To assess the effectiveness of planned investments, entrepreneurs consider a number of important economic indicators, such as payback period, net income, need for additional capital, financial stability, etc. One of the key ones is an indicator called internal rate of return. Let's take a closer look at it.

Internal rate of return is often abbreviated IRR. This term means the maximum cost of investment at which investing money in a project will remain profitable. In other words, the internal rate of return is the average return on invested capital that a given project will provide. This parameter is based on the method of discounting cash flows and allows you to make the right decision regarding the feasibility of investing.

Calculation formula and interpretation

The internal rate of return IRR is determined from the following equality:

FCF 1 /(1+IRR) + FCF 2 /(1+IRR) 2 + FCF 3 /(1+IRR) 3 + … + FCF t /(1+IRR) t - Initial Investment = 0, where

FCF t - cash flow reduced to the present moment for the period of time t,

Initial Investment - initial investment.

This coefficient is calculated by sequentially substituting into the formula the value of the discount rate at which the total present value of profit from the planned investment will correspond to the cost of these investments, i.e. the NPV indicator is 0. As a rule, the internal rate of return of a project is determined either using a schedule or through specialized programs. In the first case, the dependence of NPV on the level of the discount rate is displayed on a coordinate grid, and in the second, MS Excel is usually used to find IRR, in particular the formula =IRR(). The resulting value is compared with the price of the source of capital (if you plan to take out a loan from a bank), or simply with the interest on the deposit. Let us denote the cost of the advanced capital by CC (capital cost). As a result of the comparison, one of three options may arise:

Practice

First, let's take a simple example. Let’s assume that the implementation of the project will require an initial expenditure of 100,000 UAH. A year later, the net present value profit will be UAH 127,000. Let's calculate what the internal rate of return will be in this case: 130,000 / (1 + IRR) - 100,000 = 0. Having solved it, we find that the required coefficient is equal to: 127,000: 100,000 - 1 = 0.27, or 27 %. Now let's take a more complicated example. Let's assume that the initial investment is 90,000 rubles, the discount rate is 10%, and the cash flows are distributed over time as follows (data in thousand UAH):

• 1 year - 48.4
• 2 year - 54.5
• 3 year - 67.3
• 4 year - 20.4
• Year 5 - loss 70.4
• 6 year - 30.2
• 7 year - 55.9
• Year 8 - loss 20.1

What will NPV and IRR be equal to in this case? Here we need Excel. Let's copy our data to the top of a new sheet:

Let's place the value 0.1 in cell A4 - the discount rate. To calculate NPV we use the formula: =NPV(A4;C2:J2)+B2. Please note that we do not discount initial investments since they were made at the beginning of the year. If they were produced during the first year, then cell B2 would also need to be included in the calculation range. However, to obtain the total value of free cash flows, we must add this value. So, in a split second we get that NPV = 146.18 - 90 = 56.18. IRR is calculated even more simply. Since the data in our example was received regularly, instead of the formula =INDOH(), which requires specifying dates, we can use the function =IRR(). So, insert the expression = IRR (B2:J8) into an empty cell and instantly we get that the internal rate of profitability is 38%.

Every year the need for financial literacy is growing in all segments of the population. Hopes for a salary increase, an increase in pension or an inheritance from a rich aunt continue to die. Concern for one's own well-being has been transferred from the state to the shoulders of the citizen. Many people have a question: what to do? what to do ? and how to earn money? Therefore, studying the basics of investing and assessing the effectiveness of projects comes to the fore. The words irr, rate of return, payback period are heard more and more often in everyday conversations. If these terms are still new to you, we will look at what IRR is investment project

Internal Rate of Return (abbreviated as IRR) is an interest rate that shows the return on investment. In Russian-language literature, this indicator is called the internal rate of return (abbreviated as IRR). The criteria for the effectiveness of an investment project are two interrelated indicators - IRR and NPV (net present value). The IRR indicator shows at what rate NPV will be equal to 0, which means that the investor will simply return his investment.

The internal rate of return of an investment project is the first thing a future investor should start with when thinking about the feasibility of an investment. Depending on the comparison of the indicators IRR, NPV and r, where r is the real rate of return as a percentage, a decision is made to invest in the project. If the calculations result in NPV< 0, то вложения убыточны, если NPV >0, then you can invest.

