COST-BENEFIT ANALYSIS

It has been suggested that: "One can view cost-benefit analysis as anything from an infallible means of reaching the new Utopia to a waste of resources in attempting to measure the unmeasurable." [3] Many of the criticisms of cost-benefit analysis are equally applicable to other analytical techniques. Since analysis is difficult, costly, and trouble-some, all too often, the assertion is made that more intuitive approaches should be applied. This is not a valid argument, however, for abandoning efforts to improve techniques for cost analysis.

Basic Components of Cost-Benefit Analysis

Given adequate estimates, cost-benefit analysis offers a relatively straightforward assessment of economic efficiency, providing information on which to base decisions regarding the effective allocation of available resources among economically desirable options. A comprehensive cost-benefit analysis requires that estimates be made of both the direct and indirect costs and the tangible and intangible benefits of a program or project. Costs and benefits must then be translated into a common measure, usually (but not necessarily) a monetary unit. Costs and benefits are then compared by computing: (1) a benefit- to-cost ratio (benefits divided by costs), (2) net benefits (benefits minus costs), or (3) some other value (such as, an internal rate of return) which summarizes the results of the analysis.

The crux of cost-benefit analysis lies in a statement of the problem. As Anatol Rapoport has observed: "The success with which any problem is solved depends to a great extent on the clarity with which it is stated. In fact, the solution of the problem is, in a sense, a clarification (or concretization) of the objectives. [4] Vague statements of the problem lead to vague methods, where success is doubtful or at best, erratic. The more a given situation is clarified, the better the classification of the problem or issue, and the greater the promise of a successful solution.

In the cost-benefit approach, the resource allocation problem is clarified through an identification of: (1) an objective function, (2) constraints, (3) externalities, (4) time dimensions, and (5) risk and uncertainty. [5]

Selecting an objective function involves the identification and quantification, in dollar terms to the extent possible, of the benefits and costs associated with each alternative. Benefits are the net outcomes, both tangible and intangible, of a program or project. Specification of benefits sometimes may be relatively straightforward, as in many technical and industrial projects. For many social programs, however, benefits often are diffuse, intangible, and difficult to define and measure. Costs are somewhat easier to identify. They are the direct and indirect inputs--the resources required to carry out the program or project. The evaluation of opportunity costs--the value of foregone opportunities--may be complex, however, even for programs for which extensive impact data are available.

Constraints are the "rules of the game"--that is, the limits within which a solution must be sought. Solutions that are otherwise optimal frequently must be discarded because they do not conform to these imposed rules. Constraints are incorporated into mathematical models as parameters or boundary conditions.

Projects may have external or spillover effects--that is, side effects or unintended consequences that may be beneficial or detrimental. Since these externalities may be difficult to identify and measure, they may be excluded from the analysis initially in order to make the problem statement more manageable. The long-range effects of these phenomena must ultimately be considered, however, usually after the objective function and model have been tested and the range of feasible alternatives has been narrowed.

Costs and benefits occurring at different points in time must be made commensurable--that is, translated into a common unit of measurement. It is not sufficient merely to add the estimated benefits and subtract the estimated costs. The impact of deferred benefits and future costs must be taken into account. In so doing, the analyst encounters the problems of risk and uncertainty.

Discounting Future Costs and Benefits

In developing a cost-benefit analysis, it is important to recognize that dollar values are not equal over time. Benefits that accrue in the present usually are worth more to their recipients than benefits anticipated some time in the future. Similarly, resources invested today cost more than those invested in the future, since one option would be to invest the same funds at some rate of return that would increase their value. Therefore, the equivalent present value of future streams of both costs and benefits must be determined by multiplying each stream by an appropriate discount factor.

If the alternative is to invest available funds at some interest rate, then an appropriate discount factor can be expressed as:

1/(1+i)^n

where i is the relevant interest rate per year and n is the number of units of time into the future that the benefits and costs will accrue. If, as is the usual case, i is positive, the farther an event is in the future, the smaller is its present value. As noted previously, high discount rates mean that there is a significantly higher regard for present benefits than for equal future benefits and/or a willingness to trade some larger amount of future benefits for smaller current benefits.

The choice of the discount rate may make the difference between acceptance and rejection of a project. Unfortunately, no simple guidelines are available for determining an appropriate discount rate for public investments. Two common bases for discounting can be used, however, reflecting both local conditions and the marketplace for investments: (1) the cost of borrowing the capital necessary to finance a project or program and (2) the rate of return based that could be realized if an equivalent amount were invested for the same period of time. Thus, if a project could be financed by borrowing the necessary capital at 8 percent, or if an investment of equivalent funds could be expected to yield 10 percent, either of these percentages might be used to discount future costs and benefits.

Although the choice of a particular discount rate may be difficult to justify, the procedures for discounting are quite simple. Once an appropriate rate has been chosen, a table of discount factors can be consulted to determine the appropriate figure to apply to each year in the stream of costs and benefits. As the data in Exhibit 5 illustrate, however, the selection of the discount rate can significantly affect the final decision.

