modified internal rate of return. Internal rate of return (IRR) and its modified version (MIRR). The value of the components of the mvnd

Without investment analysis, even when starting the smallest enterprise, in modern conditions it is impossible to do. Discount rate, payback period, marginality, internal rate of return, etc., one way or another, have already become familiar to us concepts. But in this article, we would like to talk about one more parameter of investment analysis - the modified internal rate of return ( MIRR). Next, we will explain why this indicator is calculated, how to do it yourself and what value MIRR has in business planning.

What is MIRR?

MIRR) is an indicator characterizing another related parameter of investment analysis, the discount rate. MIRR characterizes such a discount rate at which the total present value of income from ongoing investments will be equal to the value of these investments. Therefore MIRR often confused with the internal rate of return (IRR), but there are some differences, which we will discuss later.

In some cases, you can do without calculating the modified internal rate of return. But it should be understood that the more complete your investment analysis is, the more meaningful and objective the business plan of the project will look. This is especially important when attracting investments or obtaining a large bank loan for business development. Then your business plan and its financial and settlement component will be checked by professionals, for whom the presence of a modified internal rate of return in your calculations will become a sign of the seriousness and professionalism of the borrower. For such specialists, a business plan without a financial model and investment analysis is of no value. Moreover, the business plan must link the calculation of financial indicators with marketing analysis, technological characteristics, etc. To see how to properly structure a business plan and develop a suitable financial model, we advise you to look at an example of such a finished document. For example, for a sample, you can say a business plan suitable for the specifics of your activity on our website.

Formula for calculating MIRR

To begin with, we note that the difference between the internal rate of return and the modified rate of internal return is, first of all, in the calculations. MIRR is rather a more extended "version". There are three basic methods for this:

1. When all values ​​of income (cash flows from the implementation of the project) are brought to the end of the project. In this case, returns are shown at a rate that is equal to the weighted average cost of capital (WACC).
2. VSN initial and repeated investments are reduced to initial values. In this case, the discount rate is used to calculate the project.
3. The Modified Internal Rate of Return is defined as the rate of return at which all expected returns adjusted to the end of the project have a present value equal to the cost of all required costs.

MIRR indicator - as an indicator of the investment attractiveness of the project

The advantage of the indicator considered in this article is that it is very often used in practice, moreover, at the highest level of top managers.

Firstly, this is due to the fact that, unlike the internal rate of return, this parameter implies that the definition of the discount rate is included in the calculation of the modified internal rate of return.

Secondly, MIRR is calculated as a percentage and therefore this parameter is much more convenient for analysis. Relative indicators are easier to compare with each other. For example, MIRR easy to compare with the rate of a bank deposit or loan to determine the feasibility of investing in a project.

Thirdly, any investment project assumes the presence of initial investments in the form of an outflow of funds, which will lead to cash inflows in the future (ideally). And in the case of starting a business, the invested funds do not always bring the same result, in the same time frame, as, for example, in the case of renting out housing or opening a bank deposit. Therefore, in order to understand what income can be expected when investing, first of all, it is necessary to determine the modified internal rate of return and payback periods.

MIRR allows you to understand how profitable and expedient it will be to invest in the project. Moreover, it will allow assessing the margin of safety and sustainability of the company.

Investment analysis is carried out, first of all, in order to determine the profitability of the project and then after what time and in what amount it will be possible to receive this profit. Therefore, one of the most important and interesting indicators of investment analysis is the estimated rate of return. In this article, we will analyze in detail what it is, how and why this indicator is calculated. In addition, this indicator may be interesting for the owners of the company to consider, as it shows how much money each invested ruble brings. And also the average rate of return allows you to compare different projects and choose the most profitable one. Therefore, it is important to correctly calculate MIRR.

Modified internal rate of return (MIRR) and its role in business planning

Modified internal rate of return ( MIRR) in business planning has a significant advantage over other indicators of investment analysis. For example, a simple internal rate of return (IRR) does not make it possible to conduct such an extended investment analysis that would allow inter-industry and macroeconomic comparisons based on this rate (norm).