The formula for calculating IRR begins with calculating NPV. Let's take an investment for a year as an example.

Then we calculate NPV:

NPV = -1500 + 2000 / (1+ r/100)* 1, where r is the interest rate

Calculation of IRR, at which NPV = 0, that is, the investor will simply return his money

• 1500 + 2000 / (1+ IRR/100)* 1= 0

The project's profitability should be 33.34%. Then the investor will break even in a year.

Calculations using a calculator

It is very convenient to carry out calculations using Excel, which any user has. The program has a built-in function for calculating the internal norm. It can be found in the “Formulas” section, then - Financial.

First you need to make a table with the values ​​of planned income and investments by year. Then select the IRR function - internal rate of return and select the table cells with values. The program will instantly calculate the IRR; this value will need to be converted into a percentage.

Excel calculates IRR using the fitting method. The maximum number of searches is usually set to 20. If the calculation has not been made after 20 attempts, then it is necessary to fill in the “assumption” in the VSD formula.

Important: For correct calculation, the values ​​must have both a plus and a minus sign. Otherwise Excel won't calculate it. The first tranche of investment is always a minus.

Calculating IRR using a graph

Many economic indicators are calculated graphically. To calculate the IRR of a project, you need to plot percentages on the x-axis, and future income on the y-axis. Then build a graph by calculating NPV using the formula above and plugging in the various r values. The point where the NPV graph intersects the X-axis will show the IRR rate.

Calculation of IRR for securities

Investments in securities also require preliminary calculations. Most often, it is necessary to determine the return on investment in bonds.

To do this, we will define several indicators:

• coupon income;
• par value of the bond;
• market current value of the bond;
• time until maturity.

1. A = coupon income for the year;

The result also shows the feasibility of the investment. The greater it is 0, the more profitable it is to buy these bonds.

How to interpret the result

All investment projects require an initial investment. This may be your own funds, or it may be borrowed funds - loans, borrowings and others. IRR shows the maximum loan rate at which the investor will not lose money.

For example, an investment project should bring 25% income per year, and the loan for the initial investment was taken out at 10% per year. The difference is + 15%. This will be the investor's income. Another option: the project brings 10% per year, and the loan was taken out at 17%. The total is 7%. The project is unprofitable.

If the investment is not borrowed, but own, then the refinancing rate is usually taken as the discount rate and compared with it. Or you can compare it with the deposit rate. For example, banks give 12% per annum, and investments should bring 8%. And although the investor will not be at a direct loss, since the money is his own, he still ends up in the red, because he could earn more at the bank.

Time deposit in Sberbank

Let's look at everyday examples. For example, a deposit in Sberbank. A bank deposit is also an investment, so you can also calculate the internal rate of return here. Let's take 5,000,000 rubles and put them in the bank for 2 years at a rate of 8% per annum without interest capitalization. Every year we will receive:

5,000,000 * 0.08 = 400,000 rubles.

2 years * 400,000 rubles = 800,000 rubles.

Let's calculate the IRR of the deposit using an Excel calculator. The value turned out to be 0.08, or 8%. If this is your own funds, then the initial capital costs nothing to you, so any bet will be profitable. But if you need to borrow money for a deposit, then this is always unprofitable, since the bank always gives loans at a higher interest rate.

Investments in microfinance organizations

There is another type of investment - not in a bank, but in microfinance organizations (abbreviated as MFOs). Many MFOs call such investments deposits, but in reality they are pure investments.

Important: investments in microfinance organizations are not deposits and are not insured by the state through the Deposit Insurance Agency.

But MFOs give high interest rates. For example, MoneyMan at the beginning of 2017 gives 21% per annum without capitalization. Let's take 5,000,000 rubles and invest them in microfinance organizations for 2 years. Let's calculate future profits:

5,000,000 * 0.21 = 1,050,000 rubles per year.

1,050,000 rubles * 2 years = 2,100,000 rubles.

The result is already more interesting. Let's take, for example, a loan for investment from the Moscow Credit Bank, which offers a consumer loan at 12.5% ​​per annum. Having made certain calculations, we get a yield of 8.5% per year, which is 0.5% higher than with a deposit in Sberbank. Our amount for 2 years turns out to be 50,000 rubles more than in Sberbank, even taking into account the consumer loan. And the total profitability will be 850,000 rubles.

