Guide to COST-BENEFIT ANALYSIS of investment projects - Ramiri

Figure C.1 Project ranking by NPV valuesFigure C.2 A case of switchingNPVProject 1NPVProject 1Project 2Project 2ixiThere are cases in which the NPV of one alternative is not greater than the other or for every i value. This is due to aphenomenon referred to as ‘switching’. Switching occurs when the NPV curves of two projects intersect one anotheras in Figure C.2. With a discount rate above x project 1 has a higher NPV, with a discount rate below x project 2 willperform better. In order to select the best option the definition of the discount rate is crucial for the selection of thebest option (and IRR cannot be used as a decision rule).The Internal Rate of ReturnThe Internal Rate of Return (IRR) is defined as the discount rate that zeroes out the net present value of flows ofcosts and benefits of an investment, that is to say the discount rate of the equation below:NPV (S) = ∑ [S t / (1+ IRR t )] = 0The Internal Rate of Return is an indicator of the relative efficiency of an investment, and should be used withcaution. The relationship between NPV and IRR is shown in the graph below.Figure C.3 The internal rate of returnNPVFigure C.4 Multiple IRRsNPVIRRiIRR’ IRR’’ IRR’’’iIf the sign of the net benefits, benefits minus costs, changes in the different years of the project’s lifespan (forexample - + - + -) there may be multiple IRRs for a single project. In these cases the IRR decision rule is impossibleto implement. Examples of this type of project are mines and nuclear power plants, where there is usually a largecash outflow at the end of the project because of decommissioning costs.210