Another advantage of the modified internal rate of return ( MIRR) is that it assumes that all cash flows will be reinvested (reinvested) at the discount rate, and not at the IRR of the project. In this way, MIRR allows more accurate evaluation of reinvestment projects.

Definition modified internal rate of return ( MIRR) is an important and indicative parameter. But on its own, it has little to offer. It is better to calculate it in conjunction with other investment analysis parameters:

• payback period;
• return on investment;
• internal rate of return;
• financial ratios, etc.

Moreover, not only the calculation of any parameter should be carried out in combination with other parameters. It is also necessary to conduct investment analysis in conjunction with comprehensive business planning. So, the calculation of which is given in the corresponding article.

Conclusions: what if you do not define a modified rate of return (MIRR)

Thus, we can conclude that modern investment analysis does not stand still. The appearance of various modifications in the calculation of the parameters of an investment project makes it possible to carry out more and more accurate forecasts and comparisons. Modified internal rate of return ( MIRR) allows you to analyze the feasibility of the project, becomes the basic element when comparing the profitability of the project and alternative options for investing free financial resources.

This indicator is an important link in the multi-stage system for analyzing cash flows (mainly income) for the project. This analysis system is divided into the following levels:

• The ratio between income and expenses (including alternative ones);
• The prospects of the business or industry;
• Income structure.

The last level is especially important because the structure of income primarily affects how investors decide to invest in a particular project. Another factor that influences an investor's decision to invest is a well-written business plan. It is important not only to carry out all the calculations, but to make sure that the automatic model changes automatically, and the correct, clear and logical structure of the business plan is also important.

Organizing your business, you should think through everything very carefully. For example, it will help you create a financial model and calculate all the necessary indicators.

In order to do everything right, as well as save your time and money, we advise you to focus on ready-made sample business plans. The advantage of a ready-made business plan is, first of all, a working automatic financial model and a clear structure that allows you to plan future activities step by step. It will also be possible to seek help from specialists in the field of professional development of business plans.

Modified internal rate of return mirr

For non-standard cash flows, the solution of the equation corresponding to the definition of the internal rate of return, in the overwhelming majority of cases (non-standard flows with a single IRR value are possible) gives several positive roots, i.e. several possible IRR values. In this case, the IRR > i criterion does not work: the IRR value may exceed the discount rate used, and the project under consideration turns out to be unprofitable (its NPV turns out to be negative).

To solve this problem in the case of non-standard cash flows, an analogue of IRR is calculated - a modified internal rate of return MIRR (it can also be calculated for projects generating standard cash flows).

MIRR is the interest rate at which, during the project implementation period n, the total amount of all discounted investments at the initial moment is accumulated, a value equal to the sum of all cash inflows accrued at the same rate d at the end of the project implementation is obtained:

(1+MIRR)n ∑ INV / (1 + i)t= ∑CFk (1+i)n-k

Decision Criteria - MIRR > i . The result is always consistent with the NPV criterion and can be used to evaluate both standard and non-standard cash flows. In addition, the MIRR indicator has another important advantage over IRR: its calculation involves reinvesting the income received at a rate equal to the discount rate (close or equal to the average market rate of return), which is more consistent with the real situation and therefore more accurately reflects the profitability of the project being evaluated.

Rate of return and profitability index p

Profitability is an important indicator of investment efficiency, since it reflects the ratio of costs and income, showing the amount of income received for each unit (ruble, dollar, etc.) of invested funds.

P =NPV/ INV x 100%

Profitability index (profitability ratio) PI- the ratio of the present value of the project to the costs, shows how many times the invested capital will increase during the implementation of the project.

PI = [∑CFk/ (1 + i)k ] / INV = P / 100% + 1

The criterion for making a positive decision when using profitability indicators is the ratio P > 0 or, equivalently, PI > 1. Of several projects, those with higher profitability are preferable.

