Internal Rate of Return (IRR)
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===Negative IRRs=== | ===Negative IRRs=== | ||
Revision as of 20:30, 13 February 2022
Developed by Pablo Leandro Capellari- s213666
Internal rate of return (IRR) is a parameter used in the financial analysis to determine the profitability of the investment, that is, it estimates the rate of return that the evaluated project could have. The term "internal" is because for the calculation of the IRR, external factors that could affect the profitability of the project, such as inflation, are not considered. In mathematical terms, the IRR is defined as the discount rate that causes the sum of the cash flows of the project to be zero[1]. In other words, if the net present value (NPV) of a project is 0 at a certain rate, that rate is the IRR[2]. Researchers in 2003[3] have validated the IRR as an alternative to the NPV as an indicator for project evaluation, considering that the IRR as from the point of view of the investor and the NPV from the point of view of the society. Its popular application is mainly because it defines the return on investment, sometimes seen as a measure of efficiency, beyond its documented limitations. For decision-makers, the IRR can be compared to the discount rate for rejecting or accepting projects. To be specific, for a project to be accepted, the IRR must be greater than the discount rate and when both are equivalent, a situation of indifference arises[1]. To resolve many deficiencies related to the traditional IRR, some researchers[4] have proposed to use the average internal rate of return (AIRR). The AIRR is based on the breakdown of the NPV of the project between the invested capital and the economic efficiency, maintaining the consistency of the NPV to decide the acceptance of a project. This breakdown generates valuable information helping to determine the uncertainty of a project allowing risk to be explored in more detail.
Contents |
Big idea
Describe the tool, concept or theory and explain its purpose. The section should reflect the current state of the art on the topic
Definition
IRR Mathematically[2]
IRR is the discount rate (interest rate) that makes the sum of the present value of the cash flows zero. If the NPV of the project is zero at the selected discount rate, then that discount rate is, by definition, the IRR. IRR is algebraically equivalent. Mathematically expressed as:
where 
is a cash flow in period 
and 
is the IRR.
Practical example
In the following example, a highway construction project is outlined to demonstrate the calculation of IRR and other parameters. For exemplification purposes, the following data have been used: The project opens in year 0 and has an evaluation period on 10 years, the project has the following first year impacts: –Time savings: 500,000 DKK. –Accident savings: 50,000 DKK. Operation and maintenance: 100,000 DKK.
| Discount rate | 0,03 |
|---|---|
| Traffic growth | 0,015 |
| Price growth | 0,01 |
In addition, different reference values have been used for this type of project, such as a discount rate of 3%, annual traffic growth of 3% and price growth of 1%.
| Year | - | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Discount factor | - | 1,09 | 1,06 | 1,03 | 1,00 | 0,97 | 0,94 | 0,92 | 0,89 | 0,86 | 0,84 | 0,81 | 0,79 | 0,77 | 0,74 |
| Traffic growth | - | 0 | 0 | 0 | 1,00 | 1,02 | 1,03 | 1,05 | 1,06 | 1,08 | 1,09 | 1,11 | 1,13 | 1,14 | 1,16 |
| Price growth | - | 0 | 0 | 0 | 1,00 | 1,01 | 1,02 | 1,03 | 1,04 | 1,05 | 1,06 | 1,07 | 1,08 | 1,09 | 1,10 |
| Construction costs | ,-10.612.090 | -3.642.423 | -3.536.333 | -3.433.333 | |||||||||||
| Scrap value | 7.440.939 | ||||||||||||||
| Operation and maintenance | -953.020 | - | - | - | -100.000 | -97.087 | -94.260 | -91.514 | -88.849 | -86.261 | -83.748 | -81.309 | -78.941 | -76.642 | -74.409 |
| Time savings | 5.372.322 | - | - | - | 500.000 | 497.646 | 495.302 | 492.970 | 490.649 | 488.338 | 486.039 | 483.750 | 481.473 | 479.205 | 476.949 |
| Accidents | 476.510 | - | - | - | 50.000 | 48.544 | 47.130 | 45.757 | 44.424 | 43.130 | 41.874 | 40.655 | 39.470 | 38.321 | 37.205 |
| NPV | 1.724.661 | ||||||||||||||
| BCR | 1,16 | ||||||||||||||
| IRR | 4,57% |
The table displays year-over-year cash flows, plus calculations for Residual Value, Net Present Value (NPV), Benefit Cost Rate (BCR), and Internal Rate of Return (IRR). For the calculation of the IRR, the Excel function "What-If" has been used, where it allows estimating the IRR generating an NPV=0.
Negative IRRs
Application
Provide guidance on how to use the tool, concept or theory and when it is applicable
Average internal rate of return (AIRR)
Personal finance
Limitations
Critically reflect on the tool/concept/theory. When possible, substantiate your claims with literature
Multiple IRRs
Incorrect ranking of projects
Projects with large differences in scale
IRR single decision factor
Annotated Bibliography
- ↑ 1.0 1.1 Hartman, Joseph C., and Ingrid C. Schafrick. «THE RELEVANT INTERNAL RATE OF RETURN». The Engineering Economist, Vol. 49, no. 2, January 2004, p. 139-58. DOI.org (Crossref), https://doi.org/10.1080/00137910490453419.
- ↑ 2.0 2.1 Patrick, Michael, and Nick French. «The internal rate of return (IRR): projections, benchmarks and pitfalls». Journal of Property Investment & Finance, vol. 34, no. 6, January 2016, p. 664-69. Emerald Insight, https://doi.org/10.1108/JPIF-07-2016-0059.
- ↑ Tang, S.L., and H. John Tang. «TECHNICAL NOTE: THE VARIABLE FINANCIAL INDICATOR IRR AND THE CONSTANT ECONOMIC INDICATOR NPV». The Engineering Economist, Vol. 48, no. 1, January 2003, p. 69-78. DOI.org (Crossref), https://doi.org/10.1080/00137910308965052.
- ↑ Hazen, Gordon, and Carlo Alberto Magni. «Average Internal Rate of Return for Risky Projects». The Engineering Economist, Vol. 66, no. 2, April 2021, p. 90-120. DOI.org (Crossref), https://doi.org/10.1080/0013791X.2021.1894284.
