# Transportation Economics/Evaluation

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.

## Background

### 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 École 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.

### 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 analysis. 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".

### 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)

### The Planning Programming Budgeting System (PPBS) - 1965

The Planning Programming Budgeting System (PPBS) 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
PPBS 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.

### 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).

### 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."

### Probabilistic Benefit-Cost Analysis

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

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

! 275 px \| 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.

## 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.

## 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:

\(1\) $P = \frac{F}{{\left( {1 + i} \right)^n }}
\,\!$

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:

$P = \frac{F}{{\left( {1 + i} \right)^n }} = \frac{{114.49}}{{\left( {1 + 0.07} \right)^2 }} = 100.00
\,\!$

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:

\(2\)
$P = A\left[ {\frac{{\left( {1 + i} \right)^n  - 1}}{{i\left( {1 + i} \right)^n }}} \right]
\,\!$

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

$P = A\left[ {\frac{{\left( {1 + i} \right)^n  - 1}}{{i\left( {1 + i} \right)^n }}} \right] = 500\left[ {\frac{{\left( {1 + 0.07} \right)^{12}  - 1}}{{0.07\left( {1 + 0.07} \right)^{12} }}} \right] = 3971
\,\!$

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.

$P_{Y = 4}  = A\left[ {\frac{{\left( {1 + i} \right)^n  - 1}}{{i\left( {1 + i} \right)^n }}} \right] = 250\left[ {\frac{{\left( {1 + 0.07} \right)^{12}  - 1}}{{0.07\left( {1 + 0.07} \right)^{12} }}} \right] = 1986
\,\!$

$P_{Y = 0}  = \frac{F}{{\left( {1 + i} \right)^n }} = \frac{{P_{Y = 4} }}{{\left( {1 + i} \right)^n }} = \frac{{1986}}{{\left( {1 + 0.07} \right)^4 }} = 1515
\,\!$

## 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).

## Examples

### Example 1: Benefit Cost Application

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!TProblem{width="40"}**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. Assume there are 250
weekdays (excluding holidays) each year and four rush hours per weekday.

  --------------------
   **Table 1: Data**
          Peak
    Passenger Trips
       Trip Time
        Off-peak
    Passenger Trips
       Trip Time
   Traffic Fatalities
  --------------------

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

  -------------------------------
   **Table 2: Model Parameters**
        Peak Value of Time
      Off-Peak Value of Time
           Value of Life
  -------------------------------

What is the benefit-cost relationship?

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!Example{width="40"}**Solution:**

**Benefits**

!Figure 1: Change in Consumers\'
Surplus{width="400"}

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
               Peak
             Off-peak
  ------------------------------

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 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
                     Peak
                   Off-peak
                    Total
  ------------------------------------------

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
              Time Saving
              Reduced Risk
                 Total
  ------------------------------------

**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)
                               0
                              1-4
                             5-29
                              30
  -----------------------------------------------------------

**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.

$P = A\left[ {\frac{{\left( {1 + i} \right)^n  - 1}}{{i\left( {1 + i} \right)^n }}} \right] = 139.72\left[ {\frac{{\left( {1 + 0.02} \right)^{26}  - 1}}{{0.02\left( {1 + 0.02} \right)^{26} }}} \right] = 2811.31
\,\!$

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

$P = \frac{F}{{\left( {1 + i} \right)^n }} = \frac{{2811.31}}{{\left( {1 + 0.02} \right)^4 }} = 2597.21
\,\!$

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):

$P = \frac{F}{{\left( {1 + i} \right)^n }} = \frac{{100}}{{\left( {1 + 0.02} \right)^{30} }} = 55.21 
\,\!$

$100 - 55.21 = 44.79 
\,\!$

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

$P = A\left[ {\frac{{\left( {1 + i} \right)^n  - 1}}{{i\left( {1 + i} \right)^n }}} \right] = 250\left[ {\frac{{\left( {1 + 0.02} \right)^4  - 1}}{{0.02\left( {1 + 0.02} \right)^4 }}} \right] = 951.93
\,\!$

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.

