The project's internal rate of return (IRR) is the indicator at which the discounted net cash flow (NPV) of the project is zero. That is, this is the discount rate at which NPV is equal to zero (the formula for calculating IRR will be based on this further).
This indicator indicates what kind of profitability the project shows, taking into account the current period of construction of the investment model (if the model is built for 7 years, then for these seven years, if for 10, then for ten years, the fact is that the same project shows different levels of profitability for different periods of model construction).
This indicator can be compared with the bank interest rate, only for an investment project. That is, if the IRR for a project for 5 years is 30%, then it can be argued that if you invest an amount in the project, then in 5 years you will receive an amount equivalent to the income that you would receive if you put the same amount in the bank at 30% per annum.
Nuances of bet calculation
When calculating and analyzing the rate, you need to take into account some features of its calculation, for example:
- as mentioned earlier, for the same project but when calculated for a different amount of time, the rate changes. The rate of return of a project for 5 years will never be equal to the rate of return for a project for 7 years.
- the internal rate of return cannot be calculated for a period shorter than the payback period of the project (for example, if the simple payback period of the project is 7 years, then you cannot calculate the IRR for 6 years);
- if you calculate the internal rate of return for some arbitrary period (for example, 7 years), then you must understand that this rate shows the percentage of profitability for exactly 7 years, but the business continues to operate and generates income (or generates a loss) and, accordingly, as was said earlier, it will change. To do this, the approximate cost of the project is calculated at the end of the model construction period and the amount of its sale is put in the model (as if we were selling our business) and the IRR is calculated taking into account this sale.
Why do we need internal rate of return?
This indicator is needed to determine the profitability of investment projects and it shows what kind of profitability the project provides in comparison with other investment options for a similar period. For an investor, this indicator allows you to compare the profitability of both several investment projects and alternative investment methods.
But, I would like to note that it is impossible to analyze the internal rate of return separately from other indicators of project efficiency, such as NPV, simple and discounted payback period.
Rate calculation formula
To calculate the internal rate of return, use
Calculation in Excel
To explain how the indicator is calculated in Excel, we present the initial data of the task. For example, cash receipts and expenditures for the project are as follows (thousand rubles):
| Income/expense item | 1 year | 2 year | 3 year | 4 year | 5 year |
| Investments | 1 000 | ||||
| Revenue from operating activities | 2 000 | 2 200 | 2 400 | 2 600 | 2 800 |
| Operating expenses | 1 800 | 1 950 | 2 100 | 2 250 | 2 400 |
| Net cash flow for the period | - 800 | 250 | 300 | 350 | 400 |
To calculate the internal rate of return in Excel, the IRR (range) function is used. The dynamics of net cash flow is chosen as the range. The IRR calculation is shown in the figure below:
As we can see, the internal rate of return in this example is 21%.
Other calculation examples
You can see how IRR is calculated using the example of a specific business plan calculation by clicking on the link or using the search form.
The two main methods for evaluating investment projects are NPV and IRR (net present value and internal rate of return). Both methods are based on discounting cash flows from the project: NPV calculates the present value of the project at a given interest rate, IRR gives an idea of what maximum loan rate can be accepted so that the project is not unprofitable. As they write in financial analysis textbooks, top managers of most companies prefer to evaluate potential investment projects in terms of % rates of return (i.e. IRR), rather than in terms of present-day monetary amounts (i.e. NPV). And this is quite understandable.
So is it possible to talk about the advantages of one method over another, and which method is better?
Why do managers love IRR so much?
In fact, it is not surprising that the internal rate of return (IRR) is used more often in practice. There is a simple explanation for this:
- using IRR does not imply determining the discount rate that is needed to calculate the NPV of the project.
- it is convenient to operate with interest rates, and not with some abstract amount of monetary units (rubles), since the % internal rate of return can be easily compared with the bank loan rate (although this is not entirely correct)
- Isn’t it true: the phrase “20% per annum” sounds much more attractive than the phrase “the present value of the project is 899 rubles.”
Of course, the first item on this list is the most important. Because determining the cost of capital for a company (the so-called WACC), which is used in calculating NPV, is itself a difficult task.
And yes, a high internal rate of return (for example, 20%) makes a strong impression on the listener and seems tempting, but all these epithets are from the realm of emotions. And investments are not a category that can be assessed based on “attractiveness” criteria.
