To understand how the internal rate of return works, and what information can be extracted from it, we cannot limit ourselves to this term alone. So let’s start by explaining terms that are closely connected with IRR. We are talking about:
- Net presentvalue (NPV)
- Required rate of return(RRR – required rate of return)
- Expected rate of return(ERR – expected rate of return)
Required rate of return – definition
This is the lowest return on investment that must be achieved for it to make any sense to invest in a project. An investor who plans to commit funds (either his own or a company’s) to a project should first determine the amount of return required. In doing so, he sets a certain minimum target.
The required rate of return can be determined using a variety of tools and calculators, or a value can be taken that simply makes sense to the investor.
Expected rate of return – what is it and how to calculate it?
This is the investment income that an investor can achieve, given historical data. In this case, too, you can limit yourself to determining the amount that is satisfactory to the investor. However, there are methods to calculate the expected rate of return based on a probability distribution.
In this case, the investor – based on historical data – can observe the probability of achieving different return values.
Example:
Mr. Thomas plans to invest in funds whose probability distribution is as follows:
- 2.5% probability that the return on investment will be 30%
- 5% probability that the rate of return on investment will be 20%
- 7.5% probability that the return on investment will be 15%
- 12.5% probability that the rate of return on investment will be 10%
- 15% probability that the return on investment will be 7.5%
- 15% probability that the rate of return on investment will be 5%
- 15% probability that the rate of return on investment will be 2.5%
- 12.5% probability that the rate of return on investment will be 0%
- 10% probability that the return on investment will be -2.5%
- 5% probability that the return on investment will be -5%
Important!
For further calculations to make sense, the sum of the probabilities must be 1. Knowing the above probability distribution (derived from the analysis of historical data), Mr. Thomas should multiply each probability value by the corresponding rate of return. The calculation will thus be as follows:
2,5% * 30% + 5% * 20% + 7,5% * 15% + 12,5% * 10% + 15% * 7,5% + 15% * 5% + 15% * 2,5% + 12,5% * 0% + 10% * (-2,5%) + 5% * (-5%) = 0,0075 + 0,01 + 0,01125 + 0.0125 + 0.01125 + 0.0075 + 0.00375 + 0 + (-0.0025) + (-0.0025) = 0.05875
Thus, in this example, the expected rate of return will be 5.875%.
In a nutshell: the required rate of return is the minimum return on an investment, the achievement of which will make it worthwhile. The expected rate of return , on the other hand, is the most likely outcome.
A promising investment should have a higher expected than required rate of return.
NPV ratio – definition, calculation, interpretation
Net present value (also net present value, net present value, NPV) is a discount method of evaluating investments – one of the most popular. NPV estimates the value of future cash flows. Thus, the net present value tells what return on a future investment should be expected in relation to the present value of money.
NPV is the sum of the discounted cash flows from the investment, minus the amount invested. Thus, this indicator compares the expenses that the investor must incur for the planned investment with the flows that the investment will generate later.
How to calculate NPV and interpret it?
There are several formulas that can be used to calculate the net present value. The following one is most commonly used:
So how to read the NPV? Any result of this indicator of 0 or more is a positive result. A planned investment whose NPV is greater than or equal to zero is a promising project.
Internal rate of return – what is it and how to calculate the profitability of an investment?
Already having some knowledge of the required and expected rate of return, as well as the net present value, we can explain what the internal rate of return – the subject of this article – is. In understanding this term, the NPV ratio in particular is crucial, since the internal rate of return is the discount rate at which the NPV equals 0.
The internal rate of return can be (and often is) presented as part of the formula for NPV. We intentionally omitted this variant when discussing NPV in order to discuss it now.
According to the above formula, the internal rate of return depends on the number of periods, and its determination is a complicated process (as part of it, NPV must be calculated repeatedly for different values of the required rate of return). The expected result is NPV=0, but in practice two results are usually used:
- positive NPV close to zero
- Negative NPV close to zero.
The results obtained should be substituted into the formula:
Accurate calculation of IRR therefore requires advanced knowledge or… a lot of trial and error – we can nicely call it the iterative method. Under it, you have to take a certain (probable) value for the IRR, and then calculate the net present value (NPV) for this rate. The result obtained should be recorded, and then a different value for the IRR should be assumed – so that the NPV result approaches zero.
Important!
Remember that if it is not possible to calculate NPV=0, two values should be considered in further calculations – a negative NPV close to zero and a positive NPV close to zero.
Is it easier to calculate the internal rate of return?
Yes, but this requires access to financial calculators that support this function or software designed for this purpose.
How to interpret the internal rate of return result?
While the (correct!) calculation of IRR is already an art in itself, it is even more important to draw the right conclusions from the results obtained. Applying some simplification, we can assume that IRR reflects the expected rate of return on investment (however, it is a more precise indicator than RRR – required rate of return).
The initial interpretation of IRR is very simple: the higher the value of the internal rate of return, the greater the chance that the planned investment will generate a higher-than-cost return. A low value indicates a low potential for investment.
However, it doesn’t stop there. The resulting IRR value by itself actually tells you very little. To properly assess the potential of an investment, you need to compare the internal rate of return with other financial indicators – such as the cost of capital or the required rate of return. An IRR higher than the other ratios indicates that the investment is worth making.
Important!
In some (very rare) cases, an investment may have two internal rates of return. This means that we can talk about the profitability of a given investment when the required rate of return falls between one IRR and the other.
A double IRR can happen, for example, when the sum of the cash flows from the total investment is negative (taking into account the initial investment), a situation that is not only unlikely but highly undesirable.
IRR value: what to compare it with?
In addition to the already extensively discussed NPV, there are other financial ratios that are worth knowing, and to which it is worth relating the IRR result. These include:
SRR – simple return rate– makes it possible to measure the ratio of the net profit from an investment to the investment-related expenses incurred. This indicator – importantly – does not take into account cash flows.
DPP – discounted payback period, or discounted payback period – is an indicator that not only allows you to estimate over what period the funds invested in the project will pay back (in the form of discounted cash flows), but also takes into account the volatility of money over time.
PI – profitability index, or investment profitability index, is a simple method that allows to assess the effectiveness of an investment. PI takes into account the value of positive cash flows from the investment and the expenses incurred in connection with its implementation.
IRR method – summary
Internal rate of return is a financial indicator that finds many practical applications in business: it is mainly used to evaluate the potential of investments (such as in stocks or real estate) and investment projects, but also to analyze annual cash flows.
IRR can also be helpful in calculating compound interest, especially when irregular cash flows from investments are expected.
If you don’t feel up to calculating the internal rate of return on your own, use calculators or software available online. Remember, however, that many of these solutions require a fee – you can always treat it as a first contribution to your planned investment.
