on the goals of the organization.

The structure of the organization reflects the allocation of individual divisions that has developed in the organization, the connections between them and the unification of divisions into a single whole. This internal variable shows the interaction between management levels and functional areas of an organization. Depending on the specific conditions and situation, material, financial and human resources, the management of the organization rearranges it to more effectively achieve goals and solve specific problems.

On a nationwide scale, an organizational structure has been formed that divides a single economic complex into separate large functional parts: industries, construction, agriculture, transport, etc. There is also division within industries. For example, in industry - mining and manufacturing, in turn, each of these large organizations is divided into even smaller structures (engineering, chemical industry, crop production, animal husbandry, food industry, etc.) up to individual enterprises.

Any individual enterprise also has its own functional structure, which, as a rule, consists of specific departments and industries, for example, a workshop, an R&D department, a sales department, a department for labor safety and environmental protection, etc. This structure is a systemic relationship between functional units and levels of management, designed to ensure that the goals of the organization are achieved in the most effective ways. Functional divisions are the various types of work performed by the organization.

The starting point in the construction of the structure is the design of the work. The organization can adopt a system of autonomous work, can be based on conveyor, modular or team forms of work. The design of the work also depends on such factors as the qualifications of the performers of the work; Availability feedback with end results the need for additional training of employees, etc.

The next step in the formation of the structure of the organization is the allocation of structural units, hierarchically linked and in constant production interaction. Organizational sizes of structural subdivisions, their rights and obligations, system of interaction and information exchange are determined. Units are assigned certain tasks and they are provided with the necessary resources.

Intraorganizational processes, formed and directed by management, include four main processes:

– management;
- coordination;
- making decisions;
- communications.

In intra-organizational life, management plays the role of a coordinating beginning, shaping and setting in motion the resources of the organization to achieve its goals. Management levels are related to the division of labor in an organization. The need to coordinate the work distributed among workers led to the emergence of levels of organization.

For coordination, management can create two types of procedures in the organization:

- direct management of actions in the form of orders, orders and proposals;
- coordination of actions through the creation of a system of rules and regulations relating to the activities of the organization.

Decision-making procedures and norms are formed differently in different organizations. They can be carried out "from the bottom up" only at the top level, or the system of "delegation of decision-making power to the lower levels of the organization" can be applied.

The norms and forms of communication that exist in an organization can have a great influence on the climate within that organization. Communication can be in written, oral or mixed forms. An important characteristic of communications is the presence of restrictions on them. All aspects of communication processes are under the influence of management and are the subject of concern for the management of the organization if it seeks to create the best atmosphere within the organization.

Technology. Technology today means a lot: first of all, it is a specific process of manufacturing products. It is also a set of ways, methods and techniques for transforming the source material into a useful thing, service, information. This is a method of solving the problems of the enterprise, a way of doing business. Technology is the subject of the closest attention on the part of management. Management must address issues of technology and implementation of their most effective use.

At any enterprise there are always problems with the introduction of the latest equipment and technologies. Technique, especially at the present time, quickly becomes morally obsolete. Scientific and technological progress constantly offers some new equipment, new technologies to improve and speed up production processes, and it is often dangerous to apply these technical innovations - you need to be sure that under the given conditions the maximum effect will be achieved when using this particular technique and technology, and not any other. Moreover, any innovation must necessarily be justified economically, that is, the expected profit, payback period, etc. are calculated. At the very beginning of the introduction of innovation, a negative result can also be obtained.

Human resources are the backbone of any organization. An organization lives and functions only because it has people. People create the product of the organization, form its culture and internal climate, carry out communications and management, that is, what the organization is depends on them. Therefore, people are the "number one subject" for management. Management forms personnel, establishes a system of relationships between them, promotes their training and promotion at work. People working in an organization differ greatly from each other in many ways: gender, age, education, nationality, marital status, etc. All these differences can have a serious impact both on the characteristics of work and the behavior of an individual employee, and on the actions of other members of the organization, on the result of work as a whole. In this regard, management should build its work with personnel in such a way as to contribute to the development of positive results of the behavior and activities of each individual and try to eliminate the negative consequences of his actions.

The division of labor along specialized lines is applied in all large organizations.

There are two types of specialized division of labor:

- horizontal - between interconnected functional units that are not subordinate to each other, but take part in the manufacture of the final product at various stages and production stages;
- vertical - management hierarchy, i.e. formal subordination of employees from top to bottom, from the head to the executor.

Organizational culture, being a comprehensive component of the organization, has a strong influence both on its internal life and on its position in the external environment. Organizational culture is made up of stable norms, ideas, principles and beliefs about how a given organization should and can respond to external influences, how to behave in an organization, what is the meaning of the organization's functioning, etc. (often expressed in slogans). The carriers of organizational culture are people, but it is developed and shaped to a large extent by management and, in particular, top management.

The state of the organization is not something permanent, changes in its internal content occur under the influence of time and as a result of managerial actions of people. At any given moment in time, the internal factor of the organization is something “given” that can be changed by achieving the set goals.

In the former USSR, the structures of organizations were created for many years, did not change for a long time, since the organizations functioned in a stable external environment, regulated by the State Planning Commission and excluding competition. The revision of the structures of the administrative apparatus, although it took place in Soviet times, was initiated from above under the leadership of ministers and pursued certain goals, for example, reducing the cost of the administrative apparatus, obtaining savings through the artificial creation of production associations.

Internal rate of return rate

The internal rate of return is an indicator that is a worthy alternative to the net present value of NPV. It is designated as IRR and in English it sounds Internal Rate of Return.

The internal rate of return IRR is a discount rate that equates the amount of the reduced income from an investment project to the amount of investment, i.e. investments pay off, but do not bring profit.

To understand this flow of economic terms, consider a project that today costs 100 thousand rubles, and in a year it will bring 110 thousand rubles. income. What is the return on such investments? The answer, it would seem, is obvious - 10%, because each invested 1000 rubles. brings 1100 rubles. In fact, this is not just an indicator of the return on investment, this is the same internal rate of return.

Suppose we need to calculate the NPV of our investment in the amount of 100 thousand rubles invested in a project with a term of 1 year. At the same time, we do not know the discount rate.

We denote this unknown rate by r and get the formula for calculating NPV:

NPV = - 100 + 110 / (1+ r)

Let's ask ourselves a question: what should be the discount rate for the project to be worth rejecting? We know that with NPV equal to zero, the project does not generate any income or loss. In other words, investments with zero NPV simply break even. Therefore, to find the break-even discount rate at which the project will neither create nor destroy investment value, we need to equate NPV to zero. Therefore, equating the above expression to zero and solving it for r, we get -100 + 110/(1+ r) = 0, or r = 0.1 = 10%.

Thus, the 10% rate is the discount rate, which is equal to the expected return on investment. This means that the internal rate of return of investments is essentially equal to the discount rate, 10% is the level at which future incomes can be discounted, and we will not receive any profit from them, but simply “go to zero”. Consequently, if the market discounted rate (here often they take the average annual interest rate at which we could receive income if we invested not in the project, but in the bank) will be higher than this level, i.e. above 10%, then the project should be abandoned. Indeed, in this scenario, it will be more profitable for us to put money in the bank than to invest in the project, since we will receive more income. If the discount rate offered by the market is below the internal rate of return, then the project should be accepted. Since such investments are more profitable compared to investments in a bank.

All of the above can be combined into the rule of internal rate of return.

Internal rate of return rule: if the internal rate of return exceeds the planned return or the return on alternative investments, then the project should be accepted. Conversely, if the internal rate of return is less than planned or less than the return on alternative investments, then the project should be rejected.

Modified internal rate of return

Analysis of investment projects based on the method of internal rate of return (IRR) suggests that all project cash flows can be invested at this rate, which is unrealistic. This drawback of the IRR method is eliminated by using the so-called modified internal rate of return or abbreviated MIRR (Modified Internal Rate of Return).

The essence of the MIRR calculation is simple: all positive cash flows from the project are increased at a % rate equal to the company's cost of capital (WACC), and then the rate is found, discounting at which we get the amount of our investment. Let's take project A as an example, the same one that was used to calculate NPV and IRR earlier.

