The most common method for determining the viability of a safety improvement is the calculation of the benefit cost ratio (BCR). The BCR refers to the safety benefit (reduction of crashes) of the modification and the present value project cost of implementing the proposed improvement. The purpose of this article is to present a practical example of how the BCR is calculated.

Determining and Adjusting for the Analysis Period

Every safety benefit calculation is done for various purposes requiring different assumptions. The following questions and key assumptions will help to determine the effort required and what analyst makes correct assumptions regarding time, inflation, service life, volume adjustments, and analysis period. The analyst should state all assumptions in their deliverables. 

1. When comparing alternatives, including build and no-build, all benefits and costs must be normalized by standardizing the analysis period. Typical practice is to use a 20 year analysis period.

2. If the service life of an asset or safety treatment is different than the analysis period, a common multiple of the two should be used. The final result can then be adjusted to the 20 year analysis period.

3. Analysis periods other than 20 years might be important to consider especially if a known change to the proposed improvements are planned. For example, if an intersection is adding a turn lane now, but the intersection will become grade separated in 10 years then 10 years should be used as the analysis period.

4. The present value of money being “invested” in the future must be accounted for with a discount rate. Typical practice in Utah is to use a 3% discount rate. Both the safety benefit and cost must be adjusted to a present value to calculate the BCR.

5. Will the traffic volumes grow during the analysis period or be held constant? When growth volumes are large they should be accounted for, however if the growth is low, holding the AADT constant can simplify the analysis. 

6. Simple comparisons of safety improvements may allow a constant AADT. While more advanced planning analysis like an Interstate Access Change Request or an Environmental Study should consider growth in AADT. Design exceptions might consider vehicle volumes depending on the exceptions requested and the scope of the project.

7. If traffic volumes are adjusted by year, consider if the growth will be constant throughout the analysis or if there will be a few years of rapid growth followed by slower growth.

Calculating a Safety Benefit

Safety benefit is the reduction in crashes resulting from a change in the roadway design, conditions, or management. Safety cost is the increase in crashes resulting from a change in the roadway conditions. The following information is needed to calculate safety benefit/cost:

1. The crash frequency for the current condition during the analysis period, often referred to as the “no build” condition.

2. The crash frequency for the proposed changes to the roadway during the analysis period. 

3. Crash cost by severity level.

Example Calculation

Scenario: The Department is considering installing high friction surface treatment (HFST) on a horizontal curve on a rural two-lane two-way roadway. The following information is provided:

1. The current predicted crash frequency (no build condition) is 0.91 crashes per year (2022) 37% of these crashes are roadway departure type crashes. 0.91 x 0.37 = 0.337 roadway departure crash frequency per year. (NOTE: typically HFST addresses ALL crash types on horizontal curves, however, the effectiveness is limited to roadway departures to emphasize the comparison with other mitigations below).

2. A traffic study estimates that the current average daily travel (ADT) is constant at 5,000 vehicles but a future development in year 3 will push AADT to 6,000 vehicles with a steady growth of 5% per year.

3. Analysis period is for 20 years with a 3% discount rate for future values.

4. CMFs for HFST are as follows (applied to roadway departure crashes only):

• Fatal = 0.52

• Sus. Serious Injury = 0.52

• Sus. Minor Injury = 0.52

• Minor injury = 0.52

• No-injury = 0.58.

5. Service life of HFST is 10-years

6. Table 1 provides the crash severity distribution (see Historic and Predictive Safety Analysis article, Table 3) and related crash costs:

Step #1: Calculate "No Build" roadway departure crashes and crash costs

This step uses the typical  severity distribution of crashes for the specific  roadway type and the calculated number of applicable crashes to determine the estimated crash frequency used for the analysis, as shown in Table 2. Table 3 shows the calculation of the average crash cost based on the crash severity distribution of the mitigated crashes.

Step #2: Apply CMF to calculate "Build" roadway departure predicted crashes and average crash costs by severity

The no-build crash frequency is multiplied by the CMF to determine the build crash frequency as shown in Table 4. The build crash frequency is then multiplied by the crash costs as shown in Table 5.

Step #3: Calculate the benefit of the change in roadway departure crashes

Step #4: Calculate the present value of the safety benefit

The totals in Table 6 do not consider the depreciation of future money compared to investments today. For a true comparison of the benefit gained and the HFST investment, the values must be compared at their present value. The next step is to discount these numbers yielding the present value of the safety benefit.

Standard spreadsheet functions can be used for present value calculations if the safety benefit is constant over the analysis period. However, because the example considers a change in ADT, the discount rate must be applied each year of the analysis period. The present value is calculated using Equation 1 below:

PVn = CCn / ((1+R)^(Yn-Ya))

PVn = The present value of the crash cost in year N

CCn = The crash cost in year N

R = The discount rate

Yn = Year N of the analysis period N

Ya = Beginning year of the analysis period N

Table 7 shows the Present Value of the crash costs calculated in Table 6. There is a safety benefit of $1,025,271 for mitigating roadway departure crashes due to the installation of HFST through the horizontal curve.

Example Calculation Observations

1. Mitigations that target specific crash types (e.g. roadway departure) should account for the proportion of crashes that are being addressed. See CMFs Article for additional information.

2. Safety benefits can be substantially influenced by the severity distribution. Some mitigations, like guardrail, have a CMF with a value higher than 1.0 for no-injury crashes, which make up the greatest proportion of total crashes. The overall change in crashes might actually increase, but the safety benefit is still substantial because guardrail is more effective for mitigating higher crash severities.

3. The base assumption in this example is that 37% of the total crashes are roadway departure crashes. However, on horizontal curves this proportion is often much higher. The estimate provided here would be considered conservatively low (i.e. the actual safety benefit will be higher than calculated). The analyst should consider if existing conditions are significantly out of proportion from the averages to help determine if the results are representative, or if specific proportions are more appropriate for use in the estimate. All of these should be documented in the assumptions.