$P = A\left[ {\frac{{\left( {1 + i} \right)^n  - 1}}{{i\left( {1 + i} \right)^n }}} \right] = 2\left[ {\frac{{\left( {1 + 0.02} \right)^{26}  - 1}}{{0.02\left( {1 + 0.02} \right)^{26} }}} \right] = 40.24
\,\!$

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

$P = \frac{F}{{\left( {1 + i} \right)^n }} = \frac{{40.24}}{{\left( {1 + 0.02} \right)^4 }} = 37.18
\,\!$

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)**
                              Benefits
                               Costs
                            Right-of-Way
                            Construction
                            Maintenance
                           Costs SubTotal
                         Net Benefit (B-C)
                         Benefit/Cost Ratio
  ----------------------------------------------------------------

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## Thought Questions

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### Decision Criteria

Which is a more appropriate decision criteria: Benefit/Cost or Benefit -
Cost? Why?

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### Is it only money that matters?

**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, aesthetics---something that
everyone agrees is beneficial. What else can you think of?

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### Can small units of time be given the same value of time as larger units of time?

In other words, do 60 improvements each saving a traveler 1 minute equal
1 improvement saving a traveler 60 minutes? Similarly, does 1
improvement saving a 1000 travelers 1 minute equal the value of time of
a single traveler of 1000 minutes. These are different problems, one is
intra-traveler and one is inter-traveler, but related.

Several issues arise.

A. Is value of time linear or non-linear? To this we must conclude the
value of time is surely non-linear. I am much more agitated waiting 3
minutes at a red light than 2, and I begin to suspect the light is
broken. Studies of ramp meters show a similar phenomena.[^2]

B. How do we apply this in a benefit-cost analysis? If we break one
project into 60 smaller projects, each with a smaller value of travel
time saved, and then we added the gains, we would get a different result
than the what obtains with a single large project. For analytical
convenience, we would like our analyses to be additive, not
sub-additive, otherwise arbitrarily dividing the project changes the
result. In particular many smaller projects will produce an undercount
that is quite significant, and result in a much lower benefit than if
the projects were bundled.

As a practical matter, every Benefit/Cost Analysis assumes a single
value of time, rather than assuming non-linear value of time. This also
helps avoiding biasing public investments towards areas with people who
have a high value of time (the rich)

On the other hand, mode choice analyses do however weight different
components of travel time differently, especially transit time (i.e.
in-vehicle time is less onerous than waiting time). The implicit value
of time for travelers does depend on the type of time (though generally
not the amount of time). Using the log-sum of the mode choice model as a
measure of benefit would implicitly account for this.

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### Are sunk costs sunk, is salvage value salvageable? A paradox in engineering economics analysis

Salvage value is defined as \"The estimated value of an asset at the end
of its useful life.\" [^3] Sunk cost is defined as \"Cost already
incurred which cannot be recovered regardless of future events.\"[^4]

It is often said in economics that \"sunk costs are sunk\", meaning they
should not be considered a cost in economic analysis, because the money
has already been spent.

Now consider two cases

In **case 1**, we have a road project that costs \$10.00 today, and at
the end of 10 years has some economic value remaining, let\'s say a
salvage value of \$5.00, which when discounted back to the present is
\$1.93 (at 10% interest). This value is the residual value of the road.
Thus, the total present cost of the project \$10.00 - \$1.93 = \$8.07.
Clearly the road cannot be moved. However, its presence makes it easier
to build future roads \... the land has been acquired and graded, some
useful material for aggregate is on-site perhaps, and can be thought of
as the amount that it reduces the cost of future generations to build
the road. Alternatively, the land could be sold for development if the
road is no longer needed, or turned into a park.

Assume the present value of the benefit of the road is \$10.00. The
benefit/cost ratio is \$10.00 over \$8.07 or 1.23. If we treat the
salvage value as a benefit rather than cost, the benefit is \$10.00 +
\$1.93 = \$11.93 and the cost is \$10, and the B/C is 1.193.

In 10 years time, the community decides to replace the old worn out road
with a new road. This is a new project. The salvage value from the
previous project is now the sunk cost of the current project (after all
the road is there and could not be moved, and so does not cost the
current project anything to exploit). So the cost of the project in 10
years time would be \$10.00 - \$5.00 = \$5.00. Discounting that to the
present is \$1.93.

