Below is the uncorrected machine-read text of this chapter, intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text of each book. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.
23 Benefit-cost analysis is an economic analysis approach that can be used to assess whether any proposed highway improvement is cost-effective (i.e., whether the benefits from implementation of the improvement exceed its costs). A limitation in the application of benefit-cost analysis to horizontal sight obstructions is that quantitative estimates for both the benefits and costs of the improvement must be available for the analysis to be performed. The costs of removing horizontal sight obstructions are difficult to generalize, because the costs can vary substantially from site to site. However, for any specific site, an estimate of the cost to remove the horizontal sight obstruction can be developed. The crash reduction benefits of removing a horizontal sight obstruction are much more difficult to quantify than the costs. There are no CMFs that represent the crash reduction effectiveness of removing a sight obstruction. CMFs for removal of horizontal sight obstructions have not been developed because: â¢ Horizontal sight obstructions have seldom been removed in a project with no other changes, so the number of projects that could be used in before-after evaluations is limited; and â¢ The frequency of sight-distance-related crashes is small and is difficult to quantify; as shown in Potts et al. (2018), sight-distance-related crashes cannot generally be distinguished from other crashes in electronic crash data and are difficult to distinguish reliably from other crashes even when hard-copy police crash reports are available. Thus, no exact benefit-cost analysis can be performed for removal or mitigation of horizontal sight obstructions. However, as explained below, benefit-cost analysis can be used to approximate the maximum amount that a highway agency should consider spending to remove or mitigate a particular horizontal sight obstruction. The basic equation used for benefit-cost analysis of any proposed highway improvement based on the potential crash reduction of the improvement is: â[ ]( )= N C , i%, IC (9)ik kB C CRF P A nk jk ij where B/C = benefit-cost ratio; CRFjk = crash reduction effectiveness (percentage reduction in crashes) for crash severity level k from implementing improvement j; Nik = expected annual crash frequency for crash severity level k at site i prior to improvement; Ck = benefit ($) per crash reduced for crash severity level k; C H A P T E R 4 Benefit-Cost Analysis
24 Design Guidelines for Horizontal Sightline Offsets ICij = implementation cost ($) for improvement j at site i; (P/A, i%, n) = uniform series present worth factor; i = discount rate or minimum attractive rate of return (percent); and n = improvement service life (years). Each specific element of the benefit-cost analysis in Equation (9) is reviewed in the following sections. 4.1 Crash Reduction for Sight Distance Improvements The CRFjk term in Equation (9) represents the proportional reduction in crash frequency for a particular severity level due to a sight distance improvement. This crash reduction effec- tiveness, or percent reduction in crashes, is expected to be highly situational. In other words, the percent reduction in crashes might be substantial at some types of sites (i.e., with critical downstream roadway elements limited from the driverâs view) and zero or near-zero at other locations. 4.2 Expected Annual Crash Frequency The expected annual crash frequency for a site prior to improvement can be estimated either from site-specific crash history data or from the crash prediction methods of the Highway Safety Manual (AASHTO 2010; AASHTO 2014). 4.3 Benefit per Crash Reduced The benefit per crash reduced represents the societal costs of crashes by severity level. The crash costs currently in use in Safety Analyst (www.safetyanalyst.org), shown in Table 2, are typical of current highway agency practice. 4.4 Improvement Service Life The service life for physical changes to the roadway to increase horizontal sight distance should be 20 years or more. Improving sight distance by clearing brush or other vegetation should be assigned a shorter service life (e.g., 5 years) if the brush or vegetation could grow back. Some mitigation measures, such as signing or marking, would typically have a substantially shorter service life than 20 years. 4.5 Discount Rate or Minimum Attractive Rate of Return A discount rate or minimum attractive rate of return of 7 percent has typically been used in benefit-cost analysis, in accordance with current federal guidelines. Crash Severity Level Comprehensive Societal Crash Costs Fatal (K) $5,722,300 Disabling Injury (A) 302,900 Evident Injury (B) 110,700 Possible Injury (C) 62,400 Property Damage Only (O) 10,120 SOURCE: www.safetyanalyst.org Table 2. Recommended value of crash costs or crash reduction benefits by crash severity level.
