Internal rate of return: the concept and calculation
To assess the effectiveness of planned investments, entrepreneurs consider a number of important economic indicators, such as payback period, net income, the need for additional capital, financial stability, etc. One of the key among them is an indicator called internal rate of return. Let's dwell on it in more detail.
Concept
The internal rate of return is often denoted by the abbreviation IRR. This term means the maximum cost of investment at which the investment of money in the project will remain profitable. In other words, the internal rate of return is the average return on invested capital that this project will provide. This parameter is based on the method of discounting cash flows and allows you to make the right decision about the appropriateness of investment.
Formula calculation and interpretation
The internal rate of return IRR is determined from the following equality:
FCF1/ (1 + IRR) + FCF2/ (1 + IRR)2+ FCF3/ (1 + IRR)3+ ... + FCFt/ (1 + IRR)t Initial Investment = 0, where
FCFt the present cash flow for the period of time t,
Initial Investment  initial investment.
This coefficient is calculated by the method of successive substitution in the formula of such a value of the discount rate at which the total present value of the profit from the planned investment will correspond to the value of these investments, i.e. The NPV indicator is equal to 0. As a rule, the internal rate of return of a project is determined either by means of a graph or by means of specialized programs. In the first case, the dependence of NPV on the level of the discount rate is displayed on the grid of coordinates, and in the second case, MS Excel is usually used to find the IRR, in particular, the formula = VNDOH (). The resulting value is compared with the price of the source of capital (if you plan to take a loan from a bank), or simply with a percentage of the deposit. Denote the cost of the advanced capital through SS (capital cost). As a result of the comparison, one of three options may arise:
 IRR> CC, invest profitable;
 IRR <CC, it is unprofitable to invest money;
 IRR = CC, there is no unequivocal assessment, other factors should be considered.
Practice
First, take a simple example.Assume that the project will require initially spend 100 000 UAH. A year later, the net present value of profit will be 127 000 UAH. 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 get that the desired ratio is: 127,000: 100,000  1 = 0.27, or 27 % Now take the example more complicated. Assume that the initial investment will amount to 90 000 rubles, the discount rate is at the level of 10%, and the cash flows are distributed over time as follows (given in thousand UAH):
 1 year  48.4
 2 year  54.5
 3 year  67.3
 4 year  20.4
 5 year  loss 70.4
 6 year  30.2
 7 year  55.9
 8 year  loss 20.1
What will be equal in this case, NPV and IRR? Here we need Excel. Copy our data to the top of the new sheet:
A 
B 
C 
D 
E 
F 
G 
H 
I 
J 

1 
Period 
0 
1 
2 
3 
4 
5 
6 
7 
8 
2 
Amount 
90 
48,4 
54,5 
67,3 
20,4 
70,4 
30,2 
55,9 
20,1 
We place in cell A4 a value of 0.1  the discount rate. To calculate NPV, we use the formula: = NPV (A4; C2: J2) + B2. Please note that we do not discount initial investments, as 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 amount 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 easier.Since the data in our example was received regularly, instead of the formula = INSH (), requiring dates, we can use the function = IRR (). So, insert the expression = IRR (B2: J8) in the free cell and instantly we see that the internal rate of return is 38%.