4. From Table 6 we can see that we anticipate only a reduction of 5 crashes over the 20 year period. The reduction of severe crashes is estimated to be 4.78% of those crashes (0.28 crashes over the 20-year period, sum of fatal and suspected serious injury crash proportions from Table 1 above), a surprisingly small number. It would be unusual to observe a severe crash in the before/after installation period because crashes are rare and random events. Using the observed crash frequency and associated severity distribution can lead to over/under estimating the safety benefit of improvements.

Effects of Different Assumptions

If the AADT was held constant at 5000 vehicles the safety benefit would be $626,104. Assuming no growth in AADT makes the calculation much simpler as the standard “PV” function can be used in a spreadsheet to avoid Tables 6 and 7 above. However the safety benefit is drastically different because the anticipated growth rate was high in the example provided. 

If an average AADT of 8502 vehicles was held constant in the calculation the safety benefit would be $1,063,262. Averaging the AADT and using the standard “PV” function can yield accurate results if the change in AADT from year to year is relatively constant.

Alternative Treatment

For considering alternative treatments the same methodology from above is applied to installing rumble strips through the curve with no HFST. The CMF for rumble strips is 0.86 and the same predicted crashes and proportion of roadway departure crashes is used (37%). Rumble strips have a service life of 10-years. The safety benefit over the 20 year analysis period is $315,893.

Calculating Present Value of Project Cost

The project cost must be normalized to the standard analysis period of 20 years to calculate the benefit cost ratio. If the project has a 20 year service life then the estimated cost of the project becomes the denominator in the benefit cost ratio calculation. For a list of service life numbers of various safety measures see the CMF article.

The true cost of a project might also include utility costs, maintenance costs, rehabilitation costs, etc. Currently these additional costs are not accounted for. The analyst can add these costs for comparison by applying the multipliers included in Table 8 to adjust service lives to a 20-year cost for comparison with the safety benefit.

A continuation of the example of the safety benefit calculation above is used to calculate the benefit cost ratio below.

Example Calculation

From the example above, calculate the benefit cost ratio of adding HFST on a horizontal curve. Assume a 3% discount rate and 1300 feet of curve length. HFST will only be applied to the travel lanes (12 feet wide). The average cost of HFST is $25/sq yd.

Step #1: Determine Treatment Cost

Total area of treatment:

1,300 ft x 2 lanes x 12 feet wide = 31,200 square feet: or 3,467 square yards

Total cost of HFST:

3,467 square yards x $25 / square yard = $87,000

Step #2: Calculate the Present Value of the Treatment Cost

Using the HFST service life of 10 years the present value of the treatment for a 20-year analysis period is calculated using the factors in table 8.

PV = $87,000 x 1.744

PV = $151,728

Step #3: Calculate the Benefit Cost Ratio (BCR)

BCR = $1,025,271 / $151,728

BCR = 6.76

Alternative Treatment

The alternative treatment of rumble strips is calculate in the same way, the resulting PV cost and BCR is as follows.

The cost of rumble strips is estimated at $0.65 per linear foot for two shoulders rumble strips and a centerline rumble strip (3 lines) with a service life of 10 years.

1,300 ft x 3 lines x $0.65 per foot x $2,534

PV = $7,710 x 1.744

PV = $4,421

BCR = $315,893/$4,421

BCR = 71.45

Comparing Alternatives

The higher BCR for rumble strips in the above examples suggests that it has the "biggest bang for the buck", however this does not mean it is the "most bang for the buck". Determining the most value for the dollar must be done using the incremental benefit-cost ratio (IBCR) method. This method is used to compare mutually exclusive alternatives. The following are steps for the IBCR method.

1. Calculate the BCR for each alternative compared to the “no build” condition. 

2. Eliminate any alternative that has a BCR < 1.0

3. Use the alternative with the highest BCR as the “victor” or preferred option of round 1. This victor becomes the basis of comparison for the next round of analysis rather than the “no build” condition. 

4. Compare each alternative with the previous round’s victor by subtracting the PV costs. If any of the alternatives yields a BCR > 1.0 then they proceed to the next round.

5. Repeat steps 3 and 4 until the final victor is found.

Steps 1, 2  and 3 have been completed in the examples above. Both alternatives have a BCR > 1.0 so both alternatives are considered in the next round. The rumble strip alternative is the victor of the first round and becomes the alternative for comparison rather than the “no build” method. Table 9 below shows the calculated difference in costs between the alternatives.

The resulting BCR is $709,378 / 146,725 (see Step #5) = 4.83. Because the BCR is greater than 1.0 the new victor is the HFST alternative. Figure 1 illustrates why HFST provides the “most bang for the buck”. Keep in mind that the slope of the safety benefit to the present value project cost line is simply the BCR (purchased benefit to the investment expended). By spending an extra $146,725 for HFST the project purchases another $709,378 in safety benefits.

As shown in Figure 1 The rumble strip alternative has the steepest slope (highest BCR), however its safety benefit “purchasing power” is significantly lower than the HFST alternative. Because the HFST alternative continues to purchase safety at a positive return on the investment, (BCR=4.83) this alternative is the preferred choice. The IBCR is important because it assures that you get the “most bang for the buck” rather than the “biggest bang for the buck”. When selecting safety projects, your goal is to ECONOMICALLY MAXIMIZE SAFETY. 

For simplicity purposes, a comparison of alternatives with the Net Safety Benefit (discounted benefits - discounted costs) should provide the same result in rankings as the incremental benefit cost ratio.

Figure 1 BCR Comparison of Alternatives