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

Internal rate of return (IRR) is a very important indicator in the work of the investor. The IRR calculation 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 current values of each of the periods of the investment event. The classical formula of this indicator looks like this:

ЧТС = ∑ ПП _к / (1 + р) ^к, 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 revenues 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 one should choose the one according to which the funds will arrive at the company’s account as early 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 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;
NTS _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 must 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%).