The benefit in 10 years time is also \$10.00, but the cost in 10 years
time was \$5.00, and the benefit/cost ratio they perceive is
\$10.00/\$5.00 = 2.00

Aggregating the two projects

-   the benefits are \$10 + \$3.86 = \$13.86
-   the costs are \$8.07 + \$1.93 = \$10.00
-   the collective benefit/cost ratio is 1.386
-   the NPV is benefits - costs = \$3.86

One might argue the salvage value is a benefit, rather than a cost
reduction. In that case

-   the benefits are \$10.00 + \$1.93 + \$3.86 = \$15.79
-   the costs are \$10.00 + \$1.93 = \$11.93
-   the collective benefit/cost ratio is 1.32
-   the NPV remains \$3.86

**Case 2** is an identical road, but now the community has a 20 year
time horizon to start. The initial cost is \$10, and the cost in 10
years time is \$5.00 (discounted to \$1.93). The benefits are \$10 now
and \$10 in 10 years time (discounted to \$3.86). There is no salvage
value at the end of the first period, nor sunk costs at the beginning of
the second period. What is the benefit cost ratio?

-   the costs are \$11.93
-   the benefits are still \$13.86
-   the benefit/cost ratio is 1.16
-   the NPV is \$1.93.

If you are the community, which will you invest in? Case 1 has an
initial B/C of 1.23 (or 1.193), Case 2 has a B/C of 1.16. But the real
benefits and real costs of the roads are identical.

The salvage value in this example is, like so much in economics (think
Pareto optimality), an accounting fiction. In this case no transaction
takes place to realize that salvage value. On the other hand, excluding
the salvage value over-estimates the net cost of the project, as it
ignores potential future uses of the project.

Time horizons on projects must be comparable to correctly assess
relative B/C ratio, yet not all projects do have the same benefit/cost
ratio.

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## Software Tools for Impact Analysis

The majority of economic impact studies for highway capacity projects
are undertaken using conventional methods. These methods tend to focus
on the direct user impacts of individual projects in terms of travel
costs and outcomes, and compare sums of quantifiable, discounted
benefits and costs. Inputs to benefit-cost analyses can typically be
obtained from readily available data sources or model outputs (such as
construction and maintenance costs, and before and after estimates of
travel demand, by vehicle class, along with associated travel times).
Valuation of changes in external, somewhat intangible costs of travel
(e.g., air pollution and crash injury) can usually be accommodated by
using *shadow price* estimates, such as obtained from FHWA-suggested
values, based on recent empirical studies.

The primary benefits included in such studies are those related to
reductions in user cost, such as travel time savings and vehicle
operating costs (e.g. fuel costs, vehicle depreciation, etc.).
Additional benefits may stem from reductions in crash rates, vehicle
emissions, noise, and other costs associated with vehicle travel.
Project costs are typically confined to expenditures on capital
investment, along with ongoing operations and maintenance costs.

A number of economic analysis tools have been developed under the
auspices of the United States Federal Highway Administration (FHWA)
permitting different forms of benefit-cost analysis for different types
of projects, at different levels of evaluation. Several of these tools
are prevalent in past impact analyses, and are described here. However,
none identifies the effects of infrastructure on the economy and
development.

### MicroBENCOST

MicroBENCOST [^5] is a sketch planning tool for estimating basic
benefits and costs of a range of highway improvement projects, including
capacity addition projects. In each type of project, attention is
focused on corridor traffic conditions and their resulting impact on
motorist costs with and without a proposed improvement. This type of
approach may be appropriate for situations where projects have
relatively isolated impacts and do not require regional modeling.

### SPASM

The Sketch Planning Analysis Spreadsheet Model (SPASM) is a benefit-cost
tool designed for screening level analysis. It outputs estimates of
project costs, cost-effectiveness, benefits, and energy and air quality
impacts. SPASM is designed to allow for comparison among multiple modes
and non-modal alternatives, such as travel demand management scenarios.
The model is comprised of three modules (worksheets) relating to public
agency costs, characteristics of facilities and trips, and a travel
demand component. Induced traffic is dealt with through the use of
elasticity-based methods, where an elasticity of vehicle-miles of travel
(VMT) with respect to travel time is defined and applied. Vehicle
emissions are estimated based on calcuations of VMT, trip length and
speeds, and assumed shares of travel occuring in cold start, hot start,
and hot stabilized conditions. Analysis is confined to a corridor level,
with all trips having the same origin, destination and length. This
feature is appropriate for analysis of linear transportation corridors,
but also greatly limits the ability to deal with traffic drawn to or
diverted from outside the corridor. DeCorla-Souza et al. (1996) [^6]
describe the model and its application to a freeway corridor in Salt
Lake City, Utah.