Criteria for Analysis

Once an objective function has been identified, the next step in the analysis is to select an indicator of "success"--that is, an index that will yield a higher value for more desirable alternatives. Conceptually, such an indicator involves the maximization of something. Businesses, for example, seek to maximize profits. Public officials are presumed to seek maximum benefits for their constituencies. An inability to quantify overall benefits, however, has led to the identification of cost minimization as the objective function in many cost-benefit analyses.

It is frequently suggested that the goal of cost-benefit analysis should be to maximize benefits and minimize costs. In reality, however, both cannot be accomplished simultaneously. Costs can be minimized by spending nothing and doing nothing, but in that case, no benefits result. Benefits derived from a particular project or program can be maximized by committing organizational resources until marginal benefits are zero. But such action may require far more resources than are available. Therefore, some composite criterion is needed. Three obvious choices are:

o Maximize benefits for given costs.

o Minimize costs while achieving a fixed level of benefits.

o Maximize net benefits (benefits minus costs).

The first cost-benefit criterion to be used in the quantitative evaluation of alternatives was the benefit/cost ratio, introduced by the Flood Control Act of 1936. A benefit/cost ratio is defined as the present value of benefits divided by the present value of costs (or average annual benefits over average annual costs). Thus, for example, if the discounted stream of benefits over the expected duration of a program or project equals $800,000 and the discounted stream of costs equals $600,000, the benefit/cost ratio is 1.33.

A variation on the basic benefit/cost ratio emphasizes the return on invested capital by segregating operational costs and subtracting them from both sides of the ratio. In the previous example, assume that the present value of operational costs represents $200,000 of the total stream of costs. Subtracting operational costs from both benefits and total costs results in the following net benefit/cost ratio:

$800,000 - $200,000 $600,000 $600,000 - $200,000 = $400,000 = 1.50

The net benefit/cost ratio becomes larger as operational costs account for an increasingly larger proportion of total costs.

Net benefit/cost ratios may be preferable in the private sector, where capital may be a greater constraint than operational expenses, especially when taxes are considered. A number of economists, however, argue for the use of gross ratios in public sector applications. Their contention is that legislative bodies should consider operational costs as well as capital costs and should give agencies credit for savings on operational costs by permitting them to spend more on capital costs.

Net benefits is the criterion recommended, if not used, most frequently in contemporary cost-benefit analysis. Net benefits measure difference, whereas benefit/cost calculations produce a ratio. The results of these two techniques are not always interchangeable. The fact that the net benefits of alternative A are greater than those of alternative B does not imply that the benefit/cost ratio of A is greater than that of B.

For example, suppose the benefits in alternative A have a present value of $300,000, and the costs have a present value of $100,000. The net benefits of this alternative would be $300,000 minus $100,000, or $200,000, and the benefit/cost ratio would be $300,000 divided by $100,000, or 3.0. If the present value of benefits in alternative B were $200,000 and that of costs $40,000, alternative B would have lower net benefits ($200,000 minus $40,000 = $160,000), but a higher benefit/cost ratio ($200,000/$40,000 = 5.0). In addition to knowing the benefit/cost ratio for a given project or program, it is also necessary to know the size of the project or program.

The size of the project is important in another respect. Suppose that two projects each offer net benefits of $10,000. One involves a present value of benefits of $2 million and a present value of costs of $1.99 million; the other project has a present value of benefits of $100,000 and a present value of costs of $90,000. Now suppose that something goes wrong, so that the calculations of costs and benefits are off by 10 percent. The first project might have a negative benefit of as much as $200,000, whereas the second would do no worse than break even.

Limitations of Cost-Benefit Analysis

Cost-benefit techniques do not solve all problems relating to the allocation of scarce organizational resources. Cost-benefit analyses provide only limited assistance in establishing priorities among various goals, and they are of limited usefulness in evaluating programs of relatively broad scope or in comparing programs with widely differing objectives.

The basic purpose of cost-benefit analysis is not simply to maximize the ratio of benefits to costs. At times, the "equalization" of benefit/cost ratios may serve as a necessary condition for achieving a desired goal. More often, however, other factors must be considered in selecting an appropriate or "best" decision. These factors include: (1) the time stream of costs and benefits and the time preference for present as opposed to future consumption of goods or services; (2) limitations imposed by revenue (budgetary) constraints; and (3) the question of whether goals and objectives can be specified in sufficient detail to permit a fuller identification of direct and indirect costs and benefits.

It is virtually impossible to eliminate the need for subjective judgment in the process of making decisions for any organization. Nonetheless, a more systematic approach to the comparison of costs and benefits, including consideration of time preference and of the marginal productivity of capital investments, can contribute significantly to a providing more rational basis for such decisions. This is particularly true when compared with the uncoordinated, haphazard, and intuitive nature of many more traditional methods. Cost-benefit analyses include the examination of expenditures in terms of programs and objectives, instead of merely by spending entities, and the consideration of total benefits of expenditures alongside total costs of inputs for alternative programs.

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