This indicator is especially informative when evaluating projects with different initial investments and different implementation periods.

The profitability criterion can give results that contradict the criterion of net present value if projects with different amounts of invested capital are considered. When making a decision, it is necessary to take into account the investment opportunities of the enterprise, as well as the consideration that the NPV indicator is more in the interests of shareholders in terms of increasing their capital.

Evaluation of investment projects of different duration

In cases where there is doubt about the correctness of the comparison using the considered indicators of projects with different implementation periods, one can resort to chain repetition method

When using this method, find the least common multiple of n implementation times for n 1 and n 2 projects being evaluated. They build new cash flows resulting from several project implementations, assuming that costs and incomes remain at the same level (the beginning of the next implementation coincides with the end of the previous one). The net present value of multiple sales will change, but the internal rate of return will remain the same, regardless of the number of repetitions, although new cash flows may be non-standard if the initial investment is greater than the income in the last period of sale.

The use of this method in practice can be associated with complex calculations, if several projects are considered and in order to match all the deadlines, each will need to be repeated several times.

The main disadvantage of the chain repetition method is the assumption that the conditions for the implementation of projects, and hence the required costs and revenues, will remain at the same level, which is almost impossible in the current market situation. Also, the re-implementation of the project itself is not always possible, especially if it is long enough or relates to areas where there is a rapid technological renewal of manufactured products.

In addition to the considered quantitative indicators of the effectiveness of capital investments, when making investment decisions, it is necessary to take into account the qualitative characteristics of the attractiveness of the project, corresponding to the following criteria:

Compliance of the considered project with the general investment strategy of the enterprise, its long-term and current plans;

The prospects of the project in comparison with the consequences of refusing to implement alternative projects;

Compliance of the project with the accepted regulatory and planned indicators regarding the level of risk, financial stability, economic growth of the organization, etc.;

Ensuring the necessary diversification of the financial and economic activities of the organization;

Compliance of the project implementation requirements with the available production and human resources;

Social consequences of the project implementation, possible impact on the reputation, image of the organization;

Compliance of the project under consideration with environmental standards and requirements.

Network management planning method in R&D planning.

The creation and development of the production of new types of products include the implementation of research and development work, design of the technological process, construction, installation and commissioning, logistics and others.

To plan work and ensure effective operational control and regulation in the course of their implementation, a network planning and management system (SPM) is used.

The network planning and management system is based on a graphic representation of the work package, reflecting their logical sequence and interconnection, as well as duration. The compiled schedule is optimized and used to manage the progress of work during their implementation. The SPU system makes it possible to:

ensure planning of the logical sequence and interconnection of a large number of works and performers;

identify work that determines the deadline for the completion of all pre-production and systematically monitor their implementation;

optimize the work plan, ensuring a uniform and rational workload of performers;

exercise control and operational regulation of the progress of work in case of violation of planned deadlines.

When using STC, the process model is depicted in the form of an oriented graph, which is called a network graph or simply a network. The schedule consists of activities and events. Work is a process that requires labor and time to complete it. For example, the development of technical specifications, the manufacture of a layout, etc. The event ends. In terms of content, it reflects the result of previous work and has no duration. Works in the network diagram are depicted by arrows, events by circles.

With the parallel execution of two or more jobs that have a single source event and lead to a single resulting event, a fictitious job is introduced, depicted on the graph as a dotted arrow. Dummy work means that the transition from one event to another does not require spending resources (temporary, labor), it models only the logical sequence and interconnection of events.

Each event and work is assigned its own code. For an event, this is its sequence number; for a job, this is the numbers of its initial and final events. The content of events and works must be reflected in a concise and clear wording and entered in the appropriate tables, for example:

0-1. Study of existing analogues.

0-2. Development of technical specifications, etc.

