U.S. Department of Transportation
Federal Highway Administration
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Federal Highway Administration Research and Technology
Coordinating, Developing, and Delivering Highway Transportation Innovations
|This report is an archived publication and may contain dated technical, contact, and link information|
Publication Number: FHWA-HRT-11-024
Date: April 2011
Safety Evaluation of the Safety Edge Treatment
Chapter 6. Benefit-Cost Analysis
This chapter presents the results of a benefit-cost analysis of the safety edge treatment based on the results in this report. Section 6.1 presents the overall approach for determining benefit-cost estimates, section 6.2 documents the components of the analysis, and section 6.3 discusses the results of the benefit-cost analysis.
The benefit-cost ratio for the safety edge treatment has been determined according to equation 6:
B/C = benefit-cost ratio
NFI = number of fatal and injury crashes per mile per year before application of the safety edge treatment
NPDO = number of PDO crashes per mile per year before application of the safety edge treatment
ESE = effectiveness (percent reduction in crashes) for application of the safety edge treatment
CFI = cost savings per crash for fatal and injury crashes reduced
CPDO = cost savings per crash for PDO crashes reduced
(P/A, i, n) = uniform series present worth factor
i = minimum attractive rate of return (discount rate), expressed as a proportion (i.e., i = 0.04, for a discount rate of 4 percent)
n = service life of safety edge treatment (years)
CCSE = cost for application of the safety edge treatment (dollars per mile)
The following sections document the components of the benefit-cost computation, including crash frequencies, treatment effectiveness, crash costs, service life, minimum attractive rate of return, uniform series present worth factor, and treatment cost.
Crash frequencies per mile per year were estimated for the benefit-cost analysis using the SPFs presented in section 4.2. Only two-lane highway sites were considered because no treatment effectiveness measure was found for multilane highway sites. Both Georgia and Indiana SPFs were used because each State has an SPF and because using the individual State SPFs constitutes a sensitivity analysis of the results. The location of the SPFs used in the benefit-cost analysis are shown in table 33.
The computation of crash frequencies was performed as illustrated in the following example of Georgia two-lane highways with paved shoulders. This example illustrates the computation of crash frequencies per mile per year for highways with a traffic volume of 1,000 vehicles per day.
SPF for total crashes from table 10: NTOT = exp (-8.921 + 1.108 ln (1,000)) = 0.282 crashes per mi per year
SPF for fatal and injury crashes from table 10: NFI = exp (-7.818 + 0.853 ln (1,000)) = 0.146 crashes per mi per year
SPF for PDO crashes from table 10: NPDO = exp (-11.414 + 1.349 ln (1,000)) = 0.123 crashes per mi per year
Since the sum of NFI (0.146) and NPDO (0.123) is less than NTOT (0.282), the values of NFI and NPDO are adjusted so that this sum is equal to NTOT, as follows:
NFI (adjusted) = 0.282 = 0.153 crashes per mi per year
NPDO (adjusted) = 0.282 = 0.129 crashes per mi per year
Based on the results of the EB evaluation presented in section 4.3.2, the crash reduction effectiveness of the safety edge treatment is 5.7 percent. Continuing the computational example for Georgia two-lane highways with paved shoulders and a traffic volume of 1,000 vehicles per day, the crash reduction from the safety edge treatment would be estimated as follows:
For fatal and injury crashes:
0.153 (0.057) = 0.008721 crashes reduced per mi per year
For PDO crashes:
0.129 (0.057) = 0.007353 crashes reduced per mi per year
The estimated crash costs used in this analysis are based on those currently used in SafetyAnalyst, as follows:
The costs are based on the latest published FHWA values.(10) The weighted average cost of a fatal and injury crash (assuming 1 percent fatal crashes, 9 percent A injury crashes, 50 percent B injury crashes, and 40 percent C injury crashes) is $150,980 per crash. Based on these crash costs, the estimated annual crash reduction benefits for the example presented above are as follows:
0.008721 (150,980) + (.007353) (4,000) = $1,346 per mi
The service life of the safety edge treatment is estimated to be 7 years, the same as the service life of a typical pavement resurfacing project.
The minimum attractive rate of return for this analysis is estimated to be 4 percent. This value is currently used in SafetyAnalyst and is representative of the real, long-term cost of capital (i.e., not including inflation).(8)
The uniform series present worth factor is applied to convert the annual crash reduction benefits to a present value. This factor is determined as shown in equation 7:
The uniform series present worth factor for a minimum attractive rate of return of 4 percent and a service life of 7 years is determined as follows:
(P/A, 4%, 7) = = 6.002
The cost of the safety edge treatment is estimated as falling in the range of $536 to 2,145 per mi for both sides of the road combined, as explained in section 5.2.
The value of the benefit-cost ratio is computed using equation 6. For the computational example previously presented, the maximum benefit-cost ratio (estimated for the minimum treatment cost of $536 per mi) is determined as follows:
B/C = = 15.07
The minimum benefit-cost ratio for the same case (estimated for the maximum treatment cost of $2,145 per mi) is determined as follows:
B/C = = 3.77
The result indicates that the safety edge treatment provides at least $3 in benefits for each dollar spent on the treatment and possibly as much as $15 in benefits for each dollar spent on the treatment depending on the thickness of the safety edge treatment provided. This example addresses sites with a traffic volume of 1,000 vehicles per day. Larger benefit-cost ratios would be expected for sites with higher traffic volumes.
The results of the benefit-cost analysis are summarized in table 34 through table 37 for application of the safety edge treatment to four types of roadways.
F&I = Fatal and injury.
PDO = Property-damage-only.
For each State and roadway type, benefit-cost analyses were performed for traffic volumes ranging from 1,000 to 20,000 vehicles per day. The overall results of the benefit-cost analysis are shown in figure 6 and figure 7.
Figure 6. Graph. Minimum benefit-cost ratios for the safety edge treatment as a function of AADT.
Figure 7. Graph. Maximum benefit-cost ratios for the safety edge treatment as a function of AADT.
For two-lane highways with paved shoulders, application of the safety edge treatment has minimum benefit-cost ratios ranging from 3.8 to 43.6 for Georgia conditions and from 3.9 to 30.6 for Indiana conditions. For two-lane highways with unpaved shoulders, the minimum benefit-cost ratios for the safety edge treatment range from 3.7 to 62.8 for Georgia conditions and 2.8 to 12.8 for Indiana conditions. In all these cases, the maximum benefit-cost ratios are at least four times the minimum benefit-cost ratios.
These results suggest that the safety edge treatment is highly cost-effective under a broad range of conditions. Even though there is uncertainty in the treatment effectiveness estimate, the safety edge treatment is likely to be a good safety investment in most situations, especially for roadways with higher volume levels, where higher crash frequencies are expected.