Any textbook says that the NPV method is preferable, since it shows the amount of added value that an investment project creates. IRR is a relative indicator that shows only at what cost of capital we will receive zero added value. Maybe there is no need to worry, and both methods will always give the same answer?
When will NPV and IRR methods lead to different conclusions?
For projects that are independent from each other, the IRR and NPV methods will always prompt the same decision: “accept” or “reject.” But we live in a world where financial resources (and not only them) are limited. And you always have to choose between two mutually exclusive projects (build a road in Yakutia or repair a bridge in Volgograd). In this case, it is not uncommon for the IRR method to tell us that project A is worth accepting, while the NPV method will “vote” for project B.
Returning to the examples from previous articles about and, if projects A and B are mutually exclusive, then the IRR method will always select project A, since 14.5%>11.8%. But with a discount rate equal to, for example, 6%, the NPV indicator will indicate project B as more preferable:
- at a cost of capital of 10%, the NPV of project A is 788 monetary units, which is greater than the NPV for project B - 491 monetary units. Therefore, Project A must be accepted!
- at a cost of capital of 6%, the NPV of project A is 1.588 monetary units, which is less than the NPV for project B - 1.724 monetary units. Therefore, Project B must be accepted!
- IRR does not depend on the cost of capital, so if you use this indicator, then project A will always look preferable
It is at this point (7.2%) that the graphs of the dependence of NPV on the discount rate for projects A and B intersect with each other. To the left of this point, the Project B line (red) is higher than the Project A line (blue). This means that at this cost of capital (below 7.2%), project B will make the investor richer than project A.
I talked about the reasons for this state of affairs in an article about calculating the NPV of investment projects. Project B is long-term, i.e. Over time, cash flows from it increase. Project A is short-term with the greatest returns in the early years, and towards the end of Project A, revenues decline. But the further into the future from today, the stronger the impact of the discount rate: after a year, an increase in the discount rate by 1% “eats” 0.93% of the cash flow, and after 4 years, an increase in the discount rate by 1% causes a decrease in cash flow by 3.65%. Therefore, the NPV of long-term project B, with an increase in the discount rate, falls faster than the NPV of project A, whose cash flows are maximum in the first years of the project. This is clearly visible in the figure: the schedule for project B is steeper than the schedule for project A.
It turns out that the NPV and IRR methods will recommend different investment projects if there is a difference in the amount of cash flows and in how they are distributed over time: large in size at the beginning of the project or at the end. This is built into the mathematics of the discounting process itself.
The fact is that the discount rate works in both directions of time - from the future to the present (discounting) and from the present to the future (accretion). That is, if we discount at 10% per annum, moving from the future to today, then we can increase the reduced cash flows from today to the future at the same rate. The internal rate of return, which we calculate using the IRR method, is both a discount rate and an investment rate.
So - when we calculate IRR, we assume that all cash flows are invested at this rate (as described, its IRR is equal to the deposit rate).
When we calculate NPV, we assume that the cash flows are discounted and invested at the company's cost of capital. And this is more correct from an economic point of view. If we get an IRR of 20%, this does not mean that we can find a bank or project that will bring us exactly that rate of return.
All mutually exclusive investment projects with cash flows that differ over time are more accurately compared using the NPV indicator, which will show you the increase in your wealth in absolute terms, rather than the potential internal return that you may never receive. The IRR method for such projects can lead to incorrect selection, as in our example with a rate of 6%.
More advantages and disadvantages of the IRR method
The advantage of the IRR indicator is the ability to evaluate the project’s “safety margin” before a possible increase in interest rates. For example, in Russia, credit resources immediately became more expensive by several percent when, on the night of December 16, 2014, the Central Bank of the Russian Federation sharply increased the refinancing rate to 17%. If we were to accept Project A, which has an IRR of 14.5%, it would become unprofitable overnight. And if we found a project with an internal rate of return equal to 20%, then even such a sharp increase in interest rates would not make our project unprofitable.
The disadvantages of the internal rate of return method include the fact that for non-standard projects several IRR values can be obtained. A standard project is where there is one negative cash flow at the very beginning (the initial investment) and several positive cash flows in the future. If positive and negative cash flows alternate, then mathematically we will get as much IRR as the number of times the cash flows from the project change sign.
For example, for a project with the following flows: (10,000), 5,000, (2,000), 4,000, 5,000, two IRRs will be obtained.
MIRR modified internal rate of return - what is it?