Thus, the modified internal rate of return method removes the conflict between NPV and IRR when choosing between two mutually exclusive projects, since it equalizes the rate of reinvestment of cash flows.

However, MIRR cancels one of the advantages of the IRR method - you have to calculate a discount rate equal to the company's cost of capital, which is always difficult.

The possibility of making opposite decisions is also preserved. If two projects are of the same scale and duration, then yes, the NPV and MIRR methods will always select the same project from two mutually exclusive projects. The same is true for projects of the same size but different duration. In this case, you need to calculate these figures based on the longest project, simply adding zero cash flows to the shorter project.

However, if mutually exclusive projects differ in scale (value of cash flows), then the conflict between the two methods is still possible. Therefore, the use of the NPV method is still preferable to the calculation of IRR or MIRR (ordinary or modified internal rate of return).

Consider 6 methods for assessing the effectiveness of investments, I will give various formulas for calculating investment ratios, a methodology (algorithm) for calculating them in Excel. These methods will be useful to investors, financial analysts, business analysts and economists. It should be noted right away that under investments we will understand various investment projects, investment objects and assets. That is, these methods can be widely used in the valuation activities of any enterprise/company.

All methods for assessing the effectiveness of investment projects can be divided into two large groups:

Statistical methods for evaluating the effectiveness of investments / investment projects

Statistical evaluation methods are the simplest class of approaches to the analysis of investments and investment projects. Despite their apparent simplicity of calculation and use, they allow drawing conclusions on the quality of investment objects, comparing them with each other and weeding out inefficient ones.

Payback period (Payback Period)

Payback period of investments or investment project (Englishpaybackperiod,PP, payback period) - this coefficient shows the period for which the initial investment (costs) in the investment project will pay off. The economic meaning of this indicator is to show the period for which the investor will return his invested money (capital).

The formula for calculating the payback period of investments (investment project)

IC ( Investment Capital) - investment capital, the initial costs of the investor in the investment object. In the formula in foreign practice, the concept is sometimes used not of investment capital, but of capital costs (cost of Capital, CC) , which essentially carries a similar meaning;

CF ( Cash flow) is the cash flow generated by the investee. Under the cash flow, sometimes in the formulas they mean net profit ( NP, Net Profit).

The formula for calculating the payback period / payback period can be written differently, this option is also often found in domestic literature on finance:

It should be noted that investment costs represent all the costs of the investor when investing in an investment project. Cash flow must be taken into account for certain periods (day, week, month, year). As a result, the payback period of investments will have a similar measurement scale.

An example of calculating the payback period of an investment project in Excel

The figure below shows an example of calculating the payback period of an investment project. We have initial data that the cost of initial costs amounted to 130,000 rubles, monthly cash flow from investments was 25,000 rubles. At the beginning, it is necessary to calculate the cash flow on an accrual basis, for this the following simple formula was used:

Cumulative cash flow is calculated in column C, C7=C6+$C$3

Since we have a discrete period, it is necessary to round this period up to 6 months.

Directions for using the payback period of investments (investment projects)

The payback period indicator is used as a comparative indicator for evaluating the effectiveness of alternative investment projects. The project, which has a faster payback period, is more efficient. This coefficient is used, as a rule, always in conjunction with other indicators, which we will discuss below.

Advantages and disadvantages of the payback period indicator

The advantages of the indicator are its speed and ease of calculation. The disadvantage of this ratio is obvious - it uses a constant cash flow in its calculation. In real conditions, it is quite difficult to predict sustainable future cash flows, so the payback period can change significantly. In order to reduce possible deviations from the payback plan, it is necessary to ensure the reliability of the sources of cash flow for the investment project. In addition, the indicator does not take into account the impact of inflation on the change in the value of money over time. The payback period of investments can be used as a screening criterion at the first stage of evaluation and selection of "heavy" investment projects.

Return on Investment Ratio (Accounting Rate of Return)

Return on investment or investment project(eng. Accounting Rate of Return, ARR,ROI, accounting rate of return, return on investment)- an indicator reflecting the profitability of the investment object without discounting.

The formula for calculating the return on investment ratio

Where:

CF Wed- average cash flow (net profit) of the investment object for the period under review (month, year);

IC ( Investment Capital) - investment capital, the initial costs of the investor in the investment object.

There is also the following version of the return on investment formula, which reflects the case when additional investments are made to the object / project during the period under review. Therefore, the average cost of capital for the period is taken. The formula then looks like:

Where:

IC 0 , IC 1 - the cost of investments (invested capital) at the beginning and end of the reporting period.

An example of calculating the return on investment (investment project) in Excel

In order to better understand the economic meaning and the calculation algorithm, we will use the Excel program. The costs incurred by the investor were only in the first period and amounted to 130,000 rubles, cash receipts from investments changed monthly, so we calculate the average receipts by month. For the billing period, any time period, quarter, year can be taken. In our case, we get the monthly profitability of the investment project. The calculation formula in Excel is as follows:

B14=AVERAGE(C5:C12)/B5

Purposes of using the profitability ratio of the investment project

This indicator is used to compare different alternative investment projects. The higher the ARR, the higher the attractiveness of this project for the investor. As a rule, this indicator is used to evaluate existing projects, where it is possible to track and statistically evaluate the effectiveness of creating a cash flow for a given investment.

Advantages and disadvantages of the return on investment ratio

The advantages of the coefficient are in its simplicity of calculation and obtaining, and this is where its advantages end. The disadvantages of this ratio include the difficulty of predicting future cash receipts / income from the project. In addition, if the project is a venture, then this indicator can greatly distort the picture of the perception of the project. ARR is usually used for external demonstration of a successful project. The indicator in its formula does not take into account changes in the value of money over time. This indicator can be used at the first stage of evaluation and selection of investment projects.

Dynamic methods for evaluating the effectiveness of investments / investment projects

Consider a number of dynamic methods for evaluating investment projects, these indicators use discounting, which is an undoubted advantage in relation to statistical methods.

Net present value (Net Present Value)

(English)Netpresentvalue,NPV, net present value, net present value, present value)- an indicator that reflects the change in cash flows and shows the difference between discounted cash income and expenses.

Net present value is used to select the most investment-attractive project.

Net present value formula

NPV is the net present value of the project;

CF t - cash flow in time period t;

CF 0 - cash flow at the initial moment. Initial cash flow equals investment capital (CF 0 = IC);

r is the discount rate (barrier rate).

Project evaluation based on the NPV criterion

An example of calculating net present value in Excel

Consider an example of calculating net present value in Excel. The program has a handy NPV (Net Present Value) function that allows you to use the discount rate in your calculations. Let's calculate NPV below in two variants.

Option number 1

So, let's analyze the algorithm for the sequential calculation of all NPV indicators.

Calculation of cash flow by years: E7=C7-D7
Time discounted cash flow: F7=E7/(1+$C$3)^A7
Summation of all discounted cash receipts for the investment project and subtracting the initial capital costs: F16 =SUM(F7:F15)-B6

Option number 2

Calculation using the built-in NPV formula. It should be noted that it is necessary to deduct the initial capital costs (B6).

NPV($C$3;E7;E8;E9;E10;E11;E12;E13;E14;E15)-B6

The results in both NPV calculation methods, as we can see, are the same.

Master class: "How to calculate net present value for a business plan"

Internal rate of return of an investment project

Internal rate of return (English) Internalrateofreturn,IRR, internal discount rate, internal rate of return, internal efficiency ratio)- shows the discount rate at which the net present value is zero.

The formula for calculating the internal rate of return of an investment project

CF ( Cash flow

IRR - internal rate of return;

CF 0 - cash flow at the initial moment. In the first period, as a rule, the cash flow equals the investment capital (CF 0 = IC).

An example of calculating the IRR of an investment project in Excel

Consider an example of calculating the internal rate of return in Excel, the program has a good IRR function (internal rate of return), which allows you to quickly calculate IRR. This function is correct to use if there is at least one positive and negative cash flow.