0. The decision to create the device has been made.

1. The study of existing analogues is completed.

2. Terms of reference completed, etc.

The STC methodology is based on the analysis of full and partial (intermediate) paths of the network diagram. A full path is any continuous sequence of activities from the initiating event to the final one. Of all the full paths, the most important is the maximum, which is called critical, since it determines the duration of the entire set of works.

In complex graphs, there may be multiple critical paths. Network planning involves, first of all, the identification of activities that lie on the critical path, with the aim of subsequent priority monitoring of the progress of these activities.

The SPU process consists of the following steps:

building a network schedule and determining the time of work;

determination of the critical path and time reserves;

analysis and optimization of the network diagram;

application of a network schedule to manage the progress of work.

The calculation of network diagrams and their optimization can be performed manually or using computer technology.

Evaluation of the effectiveness of capital investments by static methods

With one-stage capital investments, a small calculation period and small discount rates (0.05), discounting of results and costs can be omitted. Then, to assess the effectiveness of capital investments, indicators of absolute (general) and comparative economic efficiency are used.

The indicators of overall economic efficiency include:

– net income (annual economic effect);

– return on investment (profitability index, efficiency ratio);

- payback period of capital investments.

net income (annual economic effect) is calculated by the formula

ROI is set according to the formula

where is the annual profit from the implementation of the project (when assessing the effectiveness of investments, instead of profit, savings in current costs (expenses for the main type of activity) as a result of the implementation of the project can be taken; - capital investments in the designed facilities.

Estimated payback period is set according to the formula

When calculating the overall efficiency, the project is considered effective if the following conditions are met:

The standard payback period is taken depending on the nature of the investment project (5–10 years).

The indicators of comparative economic efficiency include:

– payback period of additional capital investments;

– coefficient of comparative efficiency;

- reduced construction and operating costs

Payback period for additional capital investments calculated by the formula

where additional capital investments for one of the compared options (); - increase in economic effect (income).

If the results of investments differ only in current costs and the amount of income from the main activity is not taken into account in the calculations, payback period is calculated according to the formula

where is the savings in current costs (expenses for core activities).

Comparative efficiency ratio (efficiency ratio of additional capital investments) shows the change in the annual economic result with an increase in capital investments:

Reduced construction and operating costs calculated by the formula

or . (4.17)

Annual economic effect () is calculated by the formula

When calculating comparative efficiency, a project is considered effective if the following conditions are met:

When evaluating the effectiveness of investment projects in railway transport, which differ in terms of delivery of goods, the cost of goods en route is taken into account:

where is the cost of the reduced mass of the cargo; – average price of 1 ton of cargo, rub.; - annual shipment of goods, t; - length of the section (distance of transportation) of cargo, km; – route speed of cargo delivery, km/h.

This indicator in the calculations is summed up with capital investments.

When assessing the economic efficiency of investments in projects for the development of stations and nodes, the cost of the mass of cargo in the calculations can be ignored.

When choosing a variant of a design solution and evaluating the effectiveness of investments in the construction and development of railway stations and nodes in the case when the duration of construction is not considered, any static indicators of economic efficiency can be used. The choice of calculation method depends on the nature of the initial information.

In the graduation project, the optimal option for the construction or reconstruction of stations should be chosen according to dynamic or static indicators of commercial efficiency.

To select an investment option, indicators of comparative economic efficiency are used, which involve only the cost parts that vary according to options.

Comparative economic efficiency indicators:

Comparative value of the integral effect;

Payback period of additional investments;

The coefficient of efficiency of additional investments.

Comparative value of the integral effect differs from its total value in that it does not take into account the components that do not change according to the options. If the options differ only in the size of the required investments and operating costs (current costs), then the most effective solution will correspond to the minimum sum of the reduced construction and operating costs (Zp).

Under a planned economy, the annual present costs (3 g):

Z g \u003d E n K + C, → min

where: E n - constant discount rate (= 0.12);

K - capital investments (the size of investments);

C - annual running costs.