Benefit-Cost Analysis 25 4.6 Uniform Series Present Worth Factor The annual crash cost savings should be reduced to their present worth by multiplying by the uniform series present worth factor, computed as follows: ( ) ( ) = +ï£« ï£ï£¬ ï£¶ ï£¸ï£· â +ï£« ï£ï£¬ ï£¶ ï£¸ï£· P A, %, 1 100 1 100 1 100 (10)i n i i i n n where (P/A, i%, n) = uniform series present worth factor; i = discount rate or minimum attractive rate of return (percent); and n = improvement service life (years). 4.7 Project Implementation Cost Project costs or improvement costs are referred to here as project implementation costs, rather than construction costs, since they include not only the estimated construction cost, but also the cost for additional right-of-way that may be needed. The project implementation cost is likely to vary from site to site, even for nominally similar horizontal sight obstructions, so site-specific cost estimates should be developed for each potential project. 4.8 Cost-Effectiveness Analysis The site-specific project crash reduction benefits are difficult to quantify, but it may be feasible to estimate the maximum crash reduction that could potentially occur from a given project and use that value to quantify the maximum project implementation cost that should be considered for horizontal sight obstruction removal or mitigation. The maximum potential crash reduction can be estimated by: â¢ Reviewing electronic crash history data to estimate the average annual number of crashes for the following crash types for all lanes in the primary direction of travel: rear-end, same- direction sideswipe, and run-off-road; such crashes may possibly be related to sight distance, but are known to be an overestimate of sight-distance-related crashes; â¢ Using the Highway Safety Manual (AASHTO 2010; AASHTO 2014) procedures to estimate the average annual number of crashes for those three possibly related crash types in the primary direction of travel (i.e., for two-way roadways, divide the two-way crash frequency estimate in half); or â¢ Reviewing hard-copy police crash reports and identifying the average annual number of crashes that are potentially sight distance related. A review of hard-copy police crash reports by Potts et al. (2018) suggests that the results of a hard-copy review will likely identify as potentially sight-distance-related only about 5 percent of the crashes for the three possibly related crash types. Even the estimate based on hard-copy police crash reports will likely include some crashes that are not, in fact, sight-distance-related. To be conservative, it is suggested that the estimate of the maximum likely crash reduction benefit from implementation of a sight distance improvement, maxNik in Equation (11), be estimated as follows: â¢ Multiply the total number of rear-end, same-direction sideswipe, and run-off-road crashes from electronic crash data by 0.05; or â¢ Use the number of probable sight-distance-related crashes obtained from review of hard- copy police crash reports unchanged.
26 Design Guidelines for Horizontal Sightline Offsets Equation (9) can be transformed as follows to estimate the maximum implementation cost that could be incurred while still achieving a benefit-cost ratio equal to 1.0: â[ ]( )= C , i%, (11)kmaxIC maxN P A nij k ik where maxICij = estimate of the maximum implementation cost ($) for a cost-effective improve- ment j at site i; and maxNik = estimated maximum annual crash frequency for crash severity level k at site i prior to improvement. The computed value of maxICij can then be compared to the improvement cost level esti- mated by the highway agency to decide whether the improvement is likely to be cost-effective. For example, if the improvement cost level estimated by the highway agency is low and the value of ICij determined with Equation (11) is high, then a horizontal sight distance improvement would very likely be cost-effective. If, on the other hand, the improvement cost estimated by the highway agency is high and the value of ICij is low, then a horizontal sight distance improvement would very likely not be cost-effective. A key challenge in applying benefit-cost analysis of this type is that the value of maxNik will likely always be an uncertain estimate. This challenge should be addressed by using the available crash data to make a conservative estimate. At sites with no history of crashes that could possibly be sight-distance-related, the best available estimate of maxNik may be zero. In such cases, substantial investments to remove sight distance obstructions are likely not justified, but consideration should be given to lower cost mitigation strategies (see Section 7.2). 4.9 Computational Example A computational example of the application of Equation (11) is presented here. This example addresses a particular horizontal curve on a rural two-lane highway with trees and vegetation located on the inside of the horizontal curve. The designer responsible for a planned project that includes the horizontal curve in question reviews the crash history of the curve and concludes that there have been at most three sight-distance-related crashes at the curve site in the past 5 years, and there may have been as few as one sight-distance-related crash. To be conservative, the designer decides to use the estimate of three sight-distance-related crashes in 5 years. Using the typical crash severity distribution for the site, the designer concludes that the maxi- mum annual crash reduction likely to result from removing the trees and vegetation on the inside of the curve would be: â¢ No fatalities; â¢ 0.05 disabling injuries (A injuries) per year; â¢ 0.10 evident injuries (B injuries) per year; â¢ 0.15 possible injuries (C injuries) per year; or â¢ 0.30 property-damage-only injuries per year, Assuming a project service life of 20 years and a discount rate of 7 percent, Equation (10) is applied to determine the uniform series present worth factor as follows: ï£« ï£ï£¬ ï£¶ ï£¸ï£· = +ï£« ï£ï£¬ ï£¶ ï£¸ï£· â ï£« ï£ï£¬ ï£¶ ï£¸ï£· +ï£« ï£ï£¬ ï£¶ ï£¸ï£· =, %, 1 7 100 1 7 100 1 7 100 10.59 (12) 20 20 P A i n
Benefit-Cost Analysis 27 Then, using the crash cost estimates in Table 2, Equation (11) is applied to estimate the maximum implementation cost as follows: maxIC 5722300 0.05 302,900 0.1 110700 0.15 62400 0.3 10120 10.59 $408,891 (13) ij ( )= + Ã + Ã Ã Ã + Ã Ã = This computation indicates that if the trees and vegetation on the inside of the horizontal curve that constitute the horizontal sight obstruction can be removed for a cost of $408,891 or less, this could be a cost-effective improvement project. Because of the uncertainty in the crash reduction estimate, the designer treats the value of $408,891 as a potential upper limit on project cost and not as a firm decision-making criterion. However, if the removal of the trees and vegetation, including any right-of-way or site easement needed would cost more than $408,891, the designer considers that the project would not be considered cost effective.