IRR and cash flow
Quantitative Finance
Level
2
An investment project has multiple IRRs. What must be true about this project?
A project has negative cash flows in the first few years, but positive cash flows thereafter.
The project has a large initial outlay.
The project has a negative AAR.
At least one of the future cash flows is negative.
The project cash flows must change signs at least twice.
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1 solution
A conventional cash flow has just one IRR and its cash flow is somewhat like this: − − + + + + Here, we can see that the change of signs occur only once. Based on Descartes' rule of signs, the maximum possible number of IRRs will be equal to the number of sign changes. An unconventional cash flow change its sign more than once. For example, − − + + + − − − has two changes in signs. So, it can have multiple IRRs. Hence, for having multiple IRRs changing signs at least twice is a must. N.B. The number of IRRs must be equal to or less than the number of changes in signs. In other words, complex roots are also a possibility.