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 and when it should be used for decision making. Also presented is the use of how the Net Present Value is calculated and when it should be used rather than the BCR. 

Determining and Adjusting for the Analysis Period

Every safety benefit calculation is done for various purposes requiring different assumptions. The following list helps determine the effort required and what  assumptions the analyst makes 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 (i.e. statewide average for the roadway type considered). 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):

   1. Fatal = 0.52

   2. Sus. Serious Injury = 0.52

   3. Sus. Minor Injury = 0.52

   4. Minor injury = 0.52

   5. No-injury = 0.58

5. Service life of HFST is 10 years

1. Table 1 provides the crash severity distribution (see Historic and Predictive Safety Analysis website, 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. Table 2 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

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

The safety benefit for adding HFST is $2,982,849 - $1,532,749 = $1,450,100. However for comparison purposes the value should be discounted to account for the loss of today’s investment in the future.

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

The totals in Table 4 did 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)) Equation 1

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

Equation 1 is used for each year’s crash costs in both the No Build and Build condition. For example: $87,815 / ((1+.03)^(1-0)) is $85,257. This step is iterated to create Table 5 which  shows the Present Value of the crash costs. 

There is a safety benefit of $1,026,025 for mitigating roadway departure crashes due to the installation of HFST through the horizontal curve.

Example Calculation Observations

Key example calculation observations are summarized below:

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 valued crash severities.

3. The base assumption here 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 be cognizant if existing conditions are wildly 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 issues should be documented in the assumptions.

4. From Table 4 we can see that we anticipate only a reduction of 5 crashes over the 20 year period (11.447 - 6.464 = 4.983). The reduction of severe crashes is estimated to be 4.78% of those crashes (0.24 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 emphasizing that crashes are rare and random events. Using the observed crash frequency can lead to over/under estimating the safety benefit of improvements. This is why it is preferred to use the predictive methods for safety benefit estimation rather than the historical crash frequency.

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 Table 5 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.

Other Alternative Treatment

For further discussion in comparison of alternatives 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 Utah Department of Transportation Crash Modification Factors table. 

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 6 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 Mitigation Cost

Total area of treatment 1300 ft  x 2 lanes x 12 ft = 31,200 sq feet; or 3,467 sq yds.

Total cost of HFST: 3467 sq yds x $25/sq yds = $86,675

Step #2 Calculate the Present Value of the Mitigation Cost

The scenario stated that the service life of HFST is 10 years. The present value of the HFST for the 20-year analysis period is:

PV = $86,675 x 1.744

PV = $151,161

Step #3 Calculate the Benefit Cost Ratio (BCR)

BCR = $1,025,271 / $151,161

BCR =6.78

Other Alternative

The second alternative of rumble strips is also considered. The resulting costs and BCR as as follows:

The cost of rumble strips is estimated at $0.65 per linear foot (two shoulders and centerline rumble strips will be installed, 3 lines total), with a service life of 10 years. PV cost:

1300 ft x 3 lines x $0.65/ft x 1.744 = $4,421

Resulting BCR: $317,033 / $4,421 = 71.71

Because the BCR is so much higher for rumble strips, the thriftiest alternative  is rumble strips. However, maximizing your safety return may not be achieved with the rumble strip alternative.

Comparing Alternatives

Economic comparisons should keep the following in mind:

1. The Benefit Cost Ratio answers, “How efficient is each dollar invested?”

2. The Net Present Value (Benefits-Costs) answers, “How much total safety value do we gain?”

When you are choosing between safety alternatives those two questions are not the same and only one leads to the best overall outcome. 

In the example above the most efficient investment is the rumble strip installation. However, by doing so we leave over $700,000 in potential safety benefits on the table ($1,026,025 - $317,033 = $708,992). From an economic standpoint, the correct decision is to choose the alternative with the greatest net present value. It is important to note that ratios are diagnostic, not decisive. In safety terms the net present value maximizes the total lives saved, injuries prevented, and damage avoided. The goal of the analysis is to maximize safety, not thrift. 

Comparing Benefit Cost Ratios is appropriate when you are screening projects, or allocating limited budgets across many independent projects, or when you are ranking projects that are NOT mutually exclusive (treatment A vs. B at the same site). For mutually exclusive safety alternatives the net present value comparison is used. 

The Net Present Value comparison method is done as follows:

Rumble Strips Alternative:

PV Benefits - PV Costs: $317,033 - $4,421 = $312,612

The Net Present Value for rumble strips is $312,612

HFST Alternative:

PV Benefits - PV Costs: $1,026,025 - $151,728 = $874,297

The Net Present Value for HFST is $874,297.

Because the Net Present Value is higher for HFST, it becomes the preferred alternative of the economic analysis.