E16 = VSD(E6:E15)

Advantages and Disadvantages of IRR Internal Rate of Return

+) the ability to compare investment projects with each other, having a different investment horizon;

+) the ability to compare not only projects, but also alternative investments, such as a bank deposit. If the IRR of the project is 25%, and the bank deposit is 15%, then the project is more investment attractive.

+) express evaluation of the project for its expediency of further development.

The internal rate of return is estimated with the weighted average cost of the attracted capital, which makes it possible to assess the feasibility of further development of the project.

—) the absolute increase in the cost of the investment project is not reflected;

—) cash flows often do not have a systematic structure, which makes it difficult to correctly calculate this indicator.

Master class: "How to calculate the internal rate of return for a business plan"

Investment Profitability Index

Investment profitability index (English profitability index,PI, yield index, profitability index) is an investment efficiency indicator that shows the return (profitability) of invested capital. The earnings index is the ratio of the present value of future cash flows to the value of the initial investment. The economic meaning of this ratio is an assessment of the additional value for each invested ruble.

The formula for calculating the investment profitability index

NPV - net discounted income;

n is the project implementation period;

r - discount rate (%);

IC - invested (spent) investment capital.

A variation of the investment profitability index formula

If investments in the project are not carried out at a time, but throughout the entire implementation period, then it is necessary to bring the investment capital (IC) to a single value, i.e. discount it. The formula in this case will look like this:

The higher the return on investment, the greater the return on invested capital brings this investment. This criterion is used to compare several investment projects with each other. In practice, a large profit index does not always show the effectiveness of the project, because in this case, the estimate of future income could be overestimated or the frequency of their receipt was not correctly estimated.

Project evaluation based on the PI criterion

An example of calculating the profitability index of a project in Excel

Let's consider the calculation of the profitability index as an example. The figure below shows the PI calculation in cell F18.

Column F Calculation - Discounted Cash Flow =E7/(1+$C$3)^A7
Calculation of net present value NPV in cell F16 =SUM(F7:F15)-B6
Estimation of investment profitability in cell F18 = F16/B6

If the investment costs were every year, then it was necessary to calculate the profitability index using the second formula and bring them to the present time (discount).

Discounted ROI

Discounted payback period (English Discounted Payback Period, DPP) is an indicator reflecting the period through which the initial investment costs will pay off. The formula for calculating the coefficient is similar to the formula for estimating the payback period of investments, only discounting is used

The formula for calculating the discounted payback period of investments

Where:

IC ( Investment Capital) - investment capital, the initial costs of the investor in the investment object;

CF ( Cashflow) - cash flow, which is created by the investment object;

r is the discount rate;

t is the period of evaluation of the received cash flow.

An example of calculating the discounted payback period of investment in Excel

Let's calculate the discounted payback period of investment in Excel. The figure below shows an example calculation. To do this, you must perform the following operations:

Calculate discounted cash flow in column D =C7/(1+$C$3)^A7
Calculate the accrual of capital gains in column E =E7+D8
Estimate in what period the invested investments (IC) paid off in full.

As we can see, the payback of all costs by discounted cash flow occurred in 6 months. The shorter the payback period of an investment project, the more attractive these projects are.

Advantages and disadvantages of the discounted payback period

The advantage of the coefficient is the ability to use in the formula the property of money to change its value over time due to inflationary processes. This improves the accuracy of estimating the period of return on invested capital. The complexity of using this ratio lies in accurately determining the future cash flows from the investment and estimating the discount rate. The rate may change throughout the life cycle of an investment due to various economic, political, and production factors.

Master class: "How to calculate the payback period for a business plan: instructions"

Choosing an Investment Based on Performance Evaluation Factors

The figure below shows a table of criteria for selecting an investment project/investment based on the considered coefficients. These indicators allow us to give an express assessment of the attractiveness of the project. It should be noted that these indicators are poorly used to evaluate venture projects, because it is difficult to predict what sales, income and demand will be in this project. The indicators have proven themselves well in evaluating already implemented projects with well-defined business processes.

Index	Investment selection criterion
Statistical methods for evaluating the effectiveness of investments
Payback period	PP -> min
Return on investment capital	ARR>0
Dynamic methods for evaluating the effectiveness of investments
Net present value	NPV>0
Internal rate of return	IRR>WACC
profitability index	PI>1
Discounted payback period	DPP -> min

Summary

The use of coefficients for evaluating investment projects allows you to choose the most attractive objects for investment. We have considered both statistical and dynamic evaluation methods, in practice, the former are suitable for reflecting general characteristics object, while dynamic ones allow you to more accurately evaluate the parameters of the investment. In the modern economy, in times of crisis, the use of these indicators is effective for a relatively short investment horizon. In addition to external factors, the assessment is influenced by internal ones - the difficulty of accurately determining the future cash flows from the project. The indicators give a more financial description of the life of an investment and do not reveal causal relationships with income received (it is difficult to evaluate venture projects and start-ups). At the same time, the simplicity of calculating the coefficients makes it possible to exclude unprofitable projects already at the first stage of the analysis. This completes the description of the coefficients for evaluating the effectiveness of investments. Study investment analysis, in the following articles I will talk about more complex methods for evaluating projects, thanks for your attention, Ivan Zhdanov was with you.

When evaluating projects in terms of investment attractiveness, specialists use professional terms and designations. Consider and decipher the most important performance indicators - NPV, IRR, PI.

NPV, or Net Present Value. The net present value of the project.
This indicator is equal to the difference between the amount of cash receipts (investments) available at a given time and the amount of necessary cash payments to pay off loan obligations, investments or to finance the current needs of the project. The difference is calculated based on a fixed discount rate.

In general, NPV is the result that can be obtained immediately after the decision to implement the project is made. The net present value is calculated without considering the time factor. The NPV indicator immediately makes it possible to assess the prospects of the project:
- if greater than zero- the project will bring profit to investors;
- equal to zero - it is possible to increase the volume of output without the risk of reducing the profits of investors;
- below zero - losses for investors are possible.
This indicator is an absolute measure of the effectiveness of projects, which is directly dependent on the scale of the business. Ceteris paribus, NPV grows with the amount of funding. The more impressive the investment and the volume of the planned cash flow, the greater the absolute NPV will be.

Another feature of the indicator of the net present value of the project is the dependence of its amount on the structure of the distribution of investments between individual periods of implementation. The larger the proportion of costs planned for the periods at the end of the work, the greater should be the amount of planned net income. The lowest NPV value is obtained if the full implementation of the entire volume of investment costs with the presence of the project cycle is expected.

The third distinguishing feature of the net present value indicator is the influence of the start time of the project operation (subject to the formation of a net cash flow) on the numerical value of NPV. The more time passes between the start of the project cycle and the actual beginning of the operation stage, the smaller, under other unchanged conditions, the NPV will be. In addition, the numerical value of the net present value indicator can change greatly under the influence of fluctuations in the discount rate to the volume of investments and to the amount of net cash flow.

Among the factors affecting the size of NPV, it is worth noting:
1. the pace of the production process. Higher profit - more revenue, lower costs - more profit;
2. discount rate;
3. the scale of the enterprise - the volume of investments, output, sales per unit of time.
Accordingly, there is a limitation for the application of this method: it is impossible to compare projects that have significant differences in at least one of these indicators. NPV grows along with the growth of the efficiency of capital investments in the business.
IRR, or internal rate of return (profitability).
This indicator is calculated depending on the value of NPV. IRR is the maximum possible cost of investment, as well as the level of allowable costs for a particular project.

