Guide to COST-BENEFIT ANALYSIS of investment projects - Ramiri

ANNEX CPROJECT PERFORMANCE INDICATORSThis annex explains how to calculate and use the main project performance indicators for CBA analysis: Net PresentValue (NPV), Internal Rate of Return (IRR) and the Benefit-Cost Ratio (B/C).The indicators provide concise information about project performance and are the basis for ranking projects. Thepreferred indicator is the NPV.The Net Present ValueThe Net Present Value of a project is the sum of the discounted net flows of a project. The NPV is a very conciseperformance indicator of an investment project: it represents the present amount of the net benefits (i.e. benefits lesscosts) flow generated by the investment expressed in one single value with the same unit of measurement used in theaccounting tables.Financial and economic tables are defined by inflows (I 1 , I 2 , I 3 , …), outflows (O 1 , O 2 , O 3 , …) and balances (S 1 , S 2 , S 3 ,… for time 1, 2, 3, …). Inflows and outflows are distributed over a number of years and this could generateproblems if we want to sum S at time 1 and S at time 2 and so on. These problems are due to the fact that themarginal utility of one Euro today is higher than the marginal utility of one Euro in year 2. There are two basicinterrelated reasons for this:- there exists a positive opportunity cost of numeraire: a unit benefit is worth less the further it occurs in thefuture;- individuals have positive time preferences, because of risk aversion for future events, because income is afunction that increases with time, while marginal utility for consumption decreases, and because of purepreferences for present utility compared to future utility.The aggregation of costs and benefits occurring in different years can be carried out by weighting them. This boilsdown to applying appropriate coefficients, decreasing with time in order to measure the loss of value of the numeraire.Such a coefficient is discounting factor a t = (1+i) -t , where t is the time, i is the rate of discount and a t is the coefficientfor discounting a value in year t to obtain its present value.The Net Present Value of a project is defined as:n SNPV = ∑ a tS t=0S+1S+ ... +nt=0 (1 + i) 0 (1+ i) 1 (1 + i) nWhere S t is the balance of cash flow at time t and a t is the financial discount factor chosen for discounting at time t.It is important to notice that the balance of costs and benefits in the early years of a project is usually negative and itonly becomes positive after some years. As a t decreases with time, negative values in the early years are weightedmore than the positive ones occurring in the later years of a project’s life. The value of the discount rate and thechoice of the time horizon are crucial for the determination of the NPV of a project.NPV is a very simple and precise performance indicator. A positive NPV, NPV>0, means that the project generatesa net benefit (because the sum of the weighted flows of costs and benefits is positive) and it is generally desirableeither in financial terms or in economic terms. When different options are considered, the ranking of the NPVs ofthe alternatives indicates the best one. For instance in Figure C.1 project 1 is more desirable than project 2 because itshows a higher NPV for all the discount rates (i) applied.209