### STEAM

The Surface Transportation Efficiency Analysis Model (STEAM) is a
planning-level extension of the SPASM model, designed for a fuller
evaluation of cross-modal and demand management policies. STEAM was
designed to overcome the most important limitations of its predecessor,
namely the assumption of average trip lengths within a single corridor
and the inability to analyze systemwide effects. The enhanced modeling
capabilities of STEAM feature greater compatibility with existing
four-step travel demand models, including a trip table module that is
used to calculate user benefits and emissions estimates based on changes
in network conditions and travel behavior. Also, the package features a
risk analysis component to its evaluation summary module, which
calculates the likelihood of various outcomes such as benefit-cost
ratios. An overview of STEAM and a hypothetical application are given by
DeCorla-Souza et al. (1998).[^7]

### SMITE

The Spreadsheet Model for Induced Travel Estimation (SMITE) is a sketch
planning application that was designed for inclusion with STEAM in order
to account for the effects of induced travel in traffic forecasting.
SMITE\'s design as a simple spreadsheet application allows it to be used
in cases where a conventional, four-step travel demand model is
unavailable or cannot account for induced travel effects in its
structure.[^8] SMITE applies elasticity measures that describe the
response in demand (VMT) to changes in travel time and the response in
supply (travel time) to changes in demand levels.

### SCRITS

As a practical matter, highway corridor improvements involving
intelligent transportation systems (ITS) applications to smooth traffic
flow can be considered capacity enhancements, at least in the short
term. The FHWA\'s SCRITS (SCReening for ITS) is a sketch planning tool
that offers rough estimates of ITS benefits, for screening-level
analysis. SCRITS utilizes aggregate relationships between average
weekday traffic levels and capacity to estimate travel speed impacts and
vehicle-hours of travel (VHT). Like many other FHWA sketch planning
tools, it is organized in spreadsheet format and can be used in
situations where more sophisticated modeling systems are unavailable or
insufficient.

### HERS

In addition to helping states plan and manage their highway systems, the
FHWA\'s Highway Economic Requirements System for states (HERS-ST) offers
a model for economic impacts evaluation. In one case, Luskin (2005) [^9]
use HERS-ST to conclude that Texas is under-invested in highways --
particularly urban systems and lower-order functional classes -- by 50
percent. Combining economic principles with engineering criteria, HERS
evaluates competing projects via benefit-cost ratios. Recognizing user
benefits, emissions levels, and construction and maintenance costs, HERS
operates within a GIS environment and will be evaluated under this
project, for discussion in project deliverables. Well established
software like HERS offer states and regions an oportunity to readily
pursue standardized economic impact evaluations on all projects, a key
advantage for many users, as well as the greater community.

### Summary of Software Tools

Many analytical tools, like those described above, are favored due to
their relative ease of use and employment of readily available or easily
acquired data. However, several characteristics limit their
effectiveness in evaluating the effects of new highway capacity. First,
they are almost always insufficient to describe the full range of
impacts of new highway capacity. Such methods deliberately reduce
economic analysis to the most important components, resorting to several
simplifying assumptions. If a project adds capacity to a particularly
important link in the transportation network, its effects on travel
patterns may be felt outside the immediate area. Also, the effects of
induced travel, in terms of either route switching or longer trips, may
not be accounted for in travel models based on a static, equilibrium
assignment of traffic. In the longer term, added highway capacity may
lead to the spatial reorganization of activities as a result of changes
in regional accessibility. These types of changes cannot typically be
accounted for in analysis methods.