For example, when financing a business start-up with money taken in the form of a bank loan, IRR is the maximum level of the bank's interest rate. Even a slightly higher rate will make the project obviously unprofitable. The economic meaning of calculating this indicator is that the author of the project or the head of the company can make a variety of investment decisions, having a clear framework that cannot be exceeded. The level of profitability of investment decisions should not be lower than the CC indicator - the price of the source of financing. Comparing IRR with CC, we get dependencies:
- IRR more than CC - the project should be taken into account and financed;
- IRR is less than CC - the sale must be abandoned due to unprofitability;
- IRR is equal to CC - the verge of profitability and unprofitability, improvement is needed.
In addition, one can consider IRR as a source of information about the viability of a business idea from the point of view within which the internal rate of return can be regarded as a discount rate (possible), taking into account which the project can be profitable. In this case, to make a decision, you need to compare the standard profitability and the IRR value. Accordingly, the greater the internal profitability and the difference between it and the discount rate, the more chances the project under consideration has.
PI, or Profitability Index. Index of profitability of investments.
This index shows the ratio of the return on capital to the volume of investments in the project. PI is the relative profitability of the future enterprise, as well as the discounted value of all financial receipts per unit of investment. If we take into account the indicator I, which is equal to investments in the project, then the investment profitability index is calculated by the formula PI = NPV / I.

Profitability Index is a relative indicator that gives an idea not about the real amount of net cash flow in the project, but only about its level in relation to investment costs. Accordingly, the index can be used as a tool for comparative evaluation of the effectiveness of different options, even if they involve different amounts of financial investments and investments. In the course of considering several investment projects, PI can be used as an indicator that allows you to "weed out" inefficient proposals. If the value of the PI indicator is equal to or less than one, the project will not be able to bring the necessary income and growth of investment capital, so its implementation should be abandoned.

In general, there are three options for action, based on the value of the return on investment index (PI):
- more than one - this option is cost-effective, it should be accepted for implementation;
- less than one - the project is unacceptable, since the investment will not lead to the formation of the required rate of return;
- equal to one - this direction of investment satisfies the chosen rate of return as accurately as possible.
Before making a decision, it should be taken into account that business projects with a high value of the investment profitability index are more profitable, sustainable and promising. However, it is also necessary to take into account the fact that too high figures of the profitability ratio are not always a guarantee of a high current cost of the project (and vice versa). Many of these business ideas are inefficient in implementation, which means they may have a low profitability index.

Price for developing business plans

The terms for developing business plans on average range from 4 to 20 working days.

Internal rate of return- the central criterion that the investor focuses on when deciding whether to invest in a project or not. This indicator appears in all financial models and business plans and is the heart of these documents. That is why project initiators and company representatives must know how the indicator is calculated and how not to make mistakes in the calculations.

Why the internal rate of return is key

As you know, any investment project is accompanied by a lot of mathematical calculations: analysis of past data, statistics, similar projects, drawing up financial plans, models, forecast conditions, development scenarios, etc.

In addition to the general goal of assessing the prospects of the project as accurately as possible, calculating the resources necessary for its implementation and predicting the main possible difficulties, such detailed calculations have one connecting goal - to find out the project's performance indicators.

There are 2 of them at the output: net present value (NPV - net present value) and internal rate of return (IRR - internal rate of return). At the same time, it is the internal rate of return (profitability) that is used most often due to its visibility.

But such financial documents, models, etc. often take up more than one hundred pages of printed text. And investors, as you know, are very busy people. And in business circles, they came up with an elevator test: a person (the initiator of the project) must convince him to invest in the project during the time he rides with the investor in the elevator (about 30 seconds).

How to do it? Naturally, to tell what the investor will get at the exit, that is, to estimate the probable income from the entire project and the income of the investor himself. For this purpose, there is an indicator of internal rate of return.

So what is the internal rate of return?

What does the internal rate of return say?

The internal rate of return is the rate of interest at which the project's net income, adjusted to today's prices, is 0. In other words, at this interest rate, the discounted (adjusted to today) income from the investment project fully covers the costs of investors, but no more. There is no profit generated.

For an investor, this means that at such an interest rate, he will be able to fully compensate for his investments, that is, not to lose on the project, but not to earn anything either. You can also say that this is a profit threshold - the border, after crossing which the project becomes profitable.

At first glance, a slightly lengthy definition of the internal rate of return indicates an indicator that is of decisive importance for an investor in practice, since it allows you to quickly and, most importantly, visually get an idea of the feasibility of investing in a particular project.

Note! The indicator of the internal rate of return is a relative value. This means that by itself it says little. For example, if it is known that the internal rate of return of the project is 20%, then this information is not enough for the investor to make a decision. You need to know other inputs, which will be discussed later.

In order to understand how to use this indicator, you need to be able to calculate it correctly.

How to Calculate the Internal Rate of Return

The main feature of calculating the internal rate of return is that in practice it is usually not calculated manually using any formula. Instead, the following methods for calculating the indicator are common:

graphic method;
calculation using EXCEL.

To better understand why this happens, let's turn to the mathematical essence of the internal rate of return. Let's say we have an investment project that involves certain initial investments. As stated above, the internal rate of return is the rate at which project returns (adjusted) equal the initial investment costs. However, we do not know exactly when such equality will be established: in the 1st, 2nd, 3rd or 10th year of the life of the project.

Mathematically, this equality can be represented as follows:

IZ \u003d D 1 / (1 + St) 1 + D 2 / (1 + St) 2 + D 3 / (1 + St) 3 + ... + D n / (1 + St) n,

where: FROM - initial investment in the project;

D 1, D 2 ... D n - discounted cash income from the project in the 1st, 2nd and subsequent years;

St is the rate of interest.

As you can see, it is quite difficult to extract the value of the interest rate from this formula. At the same time, if we shift the IS in this formula to the right (with a negative sign), then we get the formula for the net present value of the project (NPV - the 2nd key indicator for evaluating the effectiveness of an investment project):

NPV \u003d -FROM + D 1 / (1 + St) 1 + D 2 / (1 + St) 2 + D 3 / (1 + St) 3 + ... + D n / (1 + St) n,

where: NPV is the net present value of the project.

For more information on what you need to know in order to correctly calculate NPV, see the article.

The most obvious in this regard is the graphical selection method. For this, a graph is built, where the possible values of the interest rate are plotted along the X axis, and the NPV values are plotted along the Y axis, and the dependence of NPV on the interest rate is shown on the graph. At the point where the resulting curved line of the graph crosses the X axis, the desired value of the interest rate is found, which is the internal rate of return of the project.

However, today, the internal rate of return is usually calculated by compiling a financial model in EXCEL, so it is important for any startup initiator to understand how to calculate the indicator without the help of charts.

To calculate the internal rate of return in EXCEL, there are 2 ways:

using built-in functions;
using the Solver tool.

1. Let's start with built-in functions. To calculate the internal rate of return for the project, you need to make a table of the annual planned indicators of the project, consisting of several columns. Be sure to reflect in it such numerical values as the initial investment and subsequent annual financial results of the project.

Important! The annual financial results of the project should be taken in an undiscounted form, i.e. not brought to current prices.

For greater clarity, you can give a breakdown of the annual planned income and expenses, which ultimately add up to the financial result of the project.

Example 1

Project life year	Initial investment, rub.	Planned income for the project, rub.	Planned expenses for the project, rub.	Financial results of the project, rub.
				-100 000

After compiling such a table, it remains to apply the IRR formula to calculate the internal rate of return.

Note! In the value cell of the IRR formula, you must specify the range of amounts from the column with the financial results of the project.

However, in practice, investment projects are not always accompanied by regular cash receipts. There is always a risk of a gap: freezing the project, suspending it for other reasons, etc. In such conditions, a different formula is used, which in the Russian version of EXCEL is referred to as CHISTVNDOKH. Its difference from the previous formula is that in addition to the financial results of the project, time periods (dates) for which specific financial results are formed should be indicated.

2. To calculate the internal rate of return using the "Search for Solutions" tool, it is necessary to add a column with the values of the annual discounted financial result to the table of planned values for the project. Next, you need to indicate in a separate cell that NPV will be calculated here, and write in it a formula containing a link to another empty cell in which the internal rate of return will be calculated.

Important! In the line "Set target cell" you need to provide a link to the cell with the NPV formula. Then indicate that the target cell should be equal to 0. In the "Changing the value of the cell" field, you must refer to an empty cell, in which the indicator we need should be calculated. Next, you should use the "Search for Solutions" and calculate the value of the interest rate at which NPV turns to 0.

