Background
This case study
compares benefit/cost analysis and cost effectiveness 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 or used as the
effectiveness measure E 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 Accident Recorded
Unlighted
Lighted
Accident
Type
Day
Night
Day
Night
Property
damage
379
199
2069
836
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
For an effectiveness
measure of number of accidents prevented, this results in E = 247.
To determine the cost of the lighting, it will be assumed that the
light poles are center poles 67 meters apart with 2 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, the annual power cost is
Annual power cost =
1310 poles (2 bulbs/pole)(0.4 kilowatt/bulb) x (12 hours/day)(365
days/year) x ($0.10/kilowatt-hour) = $459,024 per year
For an effectiveness
measure of number of accidents prevented, this results in E = 247.
To determine the cost of the lighting, it will be assumed that the
light poles are center poles 67 meters apart with 2 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, the annual power cost is
Annual power cost =
1310 poles (2 bulbs/pole)(0.4 kilowatt/bulb) x (12 hours/day)(365
days/year) x ($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
If a benefit/cost
analysis is the basis for a decision on additional lighting, the
B/C ratio is B/C = 1,482,000 / 1,547,503 = 0.96
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
If a benefit/cost
analysis is the basis for a decision on additional lighting, the
B/C ratio is B/C = 1,482,000 / 1,547,503 = 0.96
Since B/C < 1.0,
the lighting is not justified. Consideration of other categories of
accidents is necessary to obtain a better basis for decisions. If a
cost-effectiveness analysis (CEA) is applied, due to a judgment
that the monetary estimates for lighting’s benefit is not accurate,
the C/E ratio is
C/E = 1,547,503 / 247
= 6265
This can serve as a
base ratio for comparison when an incremental CEA is performed for
additional accident reduction proposals. These preliminary B/C and
C/E analyses prompted the development of four lighting options:
W) Implement the plan
as detailed above; 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%.
Y) Install cheaper
poles and surrounding safety guards, plus slightly lowered lumen
bulbs (350 watts) at a cost of $2500 per pole; place the poles 67
meters apart. This is estimated to reduce the benefit by 25%.
Z) Install cheaper
equipment for $2500 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 four alternatives to determine if any are
economically justified.
2. Use a
cost-effectiveness analysis to compare the four alternatives. From
an understanding viewpoint, consider the following:
3. How many
property-damage accidents could be prevented on the unlighted
portion if it were lighted?
4. What would the
lighted, night-to-day accident ratio have to be to make alternative
Z economically justified by the B/C ratio?
5. Discuss the
analysis approaches of B/C and C/E. Does one seem more appropriate
in this type of situation than the other? Why? Can you think of
other bases that might be better for decisions for public projects
such as this one?