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IEEN 5329 Homework 7 9

Economics

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IEEN 5329

Homework 7

9.3, 9.12, 9.25, 9.32

Case study on page 243 to 245

PROBLEMS

Public Sector Economics

9 1 State the difference between public and private sector alternatives with respect to the following characteristics.

(a) Size of investment

(b) Life of project

(c) Funding

(d) MARR

9 2 Indicate whether the following characteristics are primarily associated with public sector or private sector projects.

(a) Profits

(b) Taxes

(c) Disbenefits

(d) Infinite life

(e) User fees

(f) Corporate bonds

 

9 3 Identify each cash flow as a benefit, disbenefit, or cost

(a) $500,000 annual income from tourism created by a freshwater reservoir

(b) $700,000 per year maintenance by container ship port authority

(c) Expenditure of $45 million for tunnel construction on an interstate highway

(d) Elimination of $1.3 million in salaries for county residents based on reduced international trade

(e) Reduction of $375.000 per year in car accident repairs because of improved lighting

(f) $700,000 per year loss of revenue by farmers because of highway right-of-way purchases

9.4 During its 20 years in business, Deware Construction Company has always developed its contracts under a fixed-fee or cost-plus arrangement. Now it has been offered an opportunity to participate in a project to provide cross-country highway transportation in an international setting, specifically, a country in Africa. If accepted. Deware will work as subcontractor to a larger European corporation. and the BOT form of contracting will be used with the African country government. Describe for the president of Deware at least four of the significant differences that may be expected when the BOT format is utilized in lieu of its mom traditional forms of con-tract making.

9.5 If a corporation accepts the BOT form of contracting, (a) identify two risks taken by a corporation and (b) state how these risks can he reduced by the government partner.

Project B/C Value

9.6 The estimated annual cash flows for a proposed city government project are costs of $450,000 per year, benefits of $600,000 per year, and disbenefits of $100,000 per year Determine the (a) W/C ratio and (b) value of B — C.

9.7 Use spreadsheet software such as Excel. PW analysis, and a discount rate of 5% per year to determine that the B/C value for the following estimates is 0.375, making the project not acceptable using the benefit/ cost method. (a) Enter the values and equations on the spreadsheet so they may be changed for the purpose of sensitivity analysis.

First cost = $8 million

Annual cost = $800,000 per year

Benefit = $550.000 per year

Disbenefit = $100,000 per year

(b) Do the following sensitivity analysis by changing only two cells on your spreadsheet. Change the discount rate to 3% per year, and adjust the annual cost estimate until B/C = 1.023. This makes the project just acceptable using benefit/cost analysis.

9.8 A proposed regulation regarding the removal of arsenic from drinking water is expected to have an annual cast of $200 per household per year. If it is assumed that there am 90 million households in the country and that the regulation could save 12 lives per year, what would the value of a human life have to be for the B/C ratio to be equal to 1.0?

9.9 The U.S. Environmental Protection Agency has established that 2.5% or the median household income is a reasonable amount to pay for safe drinking water. The median household income is $30,000 per year. For a regulation that would affect the health of people in 1% of the households, what would the health benefits have to equal in dollars per household (for that 1% of the households) for the B/C ratio to be equal to 1.0?

9.10 Use a spreadsheet to set up and solve Problem 9.9, and then apply the following changes. Observe the increases and decreases in the required economic value of the health benefits for each of these changes. (a) Median income is $18.000 (poorer country), and percentage of house-hold income is reduced to 2%. (b) Median income is $30.000 and 2.5% is spent on safe water, but only 0.5% of the households are affected. (c) What percentage of the households must be affected if the required health benefit and annual income both equal $18.000? Assume the 2.5% of income estimate is maintained.

9.11 The fire chief of a medium-sized city has estimated that the initial cost of a new fire station will be $4 million. Annual upkeep costs are estimated at $300,000. Benefits to citizens of $550,000 per year and dis-benefits of $90,000 per year have also been identified. Use a discount rate of 4% per year to determine if the station is economically justified by (a) the conventional B/C ratio and (b) the B — C difference.

9.12 As part of the rehabilitation of the down-town area of a southern U.S. city, the Parks and Recreation Department is planning to develop the space below several overpasses into basketball, handball, miniature golf, and tennis courts. The initial cost is expected to be $150,000 for improvements which are expected to have a 20-year life. Annual maintenance costs are projected to be $12,000. The department expects 24,000 people per year to use the facilities an average of 2 hours each. The value of the recreation has been conservatively set at $0.50 per hour. At a discount rate of 3% per year, what is the B/C ratio for the project?

9.13 The B/C ratio for a new flood control project along the banks of the Mississippi River is required to be 1.3. If the benefit is estimated at $600,000 per year and the maintenance cost is expected to total $300,000 per year, what is the allowed maximum initial cost of the project? The discount rate is 7% per year, and a project life of 50 years is expected. Solve in two ways: (a) by hand and (b) using a spread-sheet set up for sensitivity analysis.

9.14 Use the spreadsheet developed in Problem 9.13(b) to determine the B/C ratio if the initial cost is actually $3.23 million and the discount rate is now 5% per year.

9.15 The modified B/C ratio for a city-owned hospital heliport project is 1.7. If the initial cost is $1 million and the annual benefits are $150,000. What is the amount of the annual M&O costs used in the calculation, if a discount rate of 6% per year applies? The estimated life is 30 years.

9.16 Calculate the B/C ratio for the following cash flow estimates at a discount rate of 6% per year.

Item	Cash Flow
PW of benefits, $	3,800,000
AW of disbenefits, $/year	45,000
First cost,$	2,200,000
M&O costs, $/year	300,000
Life of project, Years	15

 

9.17 Hemisphere Corp. is considering a BOT contract to construct and operate a large dam with a hydroelectric power generation facility in a developing nation in the southern hemisphere. The initial cost of the dam is expected to be $30 million, and it is expected to cost $100,000 per year to operate and maintain. Benefits from flood control, agricultural development, tourism etc. are expected to be $2.8 million per year at an interest rate of 8% per year, should the dam be constructed on the basis of its conventional B/C ratio? The dam is assumed to be a permanent asset for the country (a) Solve by hand. 00 Using a spreadsheet, find the B/C ratio with only a single cell computation.

9.18 The U.S. Army Corps of Engineers is considering the feasibility of constructing a small flood control dam in an existing arroyo. The initial cost of the project will be $2.2 million, with inspection and upkeep costs of $10,000 per year. In addition, minor reconstruction will be required every 15 years at a cost of $65,000. If flood damage will be reduced from the present cost of $90,000 per year to $10,000 annually, use the benefit/cost method to determine if the dam should be constructed. Assume that the dam will be permanent and the interest rate is 12% per year.

9.19 A highway construction company is under contract to build a new roadway through a scenic area and two rural towns in Colorado. The road is expected to cost $18 million, with annual upkeep estimated at $150,000 per year. Additional income from tourists of $900,000 per year is estimated. It the road is expected to have a useful commercial