Fundamentals of Transportation/Evaluation

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A benefit-cost analysis (BCA)^[1] is often required in determining whether a project should be approved and is useful for comparing similar projects. It determines the stream of quantifiable economic benefits and costs that are associated with a project or policy. If the benefits exceed the costs, the project is worth doing; if the benefits fall short of the costs, the project is not. Benefit-cost analysis is appropriate where the technology is known and well understood or a minor change from existing technologies is being performed. BCA is not appropriate when the technology is new and untried because the effects of the technology cannot be easily measured or predicted. However, just because something is new in one place does not necessarily make it new, so benefit-cost analysis would be appropriate, e.g., for a light-rail or commuter rail line in a city without rail, or for any road project, but would not be appropriate (at the time of this writing) for something truly radical like teleportation.

The identification of the costs, and more particularly the benefits, is the chief component of the “art” of Benefit-Cost Analysis. This component of the analysis is different for every project. Furthermore, care should be taken to avoid double counting; especially counting cost savings in both the cost and the benefit columns. However, a number of benefits and costs should be included at a minimum. In transportation these costs should be separated for users, transportation agencies, and the public at large. Consumer benefits are measured by consumer’s surplus. It is important to recognize that the demand curve is downward sloping, so there a project may produce benefits both to existing users in terms of a reduction in cost and to new users by making travel worthwhile where previously it was too expensive.

Agency benefits come from profits. But since most agencies are non-profit, they receive no direct profits. Agency construction, operating, maintenance, or demolition costs may be reduced (or increased) by a new project; these cost savings (or increases) can either be considered in the cost column, or the benefit column, but not both.

Society is impacted by transportation project by an increase or reduction of negative and positive externalities. Negative externalities, or social costs, include air and noise pollution and accidents. Accidents can be considered either a social cost or a private cost, or divided into two parts, but cannot be considered in total in both columns.

If there are network externalities (i.e. the benefits to consumers are themselves a function of the level of demand), then consumers’ surplus for each different demand level should be computed. Of course this is easier said than done. In practice, positive network externalities are ignored in Benefit Cost Analysis.

[edit] Background

[edit] Early Beginnings

When Benjamin Franklin was confronted with difficult decisions, he often recorded the pros and cons on two separate columns and attempted to assign weights to them. While not mathematically precise, this “moral or prudential algebra”, as he put it, allowed for careful consideration of each “cost” and “benefit” as well as the determination of a course of action that provided the greatest benefit. While Franklin was certainly a proponent of this technique, he was certainly not the first. Western European governments, in particular, had been employing similar methods for the construction of waterway and shipyard improvements.

Ekelund and Hebert (1999) credit the French as pioneers in the development of benefit-cost analyses for government projects. The first formal benefit-cost analysis in France occurred in 1708. Abbe de Saint-Pierre attempted to measure and compare the incremental benefit of road improvements (utility gained through reduced transport costs and increased trade), with the additional construction and maintenance costs. Over the next century, French economists and engineers applied their analysis efforts to canals (Ekelund and Hebert, 1999). During this time, The Ecole Polytechnique had established itself as France’s premier educational institution, and in 1837 sought to create a new course in “social arithmetic”: “…the execution of public works will in many cases tend to be handled by a system of concessions and private enterprise. Therefore our engineers must henceforth be able to evaluate the utility or inconvenience, whether local or general, or each enterprise; consequently they must have true and precise knowledge of the elements of such investments.” (Ekelund and Hebert, 1999, p. 47). The school also wanted to ensure their students were aware of the effects of currencies, loans, insurance, amortization and how they affected the probable benefits and costs to enterprises.

In the 1840s French engineer and economist Jules Dupuit (1844, tr. 1952) published an article “On Measurement of the Utility of Public Works”, where he posited that benefits to society from public projects were not the revenues taken in by the government (Aruna, 1980). Rather the benefits were the difference between the public’s willingness to pay and the actual payments the public made (which he theorized would be smaller). This “relative utility” concept was what Alfred Marshall would later rename with the more familiar term, “consumer surplus” (Ekelund and Hebert, 1999).