After the internal profitability of the project is found, the main question arises: how to apply this information in order to correctly assess the attractiveness of investments?

Internal rate of return in the evaluation of investment projects

The attractiveness of any investment project can be determined by comparing the internal rate of return for the project with a similar indicator of another project or a comparison base.

If the investor is faced with the question of which project to invest in, then the choice should be made in favor of the one with the higher internal rate of return.

But what if there is only 1 project? In this case, the investor should compare the internal rate of return for the project with a certain universal base, which can serve as a guideline for the analysis.

Such a basis in practice is the cost of capital. If the cost of capital is below the internal rate of return of an investment project, such a project is considered to be promising. If the cost of capital, on the contrary, is higher, then it makes no sense for the investor to invest money in the project.

Instead of the cost of capital, you can use the rate of interest on an alternative risk-free investment. For example, on a bank deposit.

Example 2

A risk-free deposit in a bank can bring 10% per annum. In this case, an investment project with an internal rate of return of more than 10% will be an attractive investment option for the investor.

Limitations and Disadvantages of the Internal Rate of Return

Despite the fact that the calculation of the internal rate of return is able to help the investor as much as possible to assess the prospects for investing in a particular project, there are still a number of points that limit the practical application of the indicator:

Firstly, when choosing from alternative projects, it is not enough to compare only the internal rate of return for them among themselves. This indicator allows you to evaluate the return on the initial investment, and does not illustrate the income in its real assessment. As a consequence, projects with the same internal rate of return may have different net present value. And here the choice should be made in favor of the project, the net present value of which is greater, i.e., which will bring the investor more profit in monetary terms.
Second, an investment project can have a net present value greater than 0 for all interest rates. Such a project cannot be evaluated using the internal rate of return, since this indicator simply cannot be calculated for it.
Thirdly, in practice it is very difficult to accurately predict financial flows in the future. This is especially true for future earnings (revenues).

There are always economic, political and other risks that may lead to counterparties not paying on time. As a result, the financial model of the project and, accordingly, the value of the internal rate of return will be adjusted. So, predicting future income as accurately as possible is the number 1 task when developing a financial model.

Results

The internal rate of return is an indicator that is one of the most important in assessing the financial potential of an investment project. Investors look at it first of all.

The initiators of the project need to remember that the indicator can be calculated both using a graph and mathematically, in EXCEL (2 ways: using built-in functions and "Search for solutions"). It also helps to compare project values with known cost of capital.

In addition, it is important to understand that the indicator of the internal rate of return will clearly show the prospects of the project only in conjunction with the net present value, so it is advisable for the organization to present the calculation and NPV to the investor.

Before choosing any investment project, the Internal Rate of Return -IRR internal rate of return is calculated. At the same time, the amount of net present value is calculated at different discount rates, which can be done both manually and using automated methods. Thanks to this indicator, it is possible to determine the profitability of a possible investment and the optimal size of the loan rate. However, this method also has its drawbacks. What is IRR in practice and how to calculate the indicator using the calculation formula will be shown below.

IRR Definition and Economic Sense

The Internal Rate of Return or IRR in the Russian version is defined as the internal rate of return (IRR), or in other words, the internal rate of return, which is often called the internal rate of return.

This internal rate of return is the rate of interest at which the present value of all project cash flows (NPV) is zero. Under such conditions, the absence of losses is ensured, that is, the income from investments is identical to the costs of the project.

The economic meaning of the calculation is to:

Describe the profitability of a potential investment. The higher the value of the IRR rate of return, the higher the profitability of the project, and, accordingly, when choosing from two possible investment options, other things being equal, they choose the one where the IRR calculation showed a higher rate.
Determine the best loan rate. Since the calculation of IRR shows the maximum price at which the investment will break even, it can be correlated with the indicator of the loan rate that the company can take out for investment. If the interest on the planned loan is greater than the received IRR value, then the project will be unprofitable. And vice versa - if the loan rate is lower than the investment rate (GNI), then the borrowed funds will bring added value.

For example, if you take a loan for which you need to pay 15% per annum and invest in a project that will bring 20% per annum, then the investor earns on the project. If a mistake is made in project profitability estimates and the IRR is less than 15%, then the bank will have to pay more than the project activity will bring. The bank itself does the same, attracting money from the population and lending it to creditors at a higher percentage. Thus, by calculating the IRR, you can easily and simply find out the acceptable upper level - the limit of the cost of borrowed capital.

In fact, these opportunities are at the same time the advantages that the calculation of IRR gives the investor. The investor can compare promising projects with each other in terms of the efficiency of capital use. In addition, the advantage of using IRR is also that it allows you to compare projects with different investment periods - investment horizons. The IRR identifies the project that can generate large returns in the long run.

However, the peculiarities of GNI are that the obtained indicator does not allow for an exhaustive assessment of the investment project.

To assess investment attractiveness (including in comparison with other projects), IRR is compared, for example, with the required rate of return on capital (effective discount rate). This comparative value of practice is often taken as the weighted average cost of capital (WACC). But, instead of WACC, another rate of return can be taken - for example, the rate on a bank deposit. If after the calculations it turns out that the interest rate on a bank deposit is, for example, 15%, and the IRR of a potential project is 20%, then it is more expedient to invest money in the project, rather than place it on a deposit.

Internal Rate of Return Formula

To determine the IRR, they rely on the equation for net present value:

Based on this, for the internal rate of return, the formula will look like this:

Here r is the interest rate.

The same IRR formula in general will look like this.

Here CF t are cash flows at a point in time, and n is the number of time periods. It is important to note that the IRR indicator (as opposed to NPV) is applicable only to processes with the characteristics of an investment project - that is, for cases where one cash flow (most often the first one - the initial investment) is negative.

IRR Calculation Examples

The need to calculate the IRR is faced not only by professional investors, but also by almost any person who wants to profitably place the accumulated funds.

An example of calculating IRR for business investment

Let us give an example of using the method of calculating the internal rate of return under the condition of a constant barrier rate.

Project characteristics:

The size of the planned investment is $114,500.
Investment income:

in the first year: $30,000;
in the second year: $42,000;
in the third year: $43,000;
in the fourth year: $39,500.
The size of the compared effective barrier rate is at the level of 9.2%.

In this calculation example, the successive approximation method is used. "Types" of barrier rates are selected so that the minimum NPV values are obtained modulo. Then the approximation is carried out.

Let's recalculate the cash flows in the form of current values:

PV1 = 30000 / (1 + 0.1) = $27272.73
PV2 = 42000 / (1 + 0.1)2 = $34710.74
PV3 = 43000 / (1 + 0.1)3 = $32306.54
PV4 = 39500 / (1 + 0.1)4 = $26979.03

NPV(10.0%) = (27272.73 + 34710.74 + 32306.54 + 26979.03) - 114500 = $6769.04

PV1 = 30000 / (1 + 0.15)1 = $22684.31
PV2 = 42000 / (1 + 0.15)2 = $31758.03
PV3 = 43000 / (1 + 0.15)3 = $28273.20
PV4 = 39500 / (1 + 0.15)4 = $22584.25

NPV(15.0%) = (22684.31 + 31758.03 + 28273.20 + 22584.25) - 114500 = -9200.21$

Assuming that the NPV(r)-function is rectilinear on the segment a-b, we use the equation for approximation on this section of the straight line:

IRR calculation:

IRR = ra + (rb - ra) * NPVa /(NPVa - NPVb) = 10 + (15 - 10)* 6769.04/ (6769.04 - (-9200.21)) = 12.12%

Since a certain dependency must be saved, we check the result against it. The calculation formula is considered valid if the following conditions are met: NPV(a) > 0 > NPV(b) and r(a)< IRR < r(b).

The calculated IRR shows that the internal rate of return is 12.12%, which exceeds 9.2% (effective barrier rate), and, therefore, the project can be accepted.

To eliminate the problem of multiple definition of IRR and to avoid (with sign-variable cash flows) incorrect calculation, the NPV(r) graph is most often built.

