Calculation of IRR. Internal rate of return: definition, formula and examples

The internal rate of return (IRR) is a very important indicator in the work of the investor. The calculation of the IRR shows which minimum calculation percentage can be included in the calculation of the effectiveness of measures, with the net present value (TTS) of this project being 0.

Net Present Value (NPV)

Without determining the value of NPV, the IRR calculation of the investment project is impossible. This indicator is the sum of all current values of each of the periods of the investment event. The classical formula for this indicator is as follows:

PTS = Σ PP _to / (1 + p) ^k , where:

• CHTS - net present value;
• PP - the flow of payments;
• P - calculation rate;
• K is the period number.

PP _to / (1 + p) ^k is the current value in a certain period, and 1 / (1 + p) ^k is the discount factor for a certain period. The flow of payments is calculated as the difference between payments and receipts.

Discounting

Discounting factors represent the present value of one monetary unit of future payments. Decrease in the coefficient means an increase in the calculation of interest and a decrease in value.

The calculation of the discount factor can be represented by two formulas:

(1 + p) ⁿ = (1 + p) ^-n , where:

• FD - the factor of discounting
• N is the period number;
• P is the calculation percentage.

Current value

This index can be calculated by multiplying the discount factor by the difference between income and costs. Below is an example of calculating current values for five periods with a calculation percentage of 5% and payments of 10 thousand euros in each.

TC1 = 10,000 / 1.05 = 9523.81 euros.

TC2 = 10,000 / 1.05 / 1.05 = 9070.3 euros.

TC3 = 10,000 / 1.05 / 1.05 / 1.05 = 8638.38 euros.

TC4 = 10,000 / 1.05 / 1.05 / 1.05 / 1.05 = 82270.3 euros.

TC5 = 10,000 / 1.05 / 1.05 / 1.05 / 1.05 / 1.05 = 7835.26 euros.

As you can see, every year the discount factor increases, and the current cost decreases. This means that if an enterprise needs to choose between two transactions, then one should choose the one according to which the funds will be transferred to the company's account as early as possible.

Internal rate of return

The IRR calculation can be performed using all the above data. The canonical form of the formula for calculating the indicator is as follows:

0 = Σ1 / (1 + GND) ^k , where:

• GNI - internal percentage of profitability;
• K is the sequence of the period.

As can be seen from the formula, the net cost in this case should be 0. However, this method of calculating the IRR is not always effective. Without a financial calculator, it can not be determined if the investment project includes more than three periods. In this case, it will be expedient to use the following method:

IRR = MP _m + R _kp * (PTS _m / R), where:

• GNI - internal percentage;
• KP _m - a smaller calculation percentage;
• Р _кп - the difference between large and lower interest rates;
• TTS _m is the net present value obtained using a smaller calculation rate;
• R is the absolute difference in current values.

As you can see from the formula, to calculate the IRR you should find the net present value at two different calculation percentages. It should be taken into account that the difference in them should not be large. The maximum is 5 percent, however, it is recommended to take the rates as little as possible (2-3%).

In addition, it is necessary to take such rates of rates at which TTS would have a negative value in one case, and in the second case a positive one.

Example of IRR calculation

For a better understanding of the above material, an example should be made.

The enterprise plans an investment project for a period of five years. In the beginning will be spent 60 thousand euros. At the end of the first year, the company will invest another 5 thousand euros in the project, at the end of the second year - 2 thousand euros, at the end of the third year - one thousand euros, and another 10 thousand euros will be invested by the enterprise during the fifth year.

The company will receive income at the end of each period. After the first year, the amount of income will be 17 thousand euros, next year - 15 thousand euros, in the third year - 17 thousand euros, in the fourth - 20 thousand euros, and another 25 thousand euros the company will receive in the last year of the project. The discount rate is 6%.

Before you start calculating the internal rate of return (IRR), you need to calculate the TTS size. Its calculation is shown in the table.

As you can see, the project is profitable. CHTS is 904.6 euros. This means that the capital invested by the company paid off by 6 percent and brought another 904.6 euros "from above." Next, you must find a negative net present value. Its calculation is shown in the following table.

The table shows that the invested capital did not pay off by 7 percent. Therefore, the value of the internal payback index is between 6 and 7 percent.

IRR = 6 + (7-6) * (904.6 / 904.6 - (-812.3)) = 6.53%.

So, the GNI of the project was 6.53 percent. This means that if it is put into the calculation of the TTS, its value will be zero.

Note: when calculating manually, an error of 3-5 euros is allowed.