Question

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	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

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?

Answer 1

A)

For alternative W

from the data given in the paragraph it is clear that

the ratio of night to day accident involving property damage for the unlighted freeway section is

199/379= 0.525

and for lighted section is 839/2069 = 0.406

so if there would have been no light in the lighted section then no of accidents would have been 2069*0.525= 1086

but there are actually 839 accidents so

Effective measure of number of accidents= 1086-839= 247

now

benefit from saving one accident is 6000

so benefit from saving 247 accident is

247*6000

= 1,482,000

Now

two types of costs are involved in the process of lighting

i) installation cost and ii). annual power cost

to calculate installation cost you need to know the rate of installing per pole and total no of poles installed

since total distance is 87.8 Km and each pole is at distance of 67 m

so total number of a pole is 87.8*1000/67

= 1310

and installing each pole cost 3500

so total installation cost

=3500*1310

= 4,585,000

now Annual power cost calculation

we have to calculate total unit consumed by all the bulbs in all the poles

so total no of bulbs= no of poles* no of bulbs per pole

= 1310*2= 2620 bulbs

power of each bulb is 400W= 0.4KW

so energy consumed power*time

here time is no of hours in 1 year

= 2620*0.4 *12*365 kW yearly

so rate = energy consumed* rate per unit

= 0.1*2620*0.4*12*365

=459024

Now it is to be kept in mind that this data is for five years but installation cost is only at the beginning of the year

so

annualized cost C at 6% interest rate is given by

so EAC(Effective annual cosT)

we have to apply the method for this

Calculate EAC for installation cost
EAC1 = Discounted Investment + Maintenance Cost
EAC1 = $1,088,479
EAC1 = $1,088,479

thus total annual cost

= $1,088,479+459024

= 1,547,503

so B/C= 1,482,000/1,547,503 =0.96

Since B/C<1 the lightning is not justified as a cost is greater than the benefit

For ALTERNATIVE X

since benefit decrease by 40%

the original benefit was 1482,000

so now benefit= 0.6*1,482,000

=889,200

Now

two types of costs are involved in the process of lighting

i) installation cost and ii). annual power cost

to calculate installation cost you need to know the rate of installing per pole and total no of poles installed

since total distance is 87.8 Km and each pole is at distance of 134 m

so total number of a pole is 87.8*1000/134

= 655

and installing each pole cost 3500

so total installation cost

=3500*655

= 2,292,500

now Annual power cost calculation

we have to calculate total unit consumed by all the bulbs in all the poles

so total no of bulbs= no of poles* no of bulbs per pole

= 655*2= 1310 bulbs

power of each bulb is 400W= 0.4KW

so energy consumed power*time

here time is no of hours in 1 year

= 1310*0.4 *12*365 kW yearly

so rate = energy consumed* rate per unit

= 0.1*13100*0.4*12*365

=229,512

Now it is to be kept in mind that this data is for five years but installation cost is only at the beginning of the year

so

annualized cost C at 6% interest rate is given by

so EAC(Effective annual cosT)

we have to apply the method for this

Calculate EAC for Item 1
EAC1 = Discounted Investment + Maintenance Cost
EAC1 = $544,265.33 + $229,512.00
EAC1 = $773,777.33

consider item 1 as lighning

so B/C= 889,200/773,777 =1.149

Since B/C>1 the lightning is economically justified as cost is less than the benefit.

For ALTERNATIVE Y

since benefit decrease by 25%

the original benefit was 1482,000

so now benefit= 0.75*1,482,000

= 1,111,500

Now

two types of costs are involved in the process of lighting

i) installation cost and ii). annual power cost

to calculate installation cost you need to know the rate of installing per pole and total no of poles installed

since total distance is 87.8 Km and each pole is at distance of 67 m

so total number of a pole is 87.8*1000/67

= 1310

and installing each pole cost 2500

so total installation cost

=2500*1310

= 3,275,000

now Annual power cost calculation

we have to calculate total unit consumed by all the bulbs in all the poles

so total no of bulbs= no of poles* no of bulbs per pole

= 1310*2= 2620 bulbs

power of each bulb is 350W= 0.35KW

so energy consumed power*time

here time is no of hours in 1 year

= 2620*0.35 *12*365 kW yearly

so rate = energy consumed* rate per unit

= 0.1*2620*0.35 *12*365

=401,646 per year

Now it is to be kept in mind that this data is for five years but installation cost is only at the beginning of the year

so

annualized cost C at 6% interest rate is given by

so EAC(Effective annual cosT)

we have to apply the method for this

Calculate EAC for Item 1
EAC1 = Discounted Investment + Maintenance Cost
EAC1 = $777,521.90 + $401.00
EAC1 = $777,923

thus B/C for this is

1,11,500/777,523 = 1.429

so it is economically feasible

as cost is less than the benfit...

