This case study compares benefit/cost analysis analysis on the same information about highway lighting and its role in accident reduction.

Poor highway lighting may be one reason that proportionately more traffic accidents occur at night. Traffic accidents are categorized into six types by severity and value. For example, an accident with a fatality is valued at approximately $4 million, while an accident in which there is property damage (to the car and contents) is valued at $6000. One method by which the impact of lighting is measured compares day and night accident rates for lighted and unlighted highway sections with similar characteristics. Observed reductions in accidents seemingly caused by too low lighting can be translated into either monetary estimates of the benefits B of lighting .

Information

Freeway accident data were collected in a 5-year study. The property damage category is commonly the largest based on the accident rate. The number of accidents recorded on a section of highway is presented here.

		Number of Accidents Recorded1
		Unlighted				Lighted
Accident Type		Day		Night		Day		Night
Property damage		379		199		2069		839

The ratios of night-to-day accidents involving property damage for the unlighted and lighted freeway sections are 199/379 = 0.525 and 839/2069 = 0.406, respectively. These results indicate that the lighting was beneficial. To quantify the benefit, the accident rate ratio from the unlighted section will be applied to the lighted section. This will yield the number of accidents that were prevented. Thus, there would have been (2069)(0.525) = 1086 accidents instead of 839 if there had not been lights on the freeway. This is a difference of 247 accidents. At a cost of $6000 per accident, this results in a net annual benefit of

B = (247)($6000) = $1,482,000

To determine the cost of the lighting, it will be assumed that the light poles are center poles 67 meters apart with two bulbs each. The bulb size is 400 watts, and the installation cost is $3500 per pole. Since these data were collected over 87.8 kilometers of lighted freeway, the installed cost of the lighting is (with number of poles rounded off):

Installation cost=$3500(87.8/0.067)=3500(1310)=$4,585,000

There are a total of 87.8/0.067 = 1310 poles, and electricity costs $0.10 per kWh. Therefore,

Annual power cost = 1310 poles(2 bulbs/pole)(0.4 kilowatt/bulb)

(12 hours/day)(365 days/year)

($0.10/kilowatt-hour)

= $459,024 per year

The data were collected over a 5-year period. Therefore, the annualized cost C at i = 6% per year is

Total annual cost = $4,585,000(A/P,6%,5) + 459,024=$1,547,503

Three lighting options are considered:

W) Install light poles every 67 meters at a cost of $3500 per pole.

X) Install poles at twice the distance apart (134 meters). This is estimated to cause the accident prevention benefit to decrease by 40%.

Z) Install cheaper equipment for $2,100 per pole with 350-watt lightbulbs and place them 134 meters apart. This plan is estimated to reduce the accident prevention measure by 50% from 247 to 124.

Case Study Exercises

Determine if a definitive decision on lighting can be determined by doing the following:

1. Use a benefit/cost analysis to compare the three alternatives to determine if any are economically justified. Use excel sheet to ease your calculations, submit hand solution and excel sheet if used. Enter the value of the incremental B/C ratio between option W and Z in the answer box below use 3 decimal format (Exp: 0.675)
   

Solution hint: first calculate the Benefit and total cost of each option, perform incremental B/C analysis to select the best option.