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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.

6.1 Benefit-Cost Analysis Approach

The benefit-cost ratio for the safety edge treatment has been determined according to equation 6:

B slash C equals open parenthesis N subscript FI times E subscript SE times C subscript FI plus N subscript PDO times E subscript SE times C subscript PDO close parenthesis times open parenthesis P slash A comma i percent comma n close parenthesis all over CC subscript SE. (6)

Where:

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)

6.2 Components of the Benefit-Cost Analysis

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.

6.2.1 Crash Frequencies

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.

Table 33. SPFs used in benefit-cost analysis.

State

Roadway type

Shoulder type

Crash type and security level

Table

Georgia

Two-lane highway

Paved

All crashes

10

Georgia

Two-lane highway

Paved

F&I crashes

10

Georgia

Two-lane highway

Paved

PDO crashes

10

Indiana

Two-lane highway

Paved

All crashes

11

Indiana

Two-lane highway

Paved

F&I crashes

11

Indiana

Two-lane highway

Paved

PDO crashes

11

Georgia

Two-lane highway

Unpaved

All crashes

10

Georgia

Two-lane highway

Unpaved

F&I crashes

10

Georgia

Two-lane highway

Unpaved

PDO crashes

10

Indiana

Two-lane highway

Unpaved

All crashes

11

Indiana

Two-lane highway

Unpaved

F&I crashes

11

Indiana

Two-lane highway

Unpaved

PDO crashes

11

F&I = Fatal and injury.

PDO = Property-damage-only.

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 Parenthesis 0.146 over 0.146 plus 0.123 close parenthesis. = 0.153 crashes per mi per year

NPDO (adjusted) = 0.282 Parenthesis 0.112 over 0.146 plus 0.123 close parenthesis. = 0.129 crashes per mi per year

6.2.2 Treatment Effectiveness

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

6.2.3 Crash Costs

The estimated crash costs used in this analysis are based on those currently used in SafetyAnalyst, as follows:

  • Fatal crash = $5,800,000.
  • A injury crash = $402,000.
  • B injury crash = $80,000.
  • C injury crash = $42,000.
  • PDO crash = $4,000.(8)

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

6.2.4 Service Life

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.

6.2.5 Minimum Attractive Rate of Return

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)

6.2.6 Uniform Series Present Worth Factor

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:

Open parenthesis P slash A comma i comma n close parenthesis equals open parenthesis one plus i close parenthesis to the n power minus 1 all over i open parenthesis 1 plus i close parenthesis to the n power. (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) =(1+0.04) superscript 7 minus 1 over 0.04 (1 plus 0.04)superscript 7. = 6.002

6.2.7 Treatment Cost

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.

6.2.8 Benefit Cost Ratio

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 = (1,346) (6.002) over 536 = 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 = (1,346) (6.002) over 2,145 = 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.

6.3 Benefit-Cost Analysis Results

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.

Table 34. Benefit-cost analysis for application of safety edge treatment on Georgia two-lane roadways with paved shoulders.

AADT (vehicles/day)

1,000

5,000

10,000

15,000

20,000

Crash Frequencies

Total crashes per mile per year

0.282

1.675

3.611

5.659

7.784

F&I crashes per mile per year

0.146

0.575

1.039

1.469

1.877

PDO crashes per mile per year

0.123

1.079

2.748

4.748

6.999

F&I crashes per mile per year (adjusted)

0.153

0.583

0.991

1.337

1.646

PDO crashes per mile per year (adjusted)

0.129

1.093

2.620

4.322

6.138

Safety Benefits-Number of Crashes Reduced

F&I crashes reduced per mile per year

0.009

0.033

0.056

0.076

0.094

PDO crashes reduced per mile per year

0.007

0.062

0.149

0.246

0.350

Safety Benefits-Dollars

F&I crash reduction benefits per year ($)

1,314

5,015

8,528

11,505

14,165

PDO crash reduction benefits per year ($)

29

249

597

986

1,399

Total crash reduction benefits per year ($)

1,344

5,264

9,126

12,491

15,565

Present value of total benefits per year ($)

8,065

31,597

54,773

74,972

93,421

Treatment Cost

Minimum cost of safety edge treatment ($ per mile)

536

536

536

536

536

Maximum cost of safety edge treatment ($ per mile)

2,145

2,145

2,145

2,145

2,145

Benefit-Cost Ratio

Minimum benefit-cost ratio

3.8

14.7

25.5

35.0

43.6

Maximum benefit-cost ratio

15.0

59.0

102.2

139.9

174.3

F&I = Fatal and injury.

PDO = Property-damage-only.

Table 35. Benefit-cost analysis for application of safety edge treatment on Indiana two-lane roadways with paved shoulders.

AADT (veh/day)

1,000

5,000

10,000

15,000

20,000

Crash Frequencies

Total crashes per mile per year

0.664

2.175

3.626

4.888

6.043

F&I crashes per mile per year

0.158

0.444

0.694

0.900

1.082

PDO crashes per mile per year

0.542

1.722

2.832

3.789

4.659

F&I crashes per mile per year (adjusted)

0.150

0.446

0.713

0.938

1.139

PDO crashes per mile per year (adjusted)

0.514

1.729

2.912

3.950

4.904

Safety Benefits-Number of Crashes Reduced

F&I crashes reduced per mile per year

0.009

0.025

0.041

0.053

0.065

PDO crashes reduced per mile per year

0.029

0.099

0.166

0.225

0.280

Safety Benefits-Dollars

F&I crash reduction benefits ($)

1,291

3,841

6,138

8,072

9,804

PDO crash reduction benefits ($)

117

394

664

901

1,118

Total crash reduction benefits ($)

1,408

4,235

6,802

8,973

10,922

Present value of total benefits ($)

8,453

25,419

40,824

53,856

65,553

Treatment Cost

Minimum cost of safety edge treatment (per mile)

536

536

536

536

536

Maximum cost of safety edge treatment (per mile)

2,145

2,145

2,145

2,145

2,145

Benefit-Cost Ratio

Minimum benefit-cost ratio

3.9

11.9

19.0

25.1

30.6

Maximum benefit-cost ratio

15.8

47.4

76.2

100.5

122.3

F&I = Fatal and injury.