An example of such a schedule is presented above for two conditional projects A and B with different interest rates. The IRR value for each of them is determined by the place of intersection with the X-axis, since this level corresponds to NPV=0. So in the example it can be seen that for project A, the point of intersection with the scale will be at the point marked 14.5 (IRR = 14.5%), and for project B, the point of intersection will be the point marked 11.8 (IRR = 11.8% ).

Comparative example of private investment

Another example of the need to determine the IRR is an illustration from the life of an ordinary person who does not plan to launch any business project, but simply wants to make the most of the accumulated funds.

Suppose the presence of 6 million rubles requires either taking them to the bank at interest, or purchasing an apartment in order to rent it out for 3 years, and then sell it, returning the fixed capital. Here, IRR will be calculated separately for each decision.

In the case of a bank deposit, it is possible to place funds for 3 years at 9% per annum. On the terms offered by the bank, you can withdraw 540 thousand rubles at the end of the year, and after 3 years - take all 6 million and interest for the last year. Since a deposit is also an investment project, the internal rate of return is calculated for it. Here it will coincide with the percentage offered by the bank - 9%. If the initial 6 million rubles are already available (that is, they do not need to be borrowed and interest paid for using the money), then such investments will be profitable at any deposit rate.
In the case of buying an apartment, renting it out and selling it, the situation is similar - funds are also invested at the beginning, then income is taken and, by selling the apartment, the capital is returned. If the cost of the apartment and rent do not change, then the rent at the rate of 40 thousand per month for the year will be equal to 480 thousand rubles. The calculation of the IRR indicator for the "Apartment" project will show 8% per annum (subject to the uninterrupted delivery of the apartment during the entire investment period and the return of capital in the amount of 6 million rubles).
IRR - internal rate of return

From this follows the conclusion that, if all conditions remain unchanged, even if there is own (rather than borrowed) capital, the IRR rate will be higher in the first Bank project and this project will be considered more preferable for the investor.

At the same time, the IRR rate in the second case will remain at the level of 8% per annum, regardless of how many years the apartment will be rented out.

However, if inflation affects the cost of an apartment, and it will consistently increase annually by 10%, 9% and 8%, respectively, then by the end of the billing period the apartment can already be sold for 7 million 769 thousand 520 rubles. In the third year of the project, this increase in cash flow will demonstrate an IRR of 14.53%. In this case, the "Apartment" project will be more profitable than the "Bank" project, but only if there is own capital. If, in order to acquire the starting amount, it will be necessary to apply to another conditional bank for a loan, then, taking into account the minimum refinancing rate of 17%, the Apartment project will be unprofitable.

Calculating IRR in Excel with Functions and Graph

IRR (Internal Rate of Return), or IRR is an indicator of the internal rate of return of an investment project. It is often used to compare different proposals for growth prospects and profitability. The higher the IRR, the greater the growth prospects for this project. Calculate the GNI interest rate in Excel.

Economic meaning of the indicator

Other names: internal rate of return (profit, discount), internal rate of return (efficiency), internal rate.

The IRR coefficient shows the minimum level of profitability of an investment project. In other words, it is the interest rate at which the net present value is zero.

The formula for calculating the indicator manually:

CFt - cash flow for a certain period of time t;
IC - investments in the project at the entry (launch) stage;
t is the time period.

In practice, IRR is often compared with the weighted average cost of capital:

IRR is higher - this project should be carefully considered.
IRR is lower - it is inappropriate to invest in the development of the project.
The indicators are equal - the minimum allowable level (the company needs to adjust the cash flow).

IRR is often compared to a percentage of a bank deposit.

If the interest on the deposit is higher, then it is better to look for another investment project.

An example of calculating IRR in Excel

range of values - a reference to cells with numeric arguments for which the internal rate of return should be calculated (at least one cash flow must have a negative value);
guess - a value that is supposedly close to the value of the IRR (the argument is optional; but if the function throws an error, the argument must be specified).

Let's take the numbers:

The initial cost was 150,000, so this numerical value was included in the table with a minus sign. Now let's find the IRR. Calculation formula in Excel:

Calculations showed that the internal rate of return of an investment project is 11%. For further analysis, the value is compared with the interest rate of a bank deposit, or the cost of capital of a given project, or the GNI of another investment project.

We calculated GNI for regular cash receipts. With non-systematic admissions, it is impossible to use the IRR function, because The discount rate for each cash flow will change.

Investment project IRR: formulas and calculation examples

Let's solve the problem with the help of the CHISTWINDOH function.

We modify the table with the initial data for the example:

Mandatory arguments of the PUREWINDOH function:

values are cash flows;
dates - an array of dates in the appropriate format.

IRR calculation formula for non-systematic payments:

A significant drawback of the two previous functions is the unrealistic assumption of the reinvestment rate. To correctly account for the assumption of reinvestment, it is recommended to use the MIRR function.

Arguments:

values - payments;
financing rate - interest paid for funds in circulation;
reinvestment rate.

Assume that the discount rate is 10%. It is possible to reinvest the income received at a rate of 7% per annum. Calculate the modified internal rate of return:

The resulting rate of return is three times less than the previous result. And lower funding rates. Therefore, the profitability of this project is doubtful.

Graphical Method for Calculating IRR in Excel

The IRR value can be found graphically by plotting the net present value (NPV) against the discount rate. NPV is one of the methods for evaluating an investment project, which is based on the cash flow discounting methodology.

For example, let's take a project with the following cash flow structure:

To calculate NPV in Excel, you can use the NPV function:

Since the first cash flow occurred in the zero period, it should not be included in the array of values. The initial investment must be added to the value calculated by the NPV function.

The function discounted the cash flows of periods 1-4 at a rate of 10% (0.10). When analyzing a new investment project, it is impossible to accurately determine the discount rate and all cash flows. It makes sense to look at the dependence of NPV on these indicators. In particular, from the cost of capital (discount rate).

Calculate NPV for different discount rates:

Let's see the results on the chart:

Recall that IRR is the discount rate at which the NPV of the analyzed project is zero. Therefore, the point of intersection of the NPV graph with the x-axis is the internal profitability of the enterprise.

Internal rate of return - IRR

Definition

Internal rate of return ( English Internal Rate of Return, IRR), also known as the internal rate of return, is the discount rate at which the net present value ( English Net Present Value, NPV) of the project is zero. In other words, the present value of all expected cash flows of the project is equal to the value of the initial investment. The IRR method is based on the discounted cash flow method, and the indicator itself is widely used in capital investment budgeting and in making investment decisions as a criterion for selecting projects and investments.

IRR Formula

Project Selection Criteria

The decision rule for selecting projects can be formulated as follows:

The internal rate of return must exceed the weighted average cost of capital ( English Weighted Average Cost of Capital, WACC) involved in the implementation of the project, otherwise it should be rejected.
If several independent projects meet the criteria above, they must all be accepted. If they are mutually exclusive, then the one with the highest IRR should be accepted.

An example of calculating the internal rate of return

Suppose there are two projects with the same level of risk, initial investment, and total expected cash flows. To better illustrate the concept of time value of money, Project A's cash flows are expected to arrive somewhat earlier than Project B's.

Substitute the data presented in the table into the equation.

To solve these equations, you can use the "VSD" function of Microsoft Excel, as shown in the figure below.

Select output cell I4.
Click the button fx, Select a category " Financial", and then the function " VSD" from the list.
In field " Meaning» select data range C4:H4, leave the " Assumption» and press the button OK.

Thus, the internal rate of return of Project A is 20.27%, and Project B is 12.01%. The scheme of discounted cash flows is presented in the figure below.

Assume that the weighted average cost of capital for both projects is 9.5% (because they have the same level of risk). If they are independent then they should be accepted as the IRR is above the WACC. If they were mutually exclusive, then Project A should be accepted because of the higher IRR.

Advantages and disadvantages of the IRR method

The use of the internal rate of return method has three significant drawbacks.