Buying a bond

Let's calculate the profitability of investing in bonds. Take, for example, the bonds of Tinkoff Bank, which, by the way, are traded on the New York Stock Exchange in dollars. Let's determine the necessary indicators:

• coupon income for the year - 140 USD;
• par value of the bond - 1000 USD;
• market current value of the bond – 1166 USD;
• time to maturity – 2 years.

Let's perform several steps to calculate using the formula:

1. A = coupon income for the year;
2. B = (face value - current value) / time to maturity;
3. C = (nominal value + current value) = 2.

(140 + ((1000 – 1166)/2)) / (1000 + 1166) : 2

(140 + (-83) / 1583 = 0,036 * 100 % = 3,6 %

As we can see, there is profitability, the indicator is above zero, but it is so small that we need to think about the return on investment.

We will buy 5 million shares, converting this money into dollars at the rate of 58 rubles. for a dollar.

Total = 86,206 USD. We buy 74 bonds with them.

In 2 years we will receive a certain profitability:

• For the first year - 140 USD * 74 bonds = 10,360 USD.
• For the second year - 140 USD * 74 bonds = 10,360 USD

Total - 20,720 USD. If the exchange rate has not changed, then 20,720 * 58 rubles = 1,201,760 rubles.

But we will receive the initial investment at nominal value:

74 bonds * 1000 USD = 74,000 USD

Total in dollars: 74,000 + 20,720 - 86,206 = 8,514 USD for 2 years or 4,257 USD for each year. Let's convert into rubles at the rate of 58 rubles = 246,906 rubles per year.

Apartment purchase

Let's consider the option of investing in real estate, namely, purchasing an apartment for the purpose of renting it out, so that after a few years, for example, after 2 years, to sell it. Let's take a simplified version: after 2 years the apartment will cost the same as when purchased.

We are buying an apartment in the near Moscow region for 5 million. This will be a one-room apartment with an average area of ​​50 square meters. m. Renting such an apartment in 2017 costs approximately 25,000 rubles per month.

Let's calculate the profits:

• for the first year - 25,000 rubles * 12 months = 300,000 rubles;
• for the second year - 25,000 rubles * 12 months = 300,000 rubles.

In just 2 years - 600,000 rubles.

Let's compare the results

As we can see, investing in microfinance organizations will bring the greatest return, but this is also the highest possible risk. An apartment is not that attractive compared to a bank deposit, just like popular bonds.

When compared as a percentage, the rental yield is 6% per year. In this option, you can make a profit only when the price of the apartment rises, and sometimes it can fall.

Important: IRR does not depend on the investment period: if the return is low, then even after 10 years the IRR will not increase.

Term return on investment

It is equally important to calculate the payback period or, as they also say, the internal rate of return. To do this, you need to take two monetary indicators:

• the amount of initial investment;
• annual income minus expenses.

The calculation formula is as follows:

Initial investment: annual income minus expenses = payback period

This is a simplified calculation, but it roughly and quickly shows how interesting the investment project is. For example, in the case of buying an apartment for 5 million and renting it out for 25 thousand, the internal rate of return, or payback period, will be:

5,000,000 rubles: 300,000 rubles = 16.6 years.

Summary

Before investing in a project that looks attractive at first glance, calculate the internal rate of return (IRR) and compare it with other options. In the simplest version - with bank deposits.

To calculate IRR, use different methods, the simplest of which is calculation using an Excel calculator.

When calculating future profits, do not forget about taxes:

• in the deposit - personal income tax 13% if the bank rate is higher than the refinancing rate;
• when investing in microfinance organizations - personal income tax 13% on all income;
• when investing in securities - personal income tax 13% on profits when withdrawing funds;
• when investing in government bonds, personal income tax is not charged;
• when purchasing an apartment - property tax at the regional rate;
• when selling an apartment owned for less than 5 years - personal income tax of 13%.

When investing money, always be aware that all investment instruments are risky, they just have different degrees of risk. To distribute risk evenly, each investor needs to create a balanced portfolio, taking into account age and strategic goals. But we'll talk about this another time. Good luck!