Second, there is the general criticism of methods based on benefit-cost
analysis that they cannot account for all possible impacts of a project.
Benefit-cost methods deliberately reduce economic analysis to the most
important components and often must make simplifying assumptions. The
project-based methods described here generally do not describe the
economic effects of a project on different user or non-user groups.
Winners and losers from a new capacity project cannot be effectively
identified and differentiated.

Third, a significant amount of uncertainty and risk is involved in the
employment of project-based methods. Methods that use benefit-cost
techniques to calculate B/C ratios, rates of return, and/or net present
values are often sensitive to certain assumptions and inputs. With
transportation infrastructure projects, the choice of discount rate is
often critical, due to the long life of projects and large, up-front
costs. Also, the presumed value of travel time savings is often pivotal,
since it typically reflects the majority of project benefits. Valuations
of travel time savings vary dramatically across the traveler population,
as a function of trip purpose, traveler wage, household income, and time
of day. It is useful to test several plausible values.

Assessment procedures in the UK and other parts of Europe have moved
towards a multi-criteria approach, where economic development is only
one of several appraisal criteria. Environmental, equity, safety, and
the overall integration with other policy sectors are examined in a
transparent framework for decision makers. In the UK, the Guidance on
the Methodologies for Multi-Modal Studies (2000) [^10] provides such a
framework. These procedures require a clear definition of project goals
and objectives, so that actual effects can be tied to project
objectives, as part of the assessment procedure. This is critical for
understanding induced travel effects. Noland (2007) [^11] has argued
that this implies that comprehensive economic assessment, including
estimation of land valuation effects, is the only way to fully assess
the potential beneficial impacts of projects.

## Sample Problems

Problem
1
(Solution
1)

Problem
2
(Solution
2)

## Key Terms

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

## External Exercises

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

## Videos

-   Benefit / Cost
    Analysis
-   Benefit / Cost Analysis - Value of
    Time
-   Benefit / Cost Analysis - Value of
    Life
-   Benefit / Cost Analysis - Consumers and Producers
    Surplus
-   Benefit / Cost Analysis - An
    Example
-   Perspectives on
    Efficiency
-   Designing for Dynamic
    Systems
-   Diamond of Evaluation
-   Choosing Measures of
    Effectiveness

## References

```{=html}
<references/>
```
-   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.
-   Sunstein, C. Cost-Benefit Analysis and the Knowledge Problem
    (2014)
-   Treasury Board of Canada "Benefit-cost Analysis
    Guide",
    1998

Transportation Economics}}

[^1]: benefit-cost analysis is sometimes referred to as cost-benefit
    analysis (CBA)

[^2]: Weighting Waiting: Evaluating Perception of In-Vehicle Travel Time
    Under Moving and Stopped Conditions

[^3]: <http://www.investorwords.com/4372/salvage_value.html>

[^4]: <http://www.investorwords.com/4813/sunk_cost.html>

[^5]: McTrans. Microbencost. Web page, 2007

[^6]: P. DeCorla-Souza, H. Cohen, and K. Bhatt. Using benefit-cost
    analysis to evaluate across modes and demand management strategies.
    In Compendium of Technical Papers, 66th Annual Meeting of the
    Institute of Transportation Engineers, pages 439--445. Institute of
    Transporta- tion Engineers, ITE, 1996.

[^7]: P. DeCorla-Souza, H. Cohen, D. Haling, and J. Hunt. Using steam
    for benefit-cost analysis of transportation alternatives.
    Transportation Research Record, 1649:63--71, 1998.

[^8]: P. DeCorla-Souza and H. Cohen. Accounting for induced travel in
    evaluation of urban high- way expansion. Online resource, U.S.
    Department of Transportation, Federal Highway Administration, 1998.

[^9]: D. Luskin and Erin Mallard. Potential gains from more efficient
    spending on Texas highways. In Proceedings of the 84th Annual
    Meeting of the Transportation Research Board, January, Washington
    D.C., 2005.

[^10]: Department of Transport and the Environment. Guidance on the
    Methodologies for Multi- Modal Studies. Technical report, Department
    of Transport and the Environment, 2000.

[^11]: R.B. Noland. Transport planning and environmental assessment:
    implications of induced travel effects. International Journal of
    Sustainable Transportation, 1(1):1--28, 2007.
