General Description of Benefit/Cost

Benefit/cost analysis is a formal technique for balancing the benefits which a project produces against the cost of producing that benefit. It is not as easy as it sounds.

The first question is what is "a project." Ideally, a project is a discrete unit of activity which is self-contained and can be divided into smaller and smaller pieces with no change in the relation of costs to benefits. In the real world, projects are frequently "complementary": the benefits of one project depend at least in part on benefits derived from other projects. Further, the benefits obtained are frequently "lumpy"; they come in indivisible packages (such as "1 60-person bus" or "1 30-pupil classroom"). It might be desirable to provide the benefit of transportation for only 30 people; "project indivisibility" means that the costs will be incurred the same as if the benefits were provided for 60 people. It is possible to define projects to account for complementarities and indivisibilities, but it makes the model more complex and its interpretation less straightforward.

If what is meant by "project" is far from simple, what is meant by "benefit" and "cost" are at least as problematic. The problem with the term "project" is one of definition: one must carefully distinguish each of the many facets of the program under consideration. The problem with "benefit" and "cost" is primarily one of measurement: one knows what the benefits and costs are, the problem is to express them in a way that can be treated analytically (quantitatively).

Benefits are particularly difficult to measure. Often dollar-value is used to measure both costs and benefits. This has the advantage of relying on common units of measure: a dollar is a dollar. For most program costs, this works well: the annual budget specifies most of the costs associated with the program. But it is less effective for measuring benefits: Does the flow of revenue which they generate properly reflect the relationship between three units of low-income housing and six units of job-training programs?

Further, many public-sector programs cannot assign dollar values to the benefits they provide. There is no market for their services. Even when the market supplies a comparable service, the purchase price of the service may not adequately reflect its value. Is the true value of an education the sum of the tuition paid? That is, after all, the price offered in the market to firms providing that service. Part of the problem in this example is that not all of the value of the service is paid to the supplier: students value an education enough to forego the opportunity to earn full-time wages for the period of their studies. This cost to the student is a "dead-weight loss"; it goes to the benefit of no one. Another part of the problem is that much of the benefit of an education is "intangible," it has no price in the market because it is not a commodity which can be transferred. The value is immeasurable, it is both zero and infinite.

The value of a benefit may also vary depending on the recipient. A dollar to a starving person has a very different value compared to a dollar to a wealthy person. The benefits of a tax-relief project may be evaluated differently, depending on whether they accrue primarily to the wealthy or to the poor. It is possible to take account of the "differential impact" of projects on different client groups, again at the price of complicating the analysis.

A project may also provide benefits for other programs, sometimes even for programs serving goals which are different from those served by the original project. Projects involving transportation or housing are notorious for providing benefits that "spill over" the original project. It is very difficult to include such "externalities" in a formal analysis, simply because it is so easy to overlook them.

The problems in measuring costs are subtle, but no less significant. One is a question of constraints: Often a project must not exceed specified thresholds, such as acceptable levels of pollution, acceptable rates of unemployment, or other considerations. If the analytical model is a simple one--if it treats each constraint separately--the thresholds can be set as maximum values which may not be exceeded. If the analyst wishes to consider multiple constraints interacting on each other, "linear programming" (a mathematical tool which uses the calculus to solve multiple equations simultaneously) may be used.

Both techniques will result in a solution which comes as close as possible to the constraining limits without crossing them. The analyst must decide whether this course of action is, in fact, wise. Some constraints may be of the sort that net benefits increase as the threshold is approached: The more people in the stadium watching a homecoming game, the better--up to the point that the crowding becomes a physical danger. Other constraints are of the sort that there is always some "disbenefit," if not directly attributable to the project, then to the total system. An industry may carefully monitor its effluent into a stream, being careful not to exceed the capacity of the stream to absorb it. If a similar industry on the opposite bank follows the same procedure, severe pollution may occur in spite of the fact that neither industry has exceeded the commonly agreed constraints.

Frequently the relationship between costs and benefits changes over time. Often the costs of a project are incurred early and the benefits are spread out over the life of the project. This is usually resolved by discounting future benefits and costs to their present value. Most people prefer to enjoy the fruits of their labor immediately; a reward a year from today is not as gratifying as the same reward today. The future reward is "discounted," or marked down, by a certain amount. The size of the discount is usually determined by the other available opportunities for using one's resources (whether those resources are capital or labor). "Opportunity costs," as they are called, may be measured conservatively or aggressively, depending on one's habitual position toward risk. Local governments frequently measure their opportunity costs at the rate they pay for municipal bonds (a very conservative position). Entrepreneurs, particularly land developers, frequently exact two or three times that rate (but then, it is their business to take risks.

There is, also, the question of whether to categorize an item as a cost or a "negative benefit." If benefit/cost analysis were simply a measure of the surplus of benefits over costs, there would be no issue; a "negative benefit" would have the same effect as a cost. The analysis is concerned, however, not with the size of the difference, but with the ratio of their differences.

For example, how should we include the impact of air and noise pollution resulting from the construction of a new industrial plant? If the total value of the pollution is small relative to the other costs and benefits of the project, the point is probably not worth pursuing. Assume, for the purpose of argument, that the other costs and benefits are roughly equal and the value of the pollution is 25% of the costs (or the benefits). If the pollution is considered as a cost of the project which is imposed on the public, the benefit/cost ratio would be <1.0/1.25>, or 0.80. If, on the other hand, the pollution is considered as an internal component of the system--a disbenefit counterbalancing the other benefits of the project--then the benefit/cost ratio would be <0.75/1.0>, or 0.75. The two projects are identical in everything but definition, yet one is found to be clearly superior to the other.

There is, finally, the question of when the analysis is complete. The answer is, when all the costs and benefits have been included in the analysis. Unfortunately, that is a practical impossibility. There is always the possibility that one has failed to include a significant indirect cost or benefit, or overlooked a linkage with another system, or underestimated the joint impact of several projects together. This need not be considered a failure on the analyst's part: Much of benefit/cost analysis is an attempt to estimate the unmeasurable, to affix a quantitative value on a qualitative variable.



© 1996 A.J.Filipovitch
Revised 11 March 2005