The difference between the given construction and operating costs can be represented as:

Z g \u003d E n (K 1 -K 2) + (C 1 -C 2),

where: K 1 and K 2 - the amount of investment by options.

At present, it is advisable to calculate the reduced costs (Z p) when comparing investment options in the form of a modified form, depending on

where: C t - operating costs (current costs) in the t-th year;

α is the share of tax charges on income.

Payback period of additional investments (T), shows the time period for which additional investment costs in a more expensive option pay off due to the increase in economic results due to these additional investments. The estimated payback period (T) is determined in the general case from the equality:

where: R t , З t , K t - are given according to the options in the t-th year.

Efficiency ratio of additional investment investments(comparative efficiency coefficient) Er shows what effect in the form of an excess of annual results over costs causes an increase in investment:

where: R, Z and K 0 are given by options.

The calculated value of the efficiency coefficient E r is compared with its standard value (E n), which corresponds to the rate of return on capital that satisfies the investor. When E r > E n, a more investment-intensive option is adopted.

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.

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:

1. Describe the profitability of a potential investment. The higher the value of the IRR rate of return, the higher the project profitability indicator, 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.
2. 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 features of GNI are that the resulting indicator does not allow for an exhaustive assessment.

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.

We recalculate 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.

1. 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 starting 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.
2. 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).

From this it follows that, if all conditions remain unchanged, even with 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 consistently increases annually by 10%, 9% and 8%, respectively, then by the end of the billing period the apartment can 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.

After reading the article, the reader will be able to find out:

• what is NPV and irr of an investment project;
• how to calculate NPV;
• how to calculate the irr of an investment project;
• how to calculate mirr;
• how the performance indicators of investment projects are calculated in practice.

All investors are faced with the problem of evaluating the proposed investment projects. At the same time, it is often difficult to assess the profitability of a project when investments in it are stretched over time.

In this case, the main evaluation indicators are:

• investment project - irr - internal rate of return;
• NPV - net present value;
• mirr is the modified internal rate of return.

The indicator irr in the analysis of the effectiveness of investment projects is most often used together with the indicator of net present value NPV.

In general, all indicators that make it possible to make a decision on the feasibility of investing in projects are divided into two groups:

• dynamic, based on discounting;
• static, not involving the use of discounting.

Static methods involve the use of well-known formulas for evaluating economic efficiency, so let's dwell on dynamic indicators in more detail. The economic efficiency of the investment project npv and irr, as well as mirr are important indicators that allow investors to make the right decisions.

When analyzing investment projects, it is very important to use both groups of indicators, since they complement each other. It is in this case that the investor will be able to get an objective picture that allows him to make the right decision.

Advice! There are many financial calculators or programs, including those in the EXCEL spreadsheet editor, that allow you to calculate project performance indicators. Their use will significantly reduce the time for calculations and allow for a more thorough analysis of the feasibility of investing.

Calculation of NPV

Calculation of net present value - NPV is the difference between the amount of investment and payments on loan obligations, or, if the loan is not used, payments on the current financing of the project. The calculation is carried out on the basis of a fixed discount rate without taking into account the time factor and allows you to immediately assess the prospects of the project.

where:

• D- discount rate,
• CF k - cash inflow in period k,
• n is the number of periods,
• INVt is the volume of investments in period t.

The interpretation of the performed calculations is based on the following logical conclusions:

• if NPV is greater than zero, then the project will be profitable;
• if the NPV value is zero, the increase in output will not lead to a decrease in profits;
• if NPV is less than zero, the project is likely to be unprofitable.

This indicator is very important when evaluating investment projects and is used together with other dynamic indicators.

irr calculation

The calculation of the indicator irr of the efficiency of an investment project has an important economic meaning. The calculation of this coefficient consists in estimating the maximum allowable amount of investment that an investor can spend on the analyzed project. The disadvantage of using irr is the complexity of calculations for an investor who does not have an economic education.