PDO = Property-damage-only.

Table 36. Benefit-cost analysis for application of safety edge treatment on Georgia two-lane roadways with unpaved shoulders.

AADT (veh/day)

1,000

5,000

10,000

15,000

20,000

Crash Frequencies

Total crashes per mile per year

0.377

1.822

3.588

5.335

7.068

F&I crashes per mile per year

0.144

0.673

1.307

1.927

2.538

PDO crashes per mile per year

0.226

1.151

2.320

3.496

4.676

F&I crashes per mile per year (adjusted)

0.147

0.672

1.293

1.896

2.487

PDO crashes per mile per year (adjusted)

0.231

1.150

2.296

3.439

4.581

Safety Benefits-Number of Crashes Reduced

F&I crashes reduced per mile per year

0.008

0.038

0.074

0.108

0.142

PDO crashes reduced per mile per year

0.013

0.066

0.131

0.196

0.261

Safety Benefits-Dollars

F&I crash reduction benefits ($)

1,263

5,782

11,126

16,314

21,403

PDO crash reduction benefits ($)

53

262

523

784

1,045

Total crash reduction benefits ($)

1,316

6,044

11,649

17,098

22,447

Present value of total benefits ($)

7,898

36,277

69,920

102,624

134,730

Treatment Cost

Minimum cost of safety edge treatment (per mile)

536

536

536

536

536

Maximum cost of safety edge treatment (per mile)

2,145

2,145

2,145

2,145

2,145

Benefit-Cost Ratio

Minimum benefit-cost ratio

3.7

16.9

32.5

47.8

62.8

Maximum benefit-cost ratio

14.7

67.7

130.4

191.5

251.4

F&I = Fatal and injury.

PDO = Property-damage-only.

Table 37. Benefit-cost analysis for application of safety edge treatment on Indiana two-lane roadways with unpaved shoulders.

AADT (veh/day)

1,000

5,000

10,000

15,000

20,000

Crash Frequencies

Total crashes per mile per year

0.409

1.263

2.053

2.728

3.338

F&I crashes per mile per year

0.118

0.235

0.317

0.376

0.426

PDO crashes per mile per year

0.336

1.027

1.662

2.202

2.689

F&I crashes per mile per year (adjusted)

0.106

0.236

0.329

0.398

0.456

PDO crashes per mile per year (adjusted)

0.302

1.028

1.725

2.330

2.882

Safety Benefits-Number of Crashes Reduced

F&I crashes reduced per mile per year

0.006

0.013

0.019

0.023

0.026

PDO crashes reduced per mile per year

0.017

0.059

0.098

0.133

0.164

Safety Benefits-Dollars

F&I crash reduction benefits ($)

916

2,027

2,827

3,428

3,926

PDO crash reduction benefits ($)

69

234

393

531

657

Total crash reduction benefits ($)

985

2,261

3,221

3,959

4,583

Present value of total benefits ($)

5,914

13,572

19,331

23,762

27,507

Treatment Cost

Minimum cost of safety edge treatment (per mile)

536

536

536

536

536

Maximum cost of safety edge treatment (per mile)

2,145

2,145

2,145

2,145

2,145

Benefit-Cost Ratio

Minimum benefit-cost ratio

2.8

6.3

9.0

11.1

12.8

Maximum benefit-cost ratio

11.0

25.3

36.1

44.3

51.3

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.

This figure is a multiple line graph showing the minimum benefit-cost ratios as a function of annual average daily traffic (AADT) determined for four data sets: two roadway types in two States. The x-axis has a range in AADT of 0 to 20,000 vehicles per day, and the y axis has a range in benefit-cost ratio of 0 to 70. All of the lines are slightly curvilinear and increasing. The lines shown in the graph in decreasing order of benefit-cost ratio are: (1) Georgia two-lane roadways with unpaved shoulders, (2) Georgia two-lane roadways with paved shoulders, (3) Indiana two-lane roadways with paved shoulders, and (4) Indiana two-lane roadways with unpaved shoulders.

Figure 6. Graph. Minimum benefit-cost ratios for the safety edge treatment as a function of AADT.

This figure is a multiple line graph showing the maximum benefit-cost ratios as a function of annual average daily traffic (AADT) determined for four data sets: two roadway types in two States. The x-axis has a range in AADT of 0 to 20,000 vehicles per day, and the y axis has a range in benefit-cost ratio of 0 to 300. All of the lines are slightly curvilinear and increasing. The lines shown in the graph in decreasing order of benefit-cost ratio are: (1) Georgia two-lane roadways with unpaved shoulders, (2) Georgia two-lane roadways with paved shoulders, (3) Indiana two-lane roadways with paved shoulders, and (4) Indiana two-lane roadways with unpaved shoulders.

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.

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