Economic science studies the issues of reducing costs during project implementation and obtaining maximum profits. In this case, the main emphasis is on profit.

In financial analysis, many systems have been proposed to evaluate the effectiveness of projects, but in most cases a system of indicators of reduced cash flows is used. One of them is the IRR (internal rate of return) indicator. We will analyze the features of this indicator in the article.

What does this indicator mean?

In the economic literature, IRR is understood as a certain level of interest at which the present value of the funds invested in an investment project equals zero.

To make a decision about investing in an investment project, it is important to understand not only how much it will bring, but also how much should be invested.

In financial analysis, the investment amount is initially reduced to the current value, that is NPV is calculated. Next, the IRR will be determined, otherwise it sounds like an indicator called the internal rate of return, which shows the optimal amount of investment in a given project.

NPV and IRR indicators represent a mutually complementary system of criteria for assessing the effectiveness of the implementation of an investment project. Due to the fact that the first value is the amount of income expressed in kind, taking into account the current value of funds. Another meaning is the rate, upon reaching which the investor will receive a profit.

The calculated IRR is compared with similar rates of return currently operating in the market. But in this case, it is necessary to take into account the risks and timing of these projects.

For comparisons the rate for a deposit in a banking organization is accepted. The project will be implemented only if the IRR is higher than the average rates for investment projects and deposits.

IRR characterized by two criteria:

1. Cash flows represent net investment.
   This means that at the beginning of the implementation of an investment project, cash flows are exclusively negative, that is, the investor only invests money, but does not receive a return. After a certain period, the project acquires positive cash flows. And no further changes occur during the implementation of the project. Upon complete completion of the project, funds should only be positive. Otherwise, this criterion is called isolated , since the influence of external and internal factors is not taken into account.
2. Mixed flows Money.
   They represent an alternation of negative and positive values ​​when funds are received. In this case, economists believe that the use of the IRR method is not possible. Due to the fact that the data obtained in this way loses its reliability. For such cash flows it was developed modified internal rate of return .

Rules for using this indicator

In practice, when analyzing investment projects, experts use the results of IRR calculations as follows:

1. To determine the rate of return on an investment project. Participants decide whether there is a need to raise borrowed funds;
2. To evaluate decisions on investment projects. In this case, the results obtained are correlated with the optimal values ​​for a given sector of the economy;
3. To calculate the sustainability of the project. To achieve this, the conditions under which projects will be implemented are changing.

The use of IRR when calculating the profitability of an investment project has a number of disadvantages and advantages.

TO positive aspects This includes the possibility of comparing investment projects by duration and scale of their activities. But the main advantage of using IRR is the ability to calculate the profitability of investment flows.

Disadvantage It is considered that when the sign of the cash flow changes, the calculation of several IRR values ​​is carried out, which may give false information. When calculating this indicator, the expert is of the opinion that the funds are reinvested at the percentage that was obtained. But in fact, this does not always correspond to reality.

Based on the criteria for cash inflows into the project, it should be noted that the IRR method should be applied only if there are net inflows from the implementation of the investment project.

The procedure for calculating present value (NPV) in Excel is discussed in the following video:

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Calculation procedure and formula

In various sources there are different interpretations of the formula for calculating IRR, but the “traditional” one is the following:

The value is expressed in percentages. Some economists and analysts attribute this to the disadvantages of this assessment of the investment project, while others, on the contrary, citing the fact that percentage data is easier to interpret, consider this to be an advantage.

Apply two types of calculation of this indicator:

• graphic;
• arithmetic.

Graphical method is more visual and convenient when comparing several projects.

Manual calculation indicators characterizing project implementation options are practically not used at present. Excel or specialized programs are most often used.

Calculation example

As an example to calculate the internal rate of return, let’s take an investment project whose implementation period is designed for 5 years. The initial investment amounted to 45,000 thousand rubles. At the same time, the investor wants to receive at least 18% annually from the project.

The table provides data for calculating the internal rate of return.

