Illustration of why the IRR estimated by a single linear interpolation is only an approximation of the
actual IRR of an investment project.
Monday, 13 August 2012
How to calculate Internal Rate of Return (IRR)? (Critical Review)
By Jackie, Researcher
Area of discussion: Finance; Management & Cost Accounting
Chapter: Investment appraisal methods – Internal Rate of Return (IRR)
The objectives of this research are to analyze few different methods which are available to calculate Internal Rate of Return. There are some advantages and disadvantages of using each method as none of them are perfect. Basically, there are three types of methods which I saw students often use in examinations and these methods are usually recommended in any relevant academic text books too. They are trial and error method, reverse calculation method, and linear interpolation method. For this discussion, I have randomly taken one question from previous college’s Management Accounting exam and I will apply all these three methods into the same question and we shall see which method is more preferable, faster or perhaps easier to use.
Ideally, the Internal Rate of Return (IRR) of an investment project is the cost of capital or required rate of return which, when used to discount the cash flows of a project, it will produce a net present value of zero.
Let’s take a look at this question:
Trial and error method
Only use this method if there is no other better method available. It is very time consuming and thus, not recommended in exams.
Reverse calculation method
Highly recommended (simplest and most direct approach) especially when the discount factor is a whole number and the net cash inflow is the same for every year. Not suitable for discount factor that comes along with decimals as well as different annual net cash inflow.
Linear interpolation method
It is appropriate to use when two NPV points are known. It is suitable for condition where the discount factor comes along with decimal place or when the annual cash inflow is different. However, the main weakness is “the further the two NPV points located from each other, the less accurate and reliable the computed rate will be”. Thus, the computed figure can only serve as approximation as it was not accurate.
We say ‘approximately’ since, in using linear interpolation we have drawn a straight line between two points on a project NPV line that is in fact a curve. The straight line will not cut the x-axis at the same place as the project NPV curve, so the value we obtained by interpolation is not the actual value of the IRR, but only an estimated value.
Additional support material: PVIFA’s table
Additional readings, related links and references:
Calculating Internal Rate of Return Using Excel or a Financial Calculator
How to calculate Internal Rate of Return (IRR), and when is the time and in what situation IRR is not recommended to use?
Advantages and disadvantages of Internal Rate of Return (IRR)
Finding Internal Rate of Return (IRR) using Excel
Calculating Internal Rate of Return (IRR) and Net Present Value (NPV) using Excelhttp://www.youtube.com/watch?v=xzqpfpq6vSk&feature=related