Problem of Multiple IRRsA project may have both lending and borrowing features together. IRR method, when used to evaluate such non-conventional investment can yield multiple internal rates of return because of more than one change of signs in cash flows.

Case of Ranking Mutually Exclusive ProjectsInvestment projects are said to be mutually exclusivewhen only one investment could be accepted and others would have to be excluded.Two independent projects may also be mutually exclusive if a financial constraint is imposed.The NPV and IRR rules give conflicting ranking to the projects under the following conditions:The cash flow pattern of the projects may differ. That is, the cash flows of one project may increase over time, while those of others may decrease or vice-versa.The cash outlays of the projects may differ.The projects may have different expected lives.

Timing of cash flowsThe most commonly found condition for the conflict between the NPV and IRR methods is the difference in the timing of cash flows. Let us consider the following two Projects, M and N.

Cont…NPV Profiles of Projects M and NNPV versus IRRThe NPV profiles of two projects intersect at 10 per cent discount rate. This is called Fisher’s intersection.

Incremental approachIt is argued that the IRR method can still be used to choose between mutually exclusive projects if we adapt it to calculate rate of return on the incremental cash flows.The incremental approach is a satisfactory way of salvaging the IRR rule. But the series of incremental cash flows may result in negative and positive cash flows. This would result in multiple rates of return and ultimately the NPV method will have to be used.

Scale of investment

Project life span

REINVESTMENT ASSUMPTIONThe IRR method is assumed to imply that the cash flows generated by the project can be reinvested at its internal rate of return, whereas the NPV method is thought to assume that the cash flows are reinvested at the opportunity cost of capital.

MODIFIED INTERNAL RATE OF RETURN (MIRR)The modified internal rate of return(MIRR) is the compound average annual rate that is calculated with a reinvestment rate different than the project’s IRR.

VARYING OPPORTUNITY COST OF CAPITALThere is no problem in using NPV method when the opportunity cost of capital varies over time. If the opportunity cost of capital varies over time, the use of the IRR rule creates problems, as there is not a unique benchmark opportunity cost of capital to compare with IRR.

NPV VERSUS PIA conflict may arise between the two methods if a choice between mutually exclusive projects has to be made. NPV method should be followed.