Vilfredo Pareto (1906) developed what became known as Pareto improvement and Pareto efficiency (optimal) criteria. Simply put, a policy is a Pareto improvement if it provides a benefit to at least one person without making anyone else worse off (Boardman, 1996). A policy is Pareto efficient (optimal) if no one else can be made better off without making someone else worse off. British economists Kaldor and Hicks (Hicks, 1941; Kaldor, 1939) expanded on this idea, stating that a project should proceed if the losers could be compensated in some way. It is important to note that the Kaldor-Hicks criteria states it is sufficient if the winners could potentially compensate the project losers. It does not require that they be compensated.

[edit] Benefit-cost Analysis in the United States

Much of the early development of benefit-cost analysis in the United States is rooted in water related infrastructure projects. The US Flood Control Act of 1936 was the first instance of a systematic effort to incorporate benefit-cost analysis to public decision-making. The act stated that the federal government should engage in flood control activities if “the benefits to whomsoever they may accrue [be] in excess of the estimated costs,” but did not provide guidance on how to define benefits and costs (Aruna, 1980, Persky, 2001). Early Tennessee Valley Authority (TVA) projects also employed basic forms of benefit-cost analysis (US Army Corp of Engineers, 1999). Due to the lack of clarity in measuring benefits and costs, many of the various public agencies developed a wide variety of criteria. Not long after, attempts were made to set uniform standards.

The U.S. Army Corp of Engineers “Green Book” was created in 1950 to align practice with theory. Government economists used the Kaldor-Hicks criteria as their theoretical foundation for the restructuring of economic anlaysis. This report was amended and expanded in 1958 under the title of “The Proposed Practices for Economic Analysis of River Basin Projects” (Persky, 2001).

The Bureau of the Budget adopted similar criteria with 1952’s Circular A-47 - “Reports and Budget Estimates Relating to Federal Programs and Projects for Conservation, Development, or Use of Water and Related Land Resources”.

[edit] Modern Benefit-cost Analysis

During the 1960s and 1970s the more modern forms of benefit-cost analysis were developed. Most analyses required evaluation of:

1. The present value of the benefits and costs of the proposed project at the time they occurred
2. The present value of the benefits and costs of alternatives occurring at various points in time (opportunity costs)
3. Determination of risky outcomes (sensitivity analysis)
4. The value of benefits and costs to people with different incomes (distribution effects/equity issues) (Layard and Glaister, 1994)

[edit] The Planning Programming Budgeting System (PBBS) - 1965

The Planning Programming Budgeting System (PBBS) developed by the Johnson administration in 1965 was created as a means of identifying and sorting priorities. This grew out of a system Robert McNamara created for the Department of Defense a few years earlier (Gramlich, 1981). The PBBS featured five main elements:

1. A careful specification of basic program objectives in each major area of governmental activity.
2. An attempt to analyze the outputs of each governmental program.
3. An attempt to measure the costs of the program, not for one year but over the next several years (“several” was not explicitly defined)
4. An attempt to compare alternative activities.
5. An attempt to establish common analytic techniques throughout the government.

[edit] Office of Management and Budget (OMB) – 1977

Throughout the next few decades, the federal government continued to demand improved benefit-cost analysis with the aim of encouraging transparency and accountability. Approximately 12 years after the adoption of the PPBS system, the Bureau of the Budget was renamed the Office of Management and Budget (OMB). The OMB formally adopted a system that attempts to incorporate benefit-cost logic into budgetary decisions. This came from the Zero-Based Budgeting system set up by Jimmy Carter when he was governor of Georgia (Gramlich, 1981).

[edit] Recent Developments

Executive Order 12292, issued by President Reagan in 1981, required a regulatory impact analysis (RIA) for every major governmental regulatory initiative over $100 million. The RIA is basically a benefit-cost analysis that identifies how various groups are affected by the policy and attempts to address issues of equity (Boardman, 1996).