Advice! Despite the well-known indicators for calculating the effectiveness of the project, it must be remembered that they do not always take into account the specifics of the analyzed projects and therefore it is necessary to additionally use other analysis tools.

where:

• D 1 - discount rate corresponding to NPV 1 (positive value of net income); ;
• D 2 - discount rate corresponding to NPV 2 (negative value of net income).

Advice! IRR is a relative measure of the rate of return at which the net present value is zero. The accuracy of the indicator is the higher, the smaller the interval between D 1 - D 2, the criterion for choosing an investment project is the following ratio: IRR > D. In the case when several projects are considered, it is necessary to give preference to where the IRR is greater.

An important advantage of this indicator is that it allows you to assess the prospects of the project in terms of inflation. So, for example, if the IRR is less than the official inflation value, then it is worth more thoughtfully referring to such a project, since, in the end, the investment may not bring profit.

Advice! After calculating irr, be sure to compare it with the inflation rate! If the value of the indicator is lower, then it is necessary to make additional calculations and analyze the prospects for the overall development of the economy.

Analysis of investment indicators npv irr helps to identify differences and similarities between them.

The calculation of NPV and IRR is based on discounting the cash flows generated by the project:

• NPV allows you to calculate the present value of the project, given that the interest rate is known;
• IRR shows the maximum loan rate at which the project will definitely not be unprofitable.

The difference between these indicators is also due to the fact that NPV shows the result in monetary terms, and IRR - in percentage terms, which is often more understandable to the investor.

Modified internal rate of return MIRR

Mirr of the investment project is also used quite often. Modified internal rate of return (MIRR) is a discount rate that takes into account and balances the inflows and outflows of funds from the project. The use of this coefficient allows you to get a more objective assessment of the reinvestment rate (see).

where:

• A t - cash costs incurred by the investor during the development of the project for period t;
• S - cash receipts for the development of the project for the period t;
• k is the cost of the company's capital;
• n is the duration of the project.

The use of performance indicators in the real assessment of the effectiveness of investment

Investments npv irr: examples of problem solving. Consider an example of calculating NPV and IRR. To do this, we will presumably make a decision on the effectiveness of investing in the renovation of two apartments in order to further rent them out.

The initial investment is the same for each of the projects, but the yield for each apartment will be different. At first glance, it is more profitable to invest in apartment 1, since in three years the profit from the investment will be 1,800 thousand rubles, which is 200 thousand rubles more than the income from the second apartment.

Table 1 - Data for calculation:

Which project will be more profitable?

We accept the following simplifications:

• the discount rate is 10%;
• the investor receives income at the same time at the end of the year;
• Investments are made at the beginning of the year.

Of course, in real projects, you will have to take into account all the nuances and carry out calculations based on actual data, since otherwise you can get distorted data that will not allow you to make the right decision.

Calculate NPV for the first apartment:

Calculate NPV for the second apartment:

Conclusion: Both projects will be profitable, but the first project will bring higher profit. But, as already noted, the benefit as a result of the calculation is ambiguous. If projects are carried out during a period of high inflation, then the profitability of the first project is not at all obvious, since the value of money will depreciate. From this point of view, the second project will be more profitable.

We will calculate the investment irr in the spreadsheet editor Excel. As a result, we get: for 1 apartment IRR = 9.7%, and for the second IRR = 3.9%. Therefore, investing in the renovation of the first apartment is more profitable. As you can see, the calculation of performance indicators npv irr of investment projects helps to make the right choice.

The indicator of the modified rate of return is used when it is necessary to reduce the impact of investments in the calculations. Continuing the calculation according to our example using a spreadsheet editor, the following values ​​were obtained: for the first apartment MIRR=9.8%, for the second apartment MIRR=6.5%.

Consequently, this coefficient also confirms that investments in the renovation of the first apartment will give a large profit. But, as you have already noticed, when using the modified coefficient, the values ​​turned out to be higher.