# IRR calculation, IRR Usage Rule and Purpose, IRR Criteria, Modified...

## Calculating IRR

Thus, in order to find IRR, it is necessary to solve the equation

Then IRR = x.

There is no formula to solve such an equation. Therefore, the equation is solved by approximate methods, most often using linear interpolation:

a) at random, two discount rates are taken - rx and r2, r4 < r2;

b) using each of the bets, calculate two values ​​- N7'1 ', and NPV2;

c) the approximate value of IRR is obtained by the formula

To get a more accurate value of IRR , the calculations are repeated several times, narrowing the interval between r, and r2:

## IRR Usage Rule and Destination

If IRR & lt; r, i.e. the profitability of the project is less than that required by investors (barrier) rate of return on invested capital, the project is rejected. The required level of profitability depends on the risk of the project and the state of the financial market.

IRR estimates the return on a unit of invested capital, in contrast to the NPV - criterion that measures the absolute value, the mass of the income received. Therefore, when comparing projects IRR sometimes contradicts NPV, since the project can be more profitable (in terms of the invested ruble), but in absolute terms give less effect due to smaller scales of the investment object.

## Disadvantages of the IRR criterion

The disadvantages of the IRR criterion are as follows:

• There are objective difficulties in calculating the multi-step algorithm presented. Currently, specialists for

Such calculations are widely used by financial calculators, which make it easy to overcome this inconvenience;

• the 7th power equation, according to which has n roots, so for one project there are n values ​​ IRR. True, most often only one value fits the meaning of the task;

• When calculating IRR , it is assumed that the income received is reinvested at a rate equal to JRR. If the IRR value is significantly larger than the discount rate, then this assumption introduces significant distortions in the calculation results. However, the conclusions about the profitability of the project remain in effect, so that in the long run IRR performs its function.

Indeed, if the project has an abnormally high profitability (ie a very large value of IRR), investors will not be able to reinvest the profits with the same level of efficiency that exists for this project. This is so.

However, the value of IRR is most often not in the specific meaning of this indicator, but in the conclusion that is based on it. And the conclusion will be unambiguous: the project is abnormally profitable and, therefore, profitable.

## Modified Internal Rate of Return (MIRR)

Those who believe that the multiplicity of the IRR values ​​and the assumption of reinvestment of income at a rate equal to IRR, are really serious drawbacks of this criterion, sometimes suggest a modified version of this indicator .

The most well-known variant of the modified IRR is calculated as follows:

• All cash inflows under the project are compounded (increased) at the risk rate (usually at the rate Rm) by the end of the life of the project, since inflows are considered risky.

• All cash outflows under the project are discounted to the zero point of time at the risk-free rate Rj, since it is believed that investing money in the project does not bear any uncertainty (risk).

• The result is two payments - the inflow of (CIF) and the outflow of (COF), the distance between them (n) is equal to the life span project.

Based on these two payments, you can find a modified rate of return on the project MIRR, which will be the only one and will proceed from the assumption of reinvestment of revenues at the average market rate:

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