The assumption that all positive net cash flows will be reinvested at the project's IRR. In reality, such a scenario is unlikely, especially for projects with high values.
If at least one of the expected net cash flows is negative, the above equation can have multiple roots. This situation is known as the multiple IRR problem.
A conflict between the NPV and IRR methods may arise when evaluating mutually exclusive projects.
Internal rate of return (IRR). Formula and calculation example in Excel

In this case, one project will have a higher net present value but a lower internal rate of return, while the other will have the opposite. In such a situation, a project with a higher net present value should be preferred.

Consider the conflict between NPV and IRR in the following example.

For each project, the net present value was calculated for a range of discount rates from 1% to 30%. Based on the obtained NPV values, the following graph was constructed.

With a cost of capital between 1% and 13.092%, Project A is preferred because its net present value is higher than that of Project B. A cost of capital of 13.092% is the point of indifference because both projects have the same net present value. With a cost of capital of more than 13.092%, the implementation of Project B is already preferable.

From the point of view of IRR as the only selection criterion, Project B is more preferable. However, as can be seen from the chart, this conclusion is false if the cost of capital is less than 13.092%. Thus, it is advisable to use the internal rate of return as an additional selection criterion when evaluating several mutually exclusive projects.

Return to investment analysis methodology

IRR Internal Rate of Return

The internal rate of return is the rate of return generated by an investment. This is the one rate of return (barrier rate, discount rate), at which the net present value of the investment is zero, or this is the discount rate at which the discounted income from the project equals the investment costs. The internal rate of return determines the maximum acceptable discount rate at which funds can be invested without any loss to the owner.

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

Its value is found from the following equation:

NPV(IRR) is the net present value calculated at the IRR rate,
CFt - cash inflow in period t;
It is the amount of investments (costs) in the t-th period;
n is the total number of periods (intervals, steps) t = 0, 1, 2, …, n.

Defined: as the rate of return at which the net present value of an investment is zero.

Characterizes: least accurately, the effectiveness of the investment, in relative terms.

Synonyms: internal rate of return, internal rate of return, Internal Rate of Return.

Acronym: IRR

Disadvantages: the level of reinvestment is not taken into account, it does not show the result of the investment in absolute terms, with sign-variable flows it can be calculated incorrectly.

Acceptance criterion: IRR > R bar ef (the more the better)

Comparison conditions: any investment period and size.

The economic meaning of this indicator is that it shows the expected rate of return (ROI) or the maximum allowable level of investment costs in the project being evaluated. IRR must be higher than the weighted average price of investment resources:

IRR > Rbar eff (CC)

If this condition is met, the investor can accept the project, otherwise it must be rejected.

The advantages of the internal rate of return (IRR) indicator are that, in addition to determining the level of return on investment, it is possible to compare projects of different sizes and different durations.

The internal rate of return (IRR) measure of investment performance has three major drawbacks.

First, it is assumed by default that positive cash flows are reinvested at a rate equal to the internal rate of return.

Internal rate of return

If the IRR is close to the firm's reinvestment level, then this problem does not arise; when the IRR of a particularly attractive investment project is, for example, 80%, it means that all cash receipts must be reinvested at a rate of 80%. However, it is unlikely that the enterprise has annual investment opportunities that provide a return of 80%. In this situation, the indicator of internal rate of return (IRR) overestimates the effect of investments (in the indicator MIRR, the modified internal rate of return, this problem is eliminated).

Secondly, there is no way to determine how much money an investment will bring in absolute terms (rubles, dollars).

Thirdly, in a situation with sign-variable cash flows, several IRR values can be calculated or an incorrect value can be determined (in the Altair Investment Analysis 1.xx program, this problem has been eliminated programmatically, it will also be in Altair Investment Analysis 2.01).

Example #1. Calculating the internal rate of return at a constant barrier rate.
The amount of investment is $115,000.
Investment income in the first year: $32,000;
in the second year: $41,000;
in the third year: $43,750;
in the fourth year: $38250.
The effective barrier rate is 9.2%.

Let's solve the problem without using special programs. We use the method of successive approximation. We select barrier rates in such a way as to find the minimum values of NPV modulo, and then we carry out an approximation. Standard method - does not eliminate the problem of multiple determination of IRR and there is a possibility of incorrect calculation (with variable cash flows). To fix the problem, an NPV (r) graph is usually plotted.

Calculate for the barrier rate equal to ra=10.0%
PV1 = 32000 / (1 + 0.1) = $29090.91
PV2 = 41000 / (1 + 0.1)2 = $33884.30
PV3 = 43750 / (1 + 0.1)3 = $32870.02
PV4 = 38250 / (1 + 0.1)4 = $26125.27

NPV(10.0%) = (29090.91 + 33884.30 + 32870.02 + 26125.27) - 115000 =
= 121970,49 — 115000 = 6970,49$

Calculate for the barrier rate equal to rb=15.0%
Let's recalculate cash flows in the form of current values:
PV1 = 32000 / (1 + 0.15)1 = $27826.09
PV2 = 41000 / (1 + 0.15)2 = $31001.89
PV3 = 43750 / (1 + 0.15)3 = $28766.34
PV4 = 38250 / (1 + 0.15)4 = $21869.56

NPV(15.0%) = (27826.09 + 31001.89 + 28766.34 + 21869.56) - 115000 = 109463.88 - 115000 = - $5536.11

We make the assumption that the NPV(r) function is rectilinear in the section from point a to point b, and use the formula for approximation on the straight line section:

IRR = ra + (rb - ra) * NPVa /(NPVa - NPVb) = 10 + (15 - 10) * 6970.49 / (6970.49 - (- 5536.11)) = 12.7867%

The formula is valid if the conditions ra< IRR < rb и NPVa >0 > NPVb.

Answer: the internal rate of return is 12.7867%, which exceeds the effective barrier rate of 9.2%, therefore, the project is accepted.

Example #2. IRR at a variable barrier rate.
The investment amount is $12,800.
in the second year: $5185;
in the third year: $6270.
The barrier rate is 11.4% in the first year;
10.7% in the second year;
9.5% in the third year.
Determine the acceptability of the project by the IRR parameter.

Calculate for the discount rate equal to ra=20.0%
Let's recalculate cash flows in the form of current values:
PV1 = 7360 / (1 + 0.2) = $6133.33
PV2 = 5185 / (1 + 0.2)^2 = $3600.69
PV3 = 6270 / (1 + 0.2)^3 = $3628.47

NPV(20.0%) = (6133.33 + 3600.69 + 3628.47) - 12800 = 13362.49 - 12800 = $562.49

Calculate for the discount rate equal to rb = 25.0%

Let's recalculate cash flows in the form of current values:
PV1 = 7360 / (1 + 0.25) = $5888.00
PV2 = 5185 / (1 + 0.25)^2 = $3318.40
PV3 = 6270 / (1 + 0.25)^3 = $3210.24

NPV(25.0%) = (5888.00 + 3318.40 + 3210.24) - 12800 = 12416.64 - 12800 = -383.36

IRR = 20 + (25 - 20) * 562.49 / (562.49 - (- 383.36)) = 22.9734%.

Because barrier rate is variable, then comparison is made with the effective barrier rate.
Based on the example calculation, the effective barrier rate is 10.895%.

Answer: the internal rate of return is 22.9734%, exceeds 10.895%, therefore, the project is accepted.

The rule according to which, from two projects, a project with a large IRR is selected does not always work. After taking into account the level of reinvestment (example #3) or the barrier rate (example #4), a project with a lower IRR may be more profitable than a project with a higher IRR.

Example #3. Exception to the rule: the choice of a project with a large IRR value, the impact of the level of reinvestment of the barrier rate.
The barrier rate is 12%.
The level of reinvestment is constant and equals 10%.
The first project generates a profit equal to 200 rubles at the end of 1 year and 100 rubles at the end of the second year, and the second generates a profit equal to 160 rubles during the first 3 years and then 60 rubles each for another 4 years.
Compare two projects.

