Internal rate of return (IRR) is a very important indicator in the work of an investor. The calculation of IRR shows what minimum calculation percentage can be incorporated in the calculation of the effectiveness of measures, while the net present value (TTS) of this project should be 0.
Net Present Value (NPV)
Without determining the NPV value, the calculation of the IRR of the investment project is impossible. This indicator is the sum of all the current costs of each of the periods of the investment event. The classical formula of this indicator looks like this:
= ∑ / (1 + ) , where:
- TTS - net present value;
- PP - stream of payments;
- p - calculation rate;
- k is the number of the period.
PP k / (1 + p) k is the current value in a certain period, and 1 / (1 + p) k is the discount coefficient for a certain period. The flow of payments is calculated as the difference between payments and receipts.
Discounting
Discount factors reflect the true value of one monetary unit of upcoming payments. A decrease in the coefficient means an increase in the calculation percentage and a decrease in value.
The calculation of the discount factor can be represented by two formulas:
PD = 1 / (1 + p) n = (1 + p) -n , where:
- PD - discount factor
- n is the number of the period;
- 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 the current values for five periods with a calculation interest of 5% and payments of 10 thousand euros in each of them.
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 = 82,270.3 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 value decreases. This means that if an enterprise needs to choose between two transactions, then it is necessary to choose the one according to which the funds will arrive at the company's account as soon as possible.
Internal percentage return
IRR can be calculated using all of the above data. The canonical form of the formula for calculating the indicator is as follows:
0 = ∑1 / (1 + GNI) k , where:
- GNI - internal percentage of return;
- K is the sequence of the period.
As can be seen from the formula, the net cost in this case should be equal to 0. However, this method of calculating the IRR is not always effective. Without the availability of a financial calculator, it cannot be determined if the investment project will include more than three periods. In this case, it would be advisable to use the following methodology:
GNI = KP m + R kp * (TST m / R chts ), where:
- GNI - internal percentage;
- KP m - a lower calculation percentage;
- R KP - the difference between higher and lower interest rates;
- TTS m - net present value received using a lower calculation rate;
- P ths - the absolute difference in current values.
As can be seen from the formula, to calculate the IRR, you need to find the net present value at two different calculation percentages. It should be borne in mind that the difference in them should not be large. The maximum is 5 percent, but it is recommended to take bets with the smallest possible difference (2-3%).
In addition, it is necessary to take such rates at which the NTC would have a negative value in one case and a positive value in the second.
Example of calculating IRR
For a better understanding of the above material, an example should be considered.
The company plans an investment project for a period of five years. At the beginning, 60 thousand euros will be spent. At the end of the first year, the company invests 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 company during the fifth year.
The company will receive income at the end of each period. After the first year, the amount of revenues will be 17 thousand euros, next year - 15 thousand euros, in the third year - 17 thousand euros, in the fourth - 20 thousand euros, and the company will receive another 25 thousand euros in the last year of the project. The discount rate is 6%.
Before you begin calculating the internal rate of return (IRR), you must calculate the size of the TTS. Her calculation is displayed in the table.
Calculation of net present value with a calculation percentage of 6% | Period |
| 0 | one | 2 | 3 | four | 5 |
| Payouts | 60,000 | 5,000 | 2,000 | 3,000 | 1,000 | 10,000 |
| Income | 0 | 17,000 | 15,000 | 17,000 | 20,000 | 25,000 |
| Payment stream | -60,000 | 12,000 | 13,000 | 14,000 | 19,000 | 15,000 |
| Discount factor | one | 0.9434 | 0.89 | 0.8396 | 0.7921 | 0.7473 |
| Discounted PP | -60,000 | 11,320.8 | 11 570 | 11 754.4 | 15,049.9 | 11 209.5 |
| TTS | 904.6 |
As you can see, the project is profitable. TTS is equal to 904.6 euros. This means that the capital invested by the company paid off by 6 percent and still brought 904.6 euros “from above”. Next, find the negative net present value. Its calculation is shown in the following table.
Calculation of net present value with a calculation percentage of 7% | Period Number |
| 0 | one | 2 | 3 | four | 5 |
| Revenues, thousand euros | 60,000 | 5,000 | 2,000 | 3,000 | 1,000 | 10,000 |
| Costs, thousand euros | 0 | 17,000 | 15,000 | 17,000 | 20,000 | 25,000 |
| The flow of payments, thousand euros | -60,000 | 12,000 | 13,000 | 14,000 | 19,000 | 15,000 |
| Discount factor | one | 0.9346 | 0.8734 | 0.8163 | 07629 | 0.713 |
| Discount. flow of payments | -60,000 | 11,215.2 | 11 354.2 | 11,428.2 | 14,495.1 | 10 695 |
| TTS | -812.3 |
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.
GNI = 6 + (7-6) * (904.6 / 904.6 - (-812.3)) = 6.53%.
So, the GNI of the project amounted to 6.53 percent. This means that if it is included in the calculation of the NTC, then its value will be zero.
Note: when calculating manually, an error of 3-5 euros is allowed.