According to Robert Dorfman, (Dorfman, 1997) most modern-day benefit-cost analyses suffer from several deficiencies. The first is their attempt “to measure the social value of all the consequences of a governmental policy or undertaking by a sum of dollars and cents”. Specifically, Dorfman mentions the inherent difficultly in assigning monetary values to human life, the worth of endangered species, clean air, and noise pollution. The second shortcoming is that many benefit-cost analyses exclude information most useful to decision makers: the distribution of benefits and costs among various segments of the population. Government officials need this sort of information and are often forced to rely on other sources that provide it, namely, self-seeking interest groups. Finally, benefit-cost reports are often written as though the estimates are precise, and the readers are not informed of the range and/or likelihood of error present.

The Clinton Administration sought proposals to address this problem in revising Federal benefit-cost analyses. The proposal required numerical estimates of benefits and costs to be made in the most appropriate unit of measurement, and “specify the ranges of predictions and shall explain the margins of error involved in the quantification methods and in the estimates used” (Dorfman, 1997). Executive Order 12898 formally established the concept of Environmental Justice with regards to the development of new laws and policies, stating they must consider the “fair treatment for people of all races, cultures, and incomes.” The order requires each federal agency to identify and address “disproportionately high and adverse human health or environmental effects of its programs, policies and activities on minority and low-income populations.”

[edit] Probabilistic Benefit-Cost Analysis

Probability-density distribution of net present values approximated by a normal curve. Source: Treasury Board of Canada, Benefit-Cost Analysis Guide, 1998

Probability distribution curves for the NPVs of projects A and B. Source: Treasury Board of Canada, Benefit-Cost Analysis Guide, 1998.

Probability distribution curves for the NPVs of projects A and B, where Project A has a narrower range of possible NPVs. Source: Treasury Board of Canada, Benefit-Cost Analysis Guide, 1998

In recent years there has been a push for the integration of sensitivity analyses of possible outcomes of public investment projects with open discussions of the merits of assumptions used. This “risk analysis” process has been suggested by Flyvbjerg (2003) in the spirit of encouraging more transparency and public involvement in decision-making.

The Treasury Board of Canada’s Benefit-Cost Analysis Guide recognizes that implementation of a project has a probable range of benefits and costs. It posits that the “effective sensitivity” of an outcome to a particular variable is determined by four factors:

• the responsiveness of the Net Present Value (NPV) to changes in the variable;
• the magnitude of the variable's range of plausible values;
• the volatility of the value of the variable (that is, the probability that the value of the variable will move within that range of plausible values); and
• the degree to which the range or volatility of the values of the variable can be controlled.

It is helpful to think of the range of probable outcomes in a graphical sense, as depicted in Figure 1 (probability versus NPV).

Once these probability curves are generated, a comparison of different alternatives can also be performed by plotting each one on the same set of ordinates. Consider for example, a comparison between alternative A and B (Figure 2).

In Figure 2, the probability that any specified positive outcome will be exceeded is always higher for project B than it is for project A. The decision maker should, therefore, always prefer project B over project A. In other cases, an alternative may have a much broader or narrower range of NPVs compared to other alternatives (Figure 3).

Some decision-makers might be attracted by the possibility of a higher return (despite the possibility of greater loss) and therefore might choose project B. Risk-averse decision-makers will be attracted by the possibility of lower loss and will therefore be inclined to choose project A.

[edit] Discount rate

Both the costs and benefits flowing from an investment are spread over time. While some costs are one-time and borne up front, other benefits or operating costs may be paid at some point in the future, and still others received as a stream of payments collected over a long period of time. Because of inflation, risk, and uncertainty, a dollar received now is worth more than a dollar received at some time in the future. Similarly, a dollar spent today is more onerous than a dollar spent tomorrow. This reflects the concept of time preference that we observe when people pay bills later rather than sooner. The existence of real interest rates reflects this time preference. The appropriate discount rate depends on what other opportunities are available for the capital. If simply putting the money in a government insured bank account earned 10% per year, then at a minimum, no investment earning less than 10% would be worthwhile. In general, projects are undertaken with those with the highest rate of return first, and then so on until the cost of raising capital exceeds the benefit from using that capital. Applying this efficiency argument, no project should be undertaken on cost-benefit grounds if another feasible project is sitting there with a higher rate of return.