Analysis of investment projects based on the internal rate of return (IRR) method assumes that all cash flows of the project can be invested at this rate, which is unrealistic. This drawback of the IRR method is eliminated by using the so-called modified internal rate of return, or MIRR (M modified I internal R ate of R eturn).
The essence of the MIRR calculation is simple: all positive cash flows from the project are increased at a % rate equal to the company's cost of capital (WACC), and then the rate is found, discounting at which we will receive the amount of our investment. Let's take project A as an example, the same one that was used to calculate NPV and IRR earlier. To understand how to calculate the modified internal rate of return, look at the figure below:
Let's look at everything in order.
Action one: all flows from the project are invested (increased) at a rate of 10% (we remember that this is the cost of capital for our company).
The last cash flow is not increasing, this will be the end date of our investment project. As a result, in the fourth year the total cash flow should be equal to 15,795.
After this, the cash flows from the project will be as follows (in the red box):
This table calculates the NPV of the project after “modifying” its cash flows. As can be seen from the table, nothing has changed: the NPV of project A is, as before, equal to 788 monetary units.
That is, we ended up with only one positive cash flow at the end of year 4 and an initial investment of 10,000 instead of annual cash inflows. A single cash inflow is the equivalent of four annual positive cash flows, as evidenced by the constant NPV value.
Act two: Now we need to calculate the internal rate of return for these two cash flows, which are equivalent to the original project A. To do this, it is best to use the IRR function in Excel (this is discussed in detail):
The IRR in this case turned out to be equal to 12.1%, and not 14.5% as the IRR for the original project A. This value of 12.1% is the modified internal rate of return.
In Excel, you can calculate the MIRR directly. In the Formulas—>Financial tab there is the MVSD formula, which is responsible for calculating the modified rate of return. In the “value” cell you need to enter a link to the cells with cash flows, in the “reinvest_rate” cell - the value of the cost of capital, in our case 10%.
As can be seen from the figure, the MIRR function gives the same MIRR value that was obtained earlier by the two-step calculation, namely 12.1%.
Now you can see how the decision to choose between two investment projects A and B will change.
As can be seen from the table, at a cost of capital (discount and investment rate) of 10%, both methods “choose” project A, at a cost of capital of 6%, both methods also “vote” for the same project - project B (highlighted in blue). Compare this table with the previous one, where at the same % rates the NPV and IRR () indicators are combined.
Thus, the modified internal rate of return method eliminates the conflict between NPV and IRR when choosing between two mutually exclusive projects, since it equalizes the rate of reinvestment of cash flows. However, MIRR eliminates one of the advantages of the IRR method - you will have to calculate a discount rate equal to the company's cost of capital, which always causes difficulties.
The possibility of making opposite decisions also remains. If two projects are of the same size and duration, then yes, the NPV and MIRR methods will always select the same project from two mutually exclusive projects. The same is true for projects of the same size but different duration. In this case, you need to calculate these indicators based on the longest project, simply adding zero cash flows to the shorter project. However, if the mutually exclusive projects differ in scale (amount of cash flows), then a conflict between the two methods is still possible. Therefore, using the NPV method is still preferable to calculating IRR or MIRR (ordinary or modified internal rate of return).
“Take a step and the road will appear by itself.” Steve Jobs
If you're wondering whether you should do something or whether you should be better prepared, don't waste your whole life doubting it. You can endlessly analyze information, calculate options, assess risks and build graphs of the result depending on a variety of indicators. But the thing is that no one can accurately predict the future.
You can constantly postpone the start of the project in anticipation of better conditions - lower loan rates, economic growth, strengthening of the national currency. However, don’t expect to wait for ideal conditions to start, they will never come. Because when one obstacle disappears, another always appears in its place. The ideal day to start any project is today.
"Theorists worry about accept good decision. In business, we also worry about do good decisions."
You need to make a decision based on the information that is available today. On the way to your dream, you will still have to make adjustments to achieve the result. The best forecast always turns out to be wrong. Because it is impossible to predict the consequences of both your actions and changes in the environment over time. This can only be done in the only case - if you do nothing.
In the business world, results matter, not business plans. However, this applies to any aspect of our life. Nobody is interested in dreams, what matters is whether you managed to reach them.
“You have to jump off a cliff every time and grow wings on the way down.”. Ray Bradbury
Couldn't have said it better.
