# The Multiple IRR Problem and the No IRR Problem

## No IRR

• Internal rate of return of cash flow is the rate at which NPV or the Net Present Value becomes Zero, however, there are some cashflows whose NPV never becomes Zero.
• Illustration 1: ABC Ltd. has invested Rs. 2000 in a project for two years, the project generates a positive cash flow of Rs. 1000 in the first year and negative cash flow of Rs. 500 in the second year, let us calculate its IRR if the interest rate is 10%.
Upon solving further, we do not get any real value of x, hence (1+IRR) is unreal that implies that for the given project there is no IRR.
• Hence, we conclude that NPV for the given cash flow is Rs. -1504.13, but IRR is not defined, or in other words, there is no IRR.
• Therefore, there can be projects whose cash flow does not have an IRR but do have an NPV.
• The absence of IRR does not imply that the Investment Project is not profitable, there are equal chances of a project being profitable without having an IRR, hence NPV should always be used along with IRR to analyze the Profitability of a Project.

## Multiple IRR

• In Illustration 1 we discussed the situation where for a cash flow of a project there is no Internal Rate of Return (IRR). There can even be scenarios where a project cash flow has more than one IRR, this happens in most of the cases where the cash flow of an Investment has frequent positive and negative flows.
• Illustration 2: XYZ Ltd. has invested Rs. 5000 in a project for two years, the project generates a positive cash flow of Rs. 15000 in the first year and negative cash flow of Rs. 10000 in the second year, let us calculate its IRR if the interest rate is 10%.
• Multiple or more than one IRR does not imply that the Investment Project is not profitable, there are equal chances of a project to be profitable even if it has multiple IIR, hence NPV should always be used along with IRR to analyse the Profitability of a Project.
• In situations where the IRR value is confusing and not reliable, it is better to consider NPV value of the investment cashflow for deciding the profitability of the investment. 