A Student's Guide to Cost-Benefit Analysis for Natural Resources

Lesson 11 - Cost Effectiveness Analysis

Cost-effectiveness analysis (CEA) is an alternative to cost-benefit analysis (CBA). CEA is useful when analysts face constraints which prevent them from conducting CBA. The most common constraint is the inability or unwillingness of analysts to monetize benefits.

While CEA has been widely applied for project analysis, there has been great variation in the way it is applied; consistency is often lacking among CEA analyses. Also, the quality of the CEA studies is often poor. This stands in contrast to CBA which is well-defined both in theory and practice.

CEA usually compares a series of mutually exclusive alternative projects. Costs are monetized. Project costs are typically measured as actual expenditures rather than as opportunity costs. For example, costs might include the cost of laborers, but no charge for the opportunity cost of their travel time.

However, benefits are not monetized. Instead, a single, quantified physical measure of the principal project output is made. For example, the output may be the number of lives saved, or the tons of sediment per acre prevented, or the miles of road paved.

CEA measures costs in dollars and effectiveness in physical units. Because the two are incommensurable, they cannot be added or subtracted to obtain a single criterion measure (hence the reason that it is impossible to determine if B>C). One can only compute the ratio of costs and effectiveness in the following ways:

1) CE ratio = Ci/Ei

2) EC ratio = Ei/Ci

where: Ci = the cost of alternative i, in dollars; and, Ei = the effectiveness of alternative i, in physical units

Equation 1 represents the cost per unit of effectiveness (e.g. dollars/ton of soil). Projects can be rank ordered by CE ratio from lowest to highest. The most cost-effective project has the lowest CE ratio.

Equation 2 is the effectiveness per unit of cost (e.g., tons of soil/dollar). Projects should be rank ordered from highest to lowest EC ratios. Both the CE and EC ratios are measures of technical and not economic efficiency. Thus, they are poor or at least questionable measures of allocative efficiency.

CEA and Project Selection

A. When project scales (i.e., costs) are identical, use either the CE or EC ratios or simply the effectiveness measure (e.g., lives saved) to choose the best project. As an example see the following table:

 Cost and Effectiveness Project A Project B Project C* Budget cost \$10M \$10M \$10M Effectiveness measure, lives saved 5 10 15 CE ratio, cost/life saved \$2.0M \$1.0M \$0.67M EC ratio, lives saved/million\$ .5 life 1 life 1.5 life

* C is best project

B. If the scales (i.e., costs) of projects being compared are unequal but the effectiveness measures are equal, choose the least-cost project, lowest CE ratio or highest EC ratio (all are the same). This is, essentially a cost minimization problem.  See the table below:

 Cost/Effectiveness Project A* Project B Project C Cost measure \$5M \$10M \$15M Effectiveness measure, lives saved 10 10 10 CE ratio, cost/life \$.5M \$1M \$1.5M EC ratio, lives saved/ \$M 2 1 .66

* A is best project

C. CEA as an optimization problem:

In order to facilitate decision-making, we can specify CEA as an optimization problem, in several ways:

1. Objective function: Min Cost

S.T. Constraint:

Effectiveness measure > a specified minimum level of effectiveness

Result: least cost

2. Objective function: Min CE ratio

S.T. Constraint:

Effectiveness measure > a specified minimum level of effectiveness

Result: higher effectiveness than #1, but at higher cost

3. Objective function: Max Effectiveness measure

S.T. constraint:

Cost < a specified maximum level of cost

Result: ignores possibilities to reduce cost

4. Objective function: Min CE ratio

S.T. constraint: Cost < a specified maximum level of cost

Result: emphasizes reduction of costs

[Reference: Cost-Benefit Analysis: Concepts and Practice by Boardman, Greenberg, Vining and Weimer, 1996, Prentice-Hall. Ch. 13]