Indicators	I year	II year	III year	IV year	V year
Volume of sales	58950	60650	66920	68450	64580
Operating expenses (costs of materials, labor costs, general production and general business expenses (except depreciation), costs of selling products)	34645	35440	37560	38220	34852
Depreciation	8500	8500	8500	8500	8500
Taxable income	15805	16710	20860	21730	21228
Income tax	3161	3342	4172	4346	4246
Net profit	12644	13368	16688	17384	16982
Net cash flow (3+6)	21144	21868	25188	25884	25482

Let's determine discounted cash flow:

Let's define another NPV value:

And now we use the IRR formula, which looks like this:

This example shows that the implementation of this project makes sense, since the investor’s rate of return was set at 18%, and calculations show that the return on investment will be 40%.

Analysis of the received data

Analysis is based to compare IRR with the discount rate (r).

The resulting IRR may lead to three decisions on the part of the investor:

1. The project is not effective. Provided that the discount rate is higher than the calculated IRR value, this means that the funds invested in the project will bring losses. It is recommended to reject the project.
2. Zero effect. The discount rate and the internal rate of return are the same; such a project does not make economic sense, and it is also recommended to reject it.
3. The project is effective. The discount rate turned out to be lower than the IRR, which means that there is economic sense in implementing such a project.

When analyzing the data obtained, you should focus on the source of raising funds for the project. If an investor invests only his own funds, then IRR is his possible income from the project. In the case of raising funds from commercial banks (), IRR should be interpreted as the maximum rate on the loan obligation.

A high rate of internal return indicates the prospects of investment, and a large gap between the normatively established value indicates the safety margin of this project.

Recently we considered such an important indicator of the economic viability of any investment project as NPV, the net present value of the project. It's time to get acquainted with the second most important indicator of the effectiveness of investment projects - IRR, Internal Rate of Return.

In the Russian translation there are quite a lot of interpretations - internal rate of return, internal rate of return, internal rate of profitability, internal rate of profitability - all this means the same thing. This indicator is usually expressed as a percentage and much less often in decimals.

The economic meaning of this indicator is that in fact it shows the average annual profitability of the project on the horizon of consideration. For example, if you have calculated a project for 10 years and the IRR of your project is 15%, this means that your investment in the project will give an average of 15% per annum for 10 years.

Our expert Alexey Grebenyuk

In other words, the economic meaning can be defined as follows: this is the discount rate at which NPV project goes to zero. Accordingly, if you borrow money from a bank or, say, from a friend at 20% per annum, then you should not invest it in your project, which gives only 15% profitability.It is better to invest in some other project that will give more than 20%, otherwise there is no point in borrowing in principle. It will be effective to borrow money from a bank at 20% per annum only when your project gives IRR above 20%. In this case, you can return the money to the bank and earn yourself extra profits.

IRR calculation manually on paper is not an easy task and you need to have real mathematical abilities. Magnitude IRR is calculated by the selection method and, as I already said, it is equal to the discount rate at which the indicator NPV equal to zero. You need to do several iterations before you find the internal rate of return. Difficult? Very difficult! I myself have never counted on paper IRR. Microsoft Excel calculates IRR instantly - through the "VSD" function - as easy as shelling pears!

In addition to those discussed NPV and IRR , there is a third important indicator of the economic efficiency of any investment project - this is payback period. The economic meaning of this indicator is very simple - this is the period of time during which the project returns the invested funds to its owner. As a rule, the more capital-intensive a project we consider, the longer the payback period it has. Of course, this is not entirely necessary, but still, as a rule, it is so. For example, the payback period for a power plant will be longer than the payback period for a small store.

In investment projects there is another important dependence - usually the higher the profitability of the project, the higher the risk of its implementation. And vice versa - the lower the profitability, the lower the risk.

In the financial analysis of investment profitability, a special place is occupied by the internal rate of return. It is recommended for all organizations to calculate the indicator before choosing an investment project.

The process of its calculation and analysis will be discussed in this article.

Definition

The internal rate of return (IRR) is a certain rate that ensures that there are no losses on deposits and that income from an investment is identical to the costs of the same project. In other words, this is the limiting percentage value at which the difference between the inflow and outflow of money, that is, the net present value (NPV), is equal to zero.

It is most convenient to calculate this indicator using special programs, for example, Excel. You can also use a financial calculator.

Without the use of automated calculation methods, the percentage of the value will have to be determined through lengthy calculations. In this case, the size of the net present value is determined at various discount rates. This method is called iteration method.