Three alternative bases for the setting the government’s test discount rate have been proposed:

1. The social rate of time preference recognizes that a dollar's consumption today will be more valued than a dollar's consumption at some future time for, in the latter case, the dollar will be subtracted from a higher income level. The amount of this difference per dollar over a year gives the annual rate. By this method, a project should not be undertaken unless its rate of return exceeds the social rate of time preference.
2. The opportunity cost of capital basis uses the rate of return of private sector investment, a government project should not be undertaken if it earns less than a private sector investment. This is generally higher than social time preference.
3. The cost of funds basis uses the cost of government borrowing, which for various reasons related to government insurance and its ability to print money to back bonds, may not equal exactly the opportunity cost of capital.

Typical estimates of social time preference rates are around 2 to 4 percent while estimates of the social opportunity costs are around 7 to 10 percent.

Generally, for Benefit-Cost studies an acceptable rate of return (the government’s test rate) will already have been established. An alternative is to compute the analysis over a range of interest rates, to see to what extent the analysis is sensitive to variations in this factor. In the absence of knowing what this rate is, we can compute the rate of return (internal rate of return) for which the project breaks even, where the net present value is zero. Projects with high internal rates of return are preferred to those with low rates.

[edit] Determine a present value

The basic math underlying the idea of determining a present value is explained using a simple compound interest rate problem as the starting point. Suppose the sum of $100 is invested at 7 percent for 2 years. At the end of the first year the initial $100 will have earned $7 interest and the augmented sum ($107) will earn a further 7 percent (or $7.49) in the second year. Thus at the end of 2 years the $100 invested now will be worth $114.49.

The discounting problem is simply the converse of this compound interest problem. Thus, $114.49 receivable in 2 years time, and discounted by 7 per cent, has a present value of $100.

Present values can be calculated by the following equation:

(1)

where:

• F = future money sum
• P = present value
• i = discount rate per time period (i.e. years) in decimal form (e.g. 0.07)
• n = number of time periods before the sum is received (or cost paid, e.g. 2 years)

Illustrating our example with equations we have:

The present value, in year 0, of a stream of equal annual payments of $A starting year 1, is given by the reciprocal of the equivalent annual cost. That is, by:

(2)

where:

• A = Annual Payment

For example: 12 annual payments of $500, starting in year 1, have a present value at the middle of year 0 when discounted at 7% of: $3971

The present value, in year 0, of m annual payments of $A, starting in year n + 1, can be calculated by combining discount factors for a payment in year n and the factor for the present value of m annual payments. For example: 12 annual mid-year payments of $250 in years 5 to 16 have a present value in year 4 of $1986 when discounted at 7%. Therefore in year 0, 4 years earlier, they have a present value of $1515.

[edit] Evaluation criterion

Three equivalent conditions can tell us if a project is worthwhile

1. The discounted present value of the benefits exceeds the discounted present value of the costs
2. The present value of the net benefit must be positive.
3. The ratio of the present value of the benefits to the present value of the costs must be greater than one.

However, that is not the entire story. More than one project may have a positive net benefit. From the set of mutually exclusive projects, the one selected should have the highest net present value. We might note that if there are insufficient funds to carry out all mutually exclusive projects with a positive net present value, then the discount used in computing present values does not reflect the true cost of capital. Rather it is too low.

There are problems with using the internal rate of return or the benefit/cost ratio methods for project selection, though they provide useful information. The ratio of benefits to costs depends on how particular items (for instance, cost savings) are ascribed to either the benefit or cost column. While this does not affect net present value, it will change the ratio of benefits to costs (though it cannot move a project from a ratio of greater than one to less than one).

[edit] Examples

[edit] Example 1: Benefit Cost Application

Problem:

This problem, adapted from Watkins (1996), illustrates how a Benefit Cost Analysis might be applied to a project such as a highway widening. The improvement of the highway saves travel time and increases safety (by bringing the road to modern standards). But there will almost certainly be more total traffic than was carried by the old highway. This example excludes external costs and benefits, though their addition is a straightforward extension. The data for the “No Expansion” can be collected from off-the-shelf sources. However the “Expansion” column’s data requires the use of forecasting and modeling.