You have a great idea for a new product that will increase profits or a new system that will reduce company costs. But how can you be sure that this idea will be worth the investment? One of the main methods to find out is IRR analysis.
Any time you propose a capital expenditure, you can be sure that senior managers will want to find out the return on investment (ROI).
There are many methods you can use to calculate ROI - net present value, payback period, profitability index and internal rate of return or IRR.
Let's figure out how IRR works and in what cases it is better to use it.
What is internal rate of return?
IRR is the rate at which a project breaks even (i.e. pays for itself).
This metric is typically used by financial analysts in conjunction with net present value or NPV. This is because both methods are similar but use different variables.
With NPV, you determine the discount rate for your company and then calculate the present value of the investment based on that rate ().
But for IRR, you calculate the actual cash flow income of the project and then compare it with your company's barrier rate (i.e. the minimum expected level of profitability of your company). If the IRR is higher, then the investment is profitable.
How is IRR calculated?
This is not a simple calculation. For example, let's say you offer an investment of CU3,000 that will yield CU1,300. for each year of the next 3 years. You cannot simply use the total cash flow of CU3,900 (1,300 * 3) to determine the rate of return as it extends over a period beyond those 3 years.
Instead, you will have to use an iterative process in which you try different hurdle rates (or annual percentage rates) until your NPV is zero.
To calculate this indicator, you do not need to go deep into mathematics, - you can easily calculate it in Excel (VSD or IRR function) or on a financial calculator.
How do companies use it?
Companies typically use both NPV and IRR to evaluate investments.
NPV tells you more about expected profitability, but financial analysts " often rely on IRR in presentations to non-financial people».
This is because IRR is much more simple and intuitive.
When you speak: "If I have a project where the IRR is 14% and our corporate hurdle rate is 10%", your audience thinks: "Oh I understand. We get 4% more profit from this project".
If you were to say that the NPV of this project is CU2 million, your audience would very likely ask for a reminder of what NPV is and may become confused before you even partially explain the meaning of what “the present value of future cash flows from this investment using our 10% hurdle rate exceeds our initial investment by CU2 million.”.
The downside to this metric is that IRR is much more conceptual than NPV. Using NPV, you estimate the cash return of the company: assuming all assumptions are correct, this project will generate CU2 million. IRR doesn't give you real monetary numbers.
Likewise, IRR does not address issues of scale. For example, an IRR of 20% doesn't tell you anything about the amount of money you'll receive. Is it 20% of CU 1 million? Or from 1 unit? You don't have to be a mathematician to understand that there is a big difference between these numbers.
What mistakes do people make when using IRR?
The biggest mistake is to use IRR exclusively.
It is much better to analyze the project using at least one of the other methods - NPV and/or payback period.
Using this metric alone can lead you to make poor decisions about where to invest your company's hard-earned money, especially when comparing projects that have different timelines.
Let's say you have a one-year project with an IRR of 20% and a 10-year project with an IRR of 13%. If you base your decision on IRR alone, you can support a 20% IRR project. But that would be a mistake. You are better off with an IRR of 13% over 10 years than an IRR of 20% over one year if your corporate hurdle rate is 10% over that period.
You should also be careful about how IRR takes into account the time value of money. IRR assumes that future cash flows from a project are reinvested in IRR rather than in the company's cost of capital, and therefore it does not reflect the relationship to capital and the time value of money as accurately as NPV.
Modified internal rate of return (MIRR), which assumes that positive cash flows are reinvested in the firm's capital, more accurately reflects the cost and profitability of the project.
However, you should always use IRR in conjunction with NPV to get a more complete picture of how much return your investment will generate.
Internal Rate of Return
Application area
The internal rate of return determines the maximum acceptable discount rate at which funds can be invested without any losses for the owner.
Description
Internal rate of return IRR (I internal R ate of R eturn) is a widely used indicator of investment performance. This term refers to the discount rate at which the net present value of the investment project is zero. In practice, the value of $IRR$ is compared with a given discount rate $r$. Moreover, if $IRR> r$, then the project provides a positive value of $NPV$ and a percentage of income equal to $(IRR-r)$.