For example, the NPV at a rate of 15% is greater than zero and negative at 5. We can conclude that the IRR is in the range of rates from 5 to 15%. Then the smaller number is constantly increased and the calculation is repeated until the NPV is equal to zero.

Why do you need a calculation?

The economic meaning of the indicator is that it characterizes the following points:

• Profitability of a possible investment. When an enterprise chooses which project to invest in, it is guided by the value of this indicator. The larger the IRR, the higher the return on investment.
• Optimal loan rate. IRR is the maximum price at which an investment breaks even. If the company plans to obtain a loan for this investment, then you should pay attention to the annual rate. If the interest on the loan is greater than the received value, then the project will generate a loss.

When using an indicator to evaluate future investments, you need to consider the advantages and disadvantages of this method.

The positive aspects of using VND include:

• Comparison of possible investments with each other based on the efficiency of capital use. The company will prefer to choose the investment that, with an equal interest rate, has a higher rate.
• Comparison of projects with different investment horizons, that is, the time period for which the investment is made. In this case, when comparing the IRR of different possible deposits, the one that will bring the greatest income in the long term is identified.

The main disadvantages and negative features include:

• Difficulty in predicting payments. By calculating this value, it is impossible to predict what the size of the next deposit receipt will be. The profit margin is influenced by many different factors, risks, situations at the micro and macroeconomic level, which are not taken into account in the calculation.
• It is impossible to determine the absolute value of the influx of money. IRR is a relative indicator; it specifies only the percentage at which the contribution still breaks even.
• Reinvestment is not taken into account. Some deposits require the inclusion of interest payments. That is, there is a process of increasing the amount of investment due to profit from it. The IRR calculation does not provide for this possibility, so the indicator does not reflect the real profitability of these costs.

Formula and example

To determine the method for calculating IRR, the equation is used:

• NPV - NPV size;
• IC - initial investment amount;
• CFt - cash inflow for the time period;
• IRR - internal rate of return.

Given this equation, we can determine that the indicator is calculated using the following formula:

Where r is the interest rate.

To better understand how to calculate GNI, you need to look at an example. Let the project require an investment of 1 million rubles. According to the preliminary forecast, in the first year the income will be 100 thousand rubles, in the second - 150 thousand rubles, in the third - 200 thousand rubles, in the fourth - 270 thousand rubles.

The calculation of the indicator without the use of special programs must be done using the iteration method. To do this you need to perform a number of actions:

The data obtained indicate that the highest annual loan rate taken for a deposit is 23%.

If the organization receives obligations to repay a loan with an interest rate greater than the established amount, the project will be unprofitable. It is advisable for the company to find more favorable conditions.

Calculation in Excel

The easiest way to calculate an indicator is to use automated tools, such as Excel. This program has built-in financial formulas that allow you to make calculations very quickly.

To calculate the value there is VSD function. However, this formula will work correctly only if there is at least one positive and one negative value in the table.

The formula in the resulting cell looks like this: =VSD(E3:E12).

You can see the calculation procedure in this program in the following video:

Analysis of the result

The indicator is used to analyze the effectiveness of potential investments. To determine the feasibility of investing money, GNI is compared with a certain level of profitability. Often this is done using the weighted average cost of capital (CAC).

The SSC indicator characterizes the minimum amount of enterprise income that can provide the founders with a return on funds spent on capital contributions. Most investment decisions are made based on this figure.

Also, the interest rate on loans is often taken as an indicator of profitability. This method allows you to find out whether raising borrowed funds is effective for a given project.

The feasibility of the company’s deposits is determined based on the ratio of IRR and profitability indicator (P):

• VSD=P. This means that the investment is at the maximum permissible level. To ensure cost efficiency, the initial cost of investments should be reconsidered, flows and timing should be adjusted. Also, when analyzing investments, their comparative analysis is used.
• VSD>P. This ratio indicates that the investment will cover the costs of its provision. This investment can be considered as a possibility, the final decision should be made after further financial analysis.
• VSD<П . This means that the analyzed project has a lower profitability than the cost of capital, loans, etc. The organization is advised to abandon investments, as they will not bring profit.
• VSD1<ВСД2 . This ratio shows that one of the proposed investments is more profitable than the other.