Table 1: Data
		No Expansion	Expansion
Peak
Passenger Trips	(per hour)	18,000	24,000
Trip Time	(minutes)	50	30
Off-peak
Passenger Trips	(per hour)	9,000	10,000
Trip Time	(minutes)	35	25
Traffic Fatalities	(per year)	2	1

Note: the operating cost for a vehicle is unaffected by the project, and is $4.

Table 2: Model Parameters
Peak Value of Time	($/minute)	$0.15
Off-Peak Value of Time	($/minute)	$0.10
Value of Life	($/life)	$3,000,000

What is the benefit-cost relationship?

Solution:

Benefits

Figure 1: Change in Consumers' Surplus

A 50 minute trip at $0.15/minute is $7.50, while a 30 minute trip is only $4.50. So for existing users, the expansion saves $3.00/trip. Similarly in the off-peak, the cost of the trip drops from $3.50 to $2.50, saving $1.00/trip.

Consumers’ surplus increases both for the trips which would have been taken without the project and for the trips which are stimulated by the project (so-called “induced demand”), as illustrated above in Figure 1. Our analysis is divided into Old and New Trips, the benefits are given in Table 3.

Table 3: Hourly Benefits
TYPE	Old trips	New Trips	Total
Peak	$54,000	$9000	$63,000
Off-peak	$9,000	$500	$9,500

Note: Old Trips: For trips which would have been taken anyway the benefit of the project equals the value of the time saved multiplied by the number of trips. New Trips: The project lowers the cost of a trip and public responds by increasing the number of trips taken. The benefit to new trips is equal to one half of the value of the time saved multiplied by the increase in the number of trips. There are 250 weekdays (excluding holidays) each year and four rush hours per weekday. There are 1000 peak hours per year. With 8760 hours per year, we get 7760 offpeak hours per year. These numbers permit the calculation of annual benefits (shown in Table 4).

Table 4: Annual Travel Time Benefits
TYPE	Old trips	New Trips	Total
Peak	$54,000,000	$9,000,000	$63,000,000
Off-peak	$69,840,000	$3,880,000	$73,720,000
Total	$123,840,000	$12,880,000	$136,720,000

The safety benefits of the project are the product of the number of lives saved multiplied by the value of life. Typical values of life are on the order of $3,000,000 in US transportation analyses. We need to value life to determine how to trade off between safety investments and other investments. While your life is invaluable to you (that is, I could not pay you enough to allow me to kill you), you don’t act that way when considering chance of death rather than certainty. You take risks that have small probabilities of very bad consequences. You do not invest all of your resources in reducing risk, and neither does society. If the project is expected to save one life per year, it has a safety benefit of $3,000,000. In a more complete analysis, we would need to include safety benefits from non-fatal accidents.

The annual benefits of the project are given in Table 5. We assume that this level of benefits continues at a constant rate over the life of the project.

Table 5: Total Annual Benefits
Type of Benefit	Value of Benefits Per Year
Time Saving	$136,720,000
Reduced Risk	$3,000,000
Total	$139,720,000

Costs

Highway costs consist of right-of-way, construction, and maintenance. Right-of-way includes the cost of the land and buildings that must be acquired prior to construction. It does not consider the opportunity cost of the right-of-way serving a different purpose. Let the cost of right-of-way be $100 million, which must be paid before construction starts. In principle, part of the right-of-way cost can be recouped if the highway is not rebuilt in place (for instance, a new parallel route is constructed and the old highway can be sold for development). Assume that all of the right-of-way cost is recoverable at the end of the thirty-year lifetime of the project. The $1 billion construction cost is spread uniformly over the first four-years. Maintenance costs $2 million per year once the highway is completed.

The schedule of benefits and costs for the project is given in Table 6.

Table 6: Schedule Of Benefits And Costs ($ millions)
Time (year)	Benefits	Right-of-way costs	Construction costs	Maintenance costs
0	0	100	0	0
1-4	0	0	250	0
5-29	139.72	0	0	2
30	139.72	-100	0	2

Conversion to Present Value

The benefits and costs are in constant value dollars. Assume the real interest rate (excluding inflation) is 2%. The following equations provide the present value of the streams of benefits and costs.