Let's calculate the values of the IRR and MIRR parameters for each of the projects:
IRR1 = 141.42%.
IRR2 = 153.79%.
MIRR1 = 73.205%.
MIRR2 = 40.0%.
But at the same time, the annual yield calculated according to the MIRR model will be 73.205% for the first project, and only 40.0% for the second, despite the higher IRR. Because calculation according to the MIRR model is more accurate than IRR, then the first investment project will be accepted (if we consider only from the point of view of financial efficiency).

Example number 4. Exception to the rule: selection of a project with a large IRR value, the impact of the barrier rate.
The cost of investment for both projects is 100 rubles.
The barrier rate is 25%.
The first project generates a profit equal to 160 rubles at the end of 1 year, and the second generates a profit equal to 80 rubles for 7 years.
Compare two projects.

IRR1 = 60.0%.
IRR2 = 78.63%.
Because the validity of investment projects varies significantly, then it is not possible to compare by the DPI parameter; compare by MIRR(bar) and with NRR in annual terms.
MIRR(bar)1 = 60.0%
MIRR(bar)2 = 42.71%
Net return NRR1, per annum = 28%.
Net return NRR2, per annum = 21.84%.

Indicators MIRR (bar) and NRR, % per annum are higher for the first project, despite the lower IRR.

Example number 5. Sensitivity analysis.
The investment amount is $12,800.
Investment income in the first year: $7360;
in the second year: $5185;
in the third year: $6270.
Determine how the value of the internal rate of return will be affected by a 23.6% increase in return on investment.

The initial internal rate of return was calculated in example No. 2 and is equal to IRRin = 22.97%.
Let's determine the value of cash flows, taking into account their increase by 23.6%.
CF1 Ah = 7360 * (1 + 0.236) = $9096.96
CF2 Ah = 5185 * (1 + 0.236) = $6408.66
CF3 Ah = 6270 * (1 + 0.236) = $7749.72

Calculate for the discount rate equal to ra = 30.0%
Let's recalculate cash flows in the form of current values:
PV1 Ah = 9096.96 / (1 + 0.3)1 = $6997.661
PV2 Ah = 6408.66 / (1 + 0.3)2 = $3792.106
PV3 Ah = 7749.72 / (1 + 0.3)3 = $3527.410
NPVhr(30.0%) = (6997.661 + 3792.106 + 3527.410) - 12800 = 13593.118 - 12800 = $793.1180

Calculate for the discount rate equal to rb = 40.0%
Let's recalculate cash flows in the form of current values:
PV1 Ah = 9096.96 / (1 + 0.4)1 = $6497.828
PV2 Ah = 6408.66 / (1 + 0.4)2 = $3269.724
PV3 Ah = 7749.72 / (1 + 0.4)3 = $2824.242
NPVhr(40.0%) = (6497.828 + 3269.724 + 2824.242) - 12800 = 12591.794 - 12800 = - $208.206

IRRach \u003d 30 + (40 - 30) * 793.118 / (793.118 - (- 208.206)) \u003d 37.92%.

Let's determine the change in the internal rate of return: (IRRach - IRRout) / IRRout * 100% = (37.92 - 23.6) / 23.6 * 100% = 60.68%.

Answer. An increase in income by 23.6% led to an increase in internal rate of return by 60.68%.

Note. Discounting cash flows at a time-varying barrier rate (discount rate) complies with "Methodological guidelines No. VK 477 ..." item 6.11 (p. 140).

Internal rate of return (IRR)

Internal Rate of Return (IRR) is the discount rate at which the Net Present Value (NPV) equals zero (i.e. total income equals total investment).

Calculating the internal rate of return

In other words, this indicator reflects break even rate of return project.

An example of a graphical calculation of the IRR indicator

3. Graph of change in the level of profitability depending on the discount rate

Based on the calculated NPV values at a discount rate of 12% and 18% per annum, a graph is built. The result will be especially accurate if the graph is based on data with positive and negative values.

An example of the mathematical calculation of the IRR indicator

Let our project be designed for 1 year. Initial investment = 100 thousand rubles. Net income for the year = 120 thousand rubles. Calculate IRR.

120/(1+ IRR) 1 – 100 = 0

120/(1+ IRR) 1 = 100 (multiply both sides of the equation by (1+IRR) 1 }

120 = 100 (1+ IRR) 1

120 = 100 + 100 IRR

20 = 100 IRR

IRR = 20/100 = 0.2 or 20%

Or you can use the formula:

where r1 is the value of the selected discount rate, at which NPVi>0; r2 is the value of the selected discount rate at which NPV2<0.

ANALYSIS OF THE RESULTS

1) If someone invests in us

R < IRR

If the discount rate is below the internal rate of return IRR, then the capital invested in the project will bring a positive NPV value, therefore, the project can be accepted.

R= IRR

If the discount rate is equal to the internal rate of return IRR, then the project will not bring profit or loss, therefore, the project should be rejected.

R>IRR

If the discount rate is higher than the internal rate of return IRR, then the capital invested in the project will bring a negative NPV value, therefore, the project should be rejected.

Thus, if the project is financed entirely by a loan commercial bank(the bank invests in us), then the value IRR shows the upper limit of the acceptable level of the bank interest rate, the excess of which makes the project unprofitable.

For example: if the IRR calculated for our project = 12%, then we will take a loan only from the bank with the rate = 9, 10 or 11%.

2) If we invest (we invest in our own business, in a bank or lend to another organization)

It is worth accepting the project with a higher IRR, i.e. IRR -> max.

In fact, now we have taken the place of the bank. The higher the IRR in any project, the higher the discount rate ( R) we can use and the more income from investing our funds we will receive.

Internal rate of return

Project internal rate of return

Internal rate of return

Net internal rate of return

Internal norm method

Internal rules of the organization

Internal rate of return rate

Modified internal rate of return

Statistical methods for evaluating the effectiveness of investments / investment projects

Payback period (Payback Period)

The formula for calculating the payback period of investments (investment project)

An example of calculating the payback period of an investment project in Excel

Directions for using the payback period of investments (investment projects)

Advantages and disadvantages of the payback period indicator

Return on Investment Ratio (Accounting Rate of Return)

The formula for calculating the return on investment ratio

An example of calculating the return on investment (investment project) in Excel

Purposes of using the profitability ratio of the investment project

Advantages and disadvantages of the return on investment ratio

Dynamic methods for evaluating the effectiveness of investments / investment projects

Net present value (Net Present Value)

Net present value formula

Project evaluation based on the NPV criterion

An example of calculating net present value in Excel

Master class: "How to calculate net present value for a business plan"

Internal rate of return of an investment project

The formula for calculating the internal rate of return of an investment project

An example of calculating the IRR of an investment project in Excel

Advantages and Disadvantages of IRR Internal Rate of Return

Master class: "How to calculate the internal rate of return for a business plan"

Investment Profitability Index

The formula for calculating the investment profitability index

A variation of the investment profitability index formula

Project evaluation based on the PI criterion

An example of calculating the profitability index of a project in Excel

Discounted ROI

The formula for calculating the discounted payback period of investments

An example of calculating the discounted payback period of investment in Excel

Advantages and disadvantages of the discounted payback period

Master class: "How to calculate the payback period for a business plan: instructions"

Choosing an Investment Based on Performance Evaluation Factors

Price for developing business plans

Why the internal rate of return is key

What does the internal rate of return say?

How to Calculate the Internal Rate of Return

Internal rate of return in the evaluation of investment projects

Limitations and Disadvantages of the Internal Rate of Return

Results

IRR Definition and Economic Sense

Internal Rate of Return Formula

IRR Calculation Examples

An example of calculating IRR for business investment

Comparative example of private investment

IRR - internal rate of return

Calculating IRR in Excel with Functions and Graph

Economic meaning of the indicator

An example of calculating IRR in Excel

Investment project IRR: formulas and calculation examples

Graphical Method for Calculating IRR in Excel

Internal rate of return - IRR

Definition

IRR Formula

Project Selection Criteria

An example of calculating the internal rate of return

Advantages and disadvantages of the IRR method

Internal rate of return (IRR). Formula and calculation example in Excel

IRR Internal Rate of Return

Internal rate of return

Internal rate of return (IRR)

Calculating the internal rate of return