Cost-benefit analysis and economic assessment
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Cost benefit analysis (CBA) is the economic assessment component of overall sustainable development assessment (SDA), in the project appraisal stage. CBA assesses project costs and benefits monetarily. Benefits are defined by gains in human well being. Costs are defined in terms of their opportunity costs, which is the benefit foregone by not using resources in the best available alternative application.
SDA also requires us to consider a number of non-economic aspects (including financial, environmental, social, institutional, and technical criteria) in project appraisal. In particular, the economic analysis of projects differs from financial analysis. The latter focuses on the money profits derived from the project, using market or financial prices, whereas economic analysis uses shadow prices rather than financial prices. Shadow prices (including valuation (Valuing environmental costs and benefits) of externalities) reflect economic opportunity costs, and measure the effect of the project on the efficiency objectives in relation to the whole economy. Criteria commonly used in CBA may be expressed in economic terms (using shadow prices) or financial terms (using market prices) – our emphasis will be on economic rather than financial evaluation.
The most basic criterion for accepting a project compares costs and benefits to ensure that the net present value (NPV) of benefits is positive:
- <math>NPV = sum_{t=0}^T (B_t-C_t)/(1+r)^t</math>
where Bt and Ct are the benefits and costs in year t, r is the discount rate, and T is the time horizon.
Both benefits and costs are defined as the difference between what would occur with and without project implementation. In economic analysis B, C, and r are defined in economic terms and appropriately shadow priced using efficiency prices[1]. Alternatively, for financial analysis, B, C and r are defined in financial terms.
If projects are to be compared or ranked, the one with the highest (and positive) NPV would be preferred. Suppose NPVi = net present value for project i. Then if NPVI > NPVII project I is preferred to project II, provided also that the scale of the alternatives is roughly the same. More accurately, the scale and scope of each of the projects under review must be altered so that, at the margin, the last increment of investment yields net benefits that are equal (and greater than zero) for all the projects. Complexities may arise in the analysis of interdependent projects.
The internal rate of return (IRR) is another project criterion given by:
- <math>NPV = sum_{t=0}^T (B_t-C_t)/(1+IRR)^t = 0</math>
Thus, the IRR is the discount rate which reduces the NPV to zero. The project is acceptable if IRR > r, which in most cases implies NPV > 0 (ignoring projects where multiple roots could occur, because the annual net benefit stream changes sign several times). Problems of interpretation occur if alternative projects have widely differing lifetimes, so that the discount rate plays a critical role. If economic (shadow) prices are used, then the terminology internal economic rate of return (IERR) may be used, while the application of financial (market) prices yields the internal financial rate of return (IFRR).
Another frequently used criterion is the benefit cost ratio (BCR):
- <math>BCR = left ( sum_{t=0}^T B_t/(1+r)^t right ) bigg / left ( sum_{t=0}^T C_t/(1+r)^t right )</math>
If BCR > 1, then NPV > 0 and the project is acceptable.
Each of these criteria has its strengths and weaknesses, but NPV is probably the most useful. It may be used to derive the least cost rule, when the benefits of two alternative projects are equal (i.e., both serve the same need or demand). Then the comparison of alternatives is simplified, since the benefit streams cancel out. Thus:
- <math>NPV_I - NPV_{II} = sum_{t=0}^T [[- C_{I,t}]]/(1+r)^t</math>;
Therefore, NPVI > NPVII if
- <math> sum_{t=0}^T C_{II,t} /(1+r)^t > sum_{t=0}^T C_{I,t}/(1+r)^t</math>;
In other words the project which has the lower present value of costs is preferred. This is called the least cost alternative (when benefits are equal). However, even after selecting the least cost alternative, it is still necessary to ensure that this project has a positive NPV.
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