To compute the Present Value of Benefits in Year 5, we apply equation (2) from above.

To convert that Year 5 value to a Year 1 value, we apply equation (1)

The present value of right-of-way costs is computed as today’s right of way cost ($100 M) minus the present value of the recovery of those costs in Year 30, computed with equation (1):

The present value of the construction costs is computed as the stream of $250M outlays over four years is computed with equation (2):

Maintenance Costs are similar to benefits, in that they fall in the same time periods. They are computed the same way, as follows: To compute the Present Value of $2M in Maintenance Costs in Year 5, we apply equation (2) from above.

To convert that Year 5 value to a Year 1 value, we apply equation (1)

As Table 7 shows, the benefit/cost ratio of 2.5 and the positive net present value of $1563.31 million indicate that the project is worthwhile under these assumptions (value of time, value of life, discount rate, life of the road). Under a different set of assumptions, (e.g. a higher discount rate), the outcome may differ.

Table 7: Present Value of Benefits and Costs ($ millions)
	Present Value
Benefits	2,597.21
Costs
Right-of-Way	44.79
Construction	951.93
Maintenance	37.18
Costs SubTotal	1,033.90
Net Benefit (B-C)	1,563.31
Benefit/Cost Ratio	2.5

[edit] Thought Question

Problem

Is money the only thing that matters in Benefit-Cost Analysis? Is "converted" money the only thing that matters? For example, the value of human life in dollars?

Solution

Absolutely not. A lot of benefits and costs can be converted to monetary value, but not all. For example, you can put a price on human safety, but how can you put a price on, say, asthetics--something that everyone agrees is beneficial. What else can you think of?

[edit] Sample Problems

Problem (Solution)

[edit] Key Terms

• Benefit-Cost Analysis
• Profits
• Costs
• Discount Rate
• Present Value
• Future Value

[edit] External Exercises

Use the SAND software at the STREET website to learn how to evaluate network performance given a changing network scenario.

[edit] End Notes

1. ↑ benefit-cost analysis is sometimes referred to as cost-benefit analysis (CBA)

• Aruna, D. Social Cost-Benefit Analysis Madras Institute for Financial Management and Research, pp. 124, 1980.
• Boardman, A. et al., Cost-Benefit Analysis: Concepts and Practice, Prentice Hall, 2nd Ed,
• Dorfman, R, “Forty years of Cost-Benefit Analysis: Economic Theory Public Decisions Selected Essays of Robert Dorfman”, pp. 323, 1997.
• Dupuit, Jules. “On the Measurement of the Utility of Public Works R.H. Babcock (trans.).” International Economic Papers 2. London: Macmillan, 1952.
• Ekelund, R., Hebert, R. Secret Origins of Modern Microeconomics: Dupuit and the Engineers, University of Chicago Press, pp. 468, 1999.
• Flyvbjerg, B. et al. Megaprojects and Risk: An Anatomy of Ambition, Cambridge University Press, pp. 207, 2003.
• Gramlich, E., A Guide to Benefit-cost Analysis, Prentice Hall, pp. 273, 1981.
• Hicks, John (1941) “The Rehabilitation of Consumers’ Surplus,” Review of Economic Studies, pp. 108-116.
• Kaldor, Nicholas (1939) “Welfare Propositions of Economics and Interpersonal Comparisons of Utility,” Economic Journal, 49:195, pp. 549-552.
• Layard, R., Glaister, S., Cost-Benefit Analysis, Cambridge University Press; 2nd Ed, pp. 507, 1994.
• Pareto, Vilfredo., (1906) Manual of Political Economy. 1971 translation of 1927 edition, New York: Augustus M. Kelley.
• Perksy, J., Retrospectives: Cost-Benefit Analysis and the Classical Creed Journal of Economic Perspectives, 2001 pp. 526, 2000.
• Treasury Board of Canada “Benefit-cost Analysis Guide”, 1998 http://classwebs.spea.indiana.edu/krutilla/v541/Benfit-Cost%20Guide.pdf