Alternative Z

Since accident prevention measure become 124 so total benefit

124*6000

= 744,000

two types of costs are involved in the process of lighting

i) installation cost and ii). annual power cost

to calculate installation cost you need to know the rate of installing per pole and total no of poles installed

since total distance is 87.8 Km and each pole is at distance of 134 m

so total number of the pole is 87.8*1000/134

= 655

and installing each pole cost 2500

so total installation cost

=2500*655

= 1,637,500

now Annual power cost calculation

we have to calculate total unit consumed by all the bulbs in all the poles

so total no of bulbs= no of poles* no of bulbs per pole

= 655*2= 1310 bulbs

power of each bulb is 350W= 0.35KW

so energy consumed power*time

here time is no of hours in 1 year

= 1310*0.35 *12*365 kW yearly

so rate = energy consumed* rate per unit

= 0.1*13100*0.35*12*365

=200,823

Now it is to be kept in mind that this data is for five years but installation cost is only at the beginning of the year

so

annualized cost C at 6% interest rate is given by

so EAC(Effective annual cosT)

we have to apply the method for this

Calculate EAC for Item 1
EAC1 = Discounted Investment + Maintenance Cost
EAC1 = $388,760.95 + $200,823.00
EAC1 = $589,584

so

B/C ratio is 744000/589584 = 1.2619

thus B/C>1

so economically it is justified

Q.2

we have

we have taken the cost from part A as we have calculated for each part...

E for W is given

for X it is 60% of this =0.6*247=148

for Y it is 75% of this = 0.75*247 =185

for X it is 124 given

so Y has minimum C/E ratio... thus it is best of these alternatives

also, all those alternatives whose C/E ratio is less than the base given in question that one is better as compared to W

Q.3).

from the data given in the paragraph it is clear that

the ratio of night to day accident involving property damage for the unlighted freeway section is

199/379= 0.525

and for lighted section is 839/2069 = 0.406

so if there would have been light in the no light section then no of accidents would have been 379*0.406= 154

but there are actually 199 accidents so

Effective measure of number of accidents= 199-154= 45

so prevented damage

= 45*6000

= 270,000

Q.5.

Benefit/Cost (B/C) Analysis is defined as a systematic process for calculating and comparing benefits and costs of a project for two purposes:

1. To determine if it is a sound investment (justification/feasibility); and
2. To see how it compares with alternate projects (ranking/priority assignment). (National Academies Transportation Research Board (TRB) Economics Committee.)

Benefit/Cost analysis is also commonly referred to as Cost-Benefit Analysis, CBA, Benefit/Cost Analysis, and BCA. The analysis is identical despite the naming differences. Benefit/costs analysis is one type of economic valuation an analysis that assesses the relative value of a project in monetized estimates. As the name implies, benefit/cost analysis determines the value of a project by dividing the incremental monetized benefits related to a project by the incremental costs of that project. The result is called the Benefit/Cost Ratio and is often the primary output of the analysis process. This output may either be expressed as a ratio (2:1) or a resultant value (2). For example, a project producing $150,000 in benefits and costing $100,000 would result in a B/C ratio of 1.5:1 or 1.5 ($150,000 benefits/$100,000 costs). Projects determined to have B/C ratios greater than one are said to be Efficient investments; in that, each dollar invested in the project returns more than $1.00 in benefits. Projects determined to have a B/C ratio less than one are Inefficient investments since the costs of the project are greater than incremental benefits created by the project. Projects with a B/C ratio of exactly one benefits are determined to be exactly the same as costs are said to be At Cost Efficiency. (B/C ratios are nearly always positive, ranging from zero to 15 or higher for some TSM&O strategies. B/C ratios may be negative; however. A negative value indicates that the project is expected to generate greater disbenefits than actual benefits; meaning that on a net basis, the project would make conditions worse rather than better.)

Benefit/cost ratios can be used to compare the relative value of different projects. Various projects may be prioritized (in terms of economic efficiency), assessing each project individually and calculating the B/C ratio for each project. In comparing the various projects, those projects with the highest B/C ratio would be ranked as the most efficient.

Cost-Effectiveness Analysis (CEA) is a type of economic evaluation that examines both the costs and health outcomes of alternative intervention strategies.CEA compares the cost of an intervention to its effectiveness as measured in natural health outcomes (e.g., "cases prevented" or "years of life saved").

• CEA results are presented in a cost-effectiveness ratio, which expresses cost per health outcome (e.g., cost per case prevented and cost per life year gained).
• CEA is generally used to either:
  • compare alternative programs with a common health outcome, or
  • assess the consequences of expanding an existing program.
  • Decisionmakers are often faced with the challenges of resource allocation. Resources are scarce; therefore, they must be allocated judiciously. CEA is used to identify the most cost-effective strategies from a set of options that have similar results.

    For example, the federal government might have to allocate scarce resources to:

  • provide a new facility to assist in the development and procurement of vaccines, or
  • enhance the current public health vaccine delivery.

These options have a common health outcome: the number of cases of a disease prevented by the vaccine. CEA can be used to identify the option that prevents the most cases at the least cost.

CEA differs from a cost-benefit analysis (CBA) and cost-utility analysis (CUA) in that:

• CEA expresses outcomes in natural units (e.g., "cases prevented" or "number of lives saved"), whereas
• CBA assigns dollar values to the outcomes attributable to the program, and
• CUA is a specialized form of CEA that includes a quality-of-life component associated with morbidity using common health indices such as quality-adjusted life years (QALYs) and disability-adjusted life years (DALYs).

Advantages of CEA over CBA and CUA Compared with CBA and CUA, CEA is:

• less time- and resource-intensive,
• easier to understand, and
• more readily suited to decision making.