The internal rate of return is determined by the formula:
$$NPV = \sum \limits_(i=0)^(n) \frac(CF_i)((1+IRR)^i) - \sum \limits_(i=0)^(n)\frac(CI_i) ((1+IRR)^i), \,\mbox (at) \, NPV = 0$$
The value of $IRR$ can be determined in one more way. To do this, $NPV$ is first calculated at various levels of the discount rate $r$ until $NPV$ becomes negative. After this, the value of $IRR$ is found using the formula:
$IRR=r_a+(r_b - r_a)\frac(NPV_a)(NPV_a - NPV_b)$,
the inequality $NPV \_a > 0 > NPV \_b \, \mbox (and)\,\ r\_b > IRR > r\_a$ must be observed.
The advantage of the $IRR$ indicator is that it makes it possible to compare projects of different scales and different durations. For example, the efficiency of a project with $IRR$ equal to 30% is sufficient if for its implementation it is necessary to use a bank loan worth 10% per annum.
Disadvantages of the internal rate of return indicator:
- By default, it is assumed that positive cash flows are reinvested at a rate equal to the internal rate of return. When the $IRR$ of a particularly attractive investment project is, for example, 80%, it means that all cash proceeds must be reinvested at a rate of 80%. However, it is unlikely that a business has the annual investment capacity to achieve an 80% return. In this situation, the internal rate of return ($IRR$) overestimates the effect of investment. If $IRR$ is close to the firm's reinvestment level, then this problem does not arise.
- There is no way to determine how much money an investment will bring in absolute values (rubles, dollars).
- With arbitrary alternation of cash inflows and outflows in the case of one project, several $IRR$ values may exist. Therefore, it is impossible to make an unambiguous decision based on the $IRR$ indicator.
If there are several alternative projects with the same values of $NPV$, $IRR$, then when choosing the final investment option, the duration of the investment is taken into account. Duration (D) is the weighted average life cycle of an investment project or its effective duration. It allows you to bring the most diverse projects in terms of their characteristics (by terms, number of payments in a period, methods of calculating the interest due) to a single standard. This method is based on calculating when a project will generate income and how much income will be received each month, quarter or year throughout its life. As a result, managers receive information about how long it takes for investments to pay off with income given to the current date. To calculate duration, use the following formula:
$D=\frac(\sum \limits_(i=1)^(n) i*PV_i)(\sum \limits_(i=1)^(n)PV_i)$,
where $PV_i=\frac(CF_i)((1+r)^i)$ is the current value of income for i periods until the end of the project,
$i$ - periods of income receipt.
Recently we considered such an important indicator of the economic viability of any investment project as NPV, the net present value of the project. It's time to get acquainted with the second most important indicator of the effectiveness of investment projects - IRR, Internal Rate of Return.
In the Russian translation there are quite a lot of interpretations - internal rate of return, internal rate of return, internal rate of profitability, internal rate of profitability - all this means the same thing. This indicator is usually expressed as a percentage and much less often in decimal fractions.
The economic meaning of this indicator is that in fact it shows the average annual profitability of the project on the horizon of consideration. For example, if you have calculated a project for 10 years and the IRR of your project is 15%, this means that your investment in the project will give an average of 15% per annum for 10 years.
Our expert Alexey Grebenyuk
In other words, the economic meaning can be defined as follows: this is the discount rate at which NPV project goes to zero. Accordingly, if you borrow money from a bank or, say, from a friend at 20% per annum, then you should not invest it in your project, which gives only 15% profitability.It is better to invest in some other project that will give more than 20%, otherwise there is no point in borrowing in principle. It will be effective to borrow money from a bank at 20% per annum only when your project gives IRR above 20%. In this case, you can return the money to the bank and earn yourself extra profits.
IRR calculation manually on paper is not an easy task and you need to have real mathematical abilities. Magnitude IRR is calculated by the selection method and, as I already said, it is equal to the discount rate at which the indicator NPV equal to zero. You need to do several iterations before you find the internal rate of return. Difficult? Very difficult! I myself have never counted on paper IRR. Microsoft Excel calculates IRR instantly - through the "VSD" function - as easy as shelling pears!
In addition to those discussed NPV and IRR , there is a third important indicator of the economic efficiency of any investment project - this is payback period. The economic meaning of this indicator is very simple - this is the period of time during which the project returns the invested funds to its owner. As a rule, the more capital-intensive a project we consider, the longer the payback period it has. Of course, this is not entirely necessary, but still, as a rule, it is so. For example, the payback period for a power plant will be longer than the payback period for a small store.
In investment projects there is another important dependence - usually the higher the profitability of the project, the higher the risk of its implementation. And vice versa - the lower the profitability, the lower the risk.
