The internal rate of return (IRR) is a common source of error in a financial model. This tutorial covers how to calculate an IRR in Excel, and assumes that the reader is already familiar with the mathematical concept of the IRR.
The IRR can be defined as a discount rate which, when applied to a series of cash flows, generates a nil net present value (NPV). There may be more than one IRR in certain situations; additionally, Excel makes this calculation deceptively simple, at the risk of errors.
The NPV is the discounted value of a stream of cash flows generated from a project or investment. IRR computes the break even rate of return for which the NPV equals to zero. It is an indicator of the efficiency or quality of an investment, as opposed to the NPV which indicates value or magnitude.
The IRR is the annualised effective compounded return rate, denoted by ‘r’. Mathematically, it can be formulated as:
r=IRR % n = time period of the project / investment
What is the best way to calculate the IRR of a set of cash flows?
In this tutorial we will discuss the possible methods to calculate the IRR:
Using a trial and error method (to assist understanding)
Using a 1-dimension data table
Calculating IRR using Excel function NPV()
Calculating IRR using XIRR
The downloadable Excel workbook above has been prepared to demonstrate the IRR calculation. For ease of reference, we recommend you download the workbook while reading this tutorial.
Trial and error method for IRR calculations in Excel
IRR is the discount rate for which NPV equals zero, and could be calculated by a trial and error process.
NPV(IRR(…), …) = 0
XNPV(XIRR(…), …) = 0
The trial and error process is as follows:
Start with a guess of the discount rate ‘r’
Calculate NPV using the ‘r’ – refer to our tutorials on how to calculate an NPV with or without Excel formulae
If the NPV is close to zero, then ‘r’ is the IRR
If the NPV is positive, increase ‘r’
If the NPV is negative, decrease ‘r’
Continue the process until NPV reaches zero
Using the example in the workbook:
Screenshot 1: Project NPV at r = 10%
Refer to screenshot 2: Let us now try ‘r’ of 18%. The NPV is -$0.87 million. It is negative, but the NPV is closer to zero this time.
Therefore, we could guess that the IRR should be slightly lower than 18%.
Screenshot 2: Project NPV at r = 18%
The trial and error process can be more tedious than calculating an NPV itself.
Next, we will show you the approach of guessing the IRR with the help of a 1-dimension data table.
Using a 1-dimension data table to spot the root
We recommended presenting NPV at various discount rates using a quick 1-dimension data table, with discount rates as the vertical parameter as shown in screenshot 3.
Screenshot 3: Data table of NPV at various discount rates
Let us plot the above data table in a chart - see screenshot 4. It becomes clear that the IRR is between 17.50% and 18.00%. To be precise, the IRR is 17.53%, which we could get using the Excel function.
Screenshot 4: NPV chart at various discount rates
Using IRR() in Excel
IRR(CF1, CF2, …)
We could calculate IRR using Excel function IRR(), but similar to NPV(), it has some limitations:
Using XIRR() function In Excel
Due to its limitation, the IRR function (without the X) is best avoided. The more robust function would be XIRR(). It returns the internal rate of return for a schedule of cash flows that is not necessarily periodic.
XIRR() is an added-in function in Excel and the syntax is: XIRR(CFi, dates)
Screenshot 5: Using XIRR function in Excel
As demonstrated in screenshot 5, the calculated IRR is 17.53%. We could double check the calculation by feeding the IRR back into the NPV calculation as a discount rate, for which NPV equals zero.
COMMON APPLICATIONS OF IRR
Capital budgeting: Investment decision tool
IRR is a metric to decide whether a single project is worth investing in. Theoretically, a simple decision making benchmark could be set to accept a project if the IRR exceeds the cost of capital, and rejected if this IRR is less than the cost of capital.
You should be aware of the limitation of the IRR, such as a project with multiple IRRs or no IRR. In addition, IRR neglects the size of the project, and assumes that cash flows are reinvested at a constant rate.
IRR is commonly used in optimising the toll/tariff regime in project finance transactions, such as in public, private partnerships (PPP) schemes. This could be done during the bidding process based on the expected IRR. Alternatively, a tariff could be adjusted in order to provide a minimum IRR threshold for the concessionaire.
Corality Training Academy - SMART CAMPUS
There are numerous other tutorials and free resources related to financial modelling in Corality's SMART Campus.
Some of the more popular courses that relate to this topic include:
Financial Modelling for Mining Projects
Financial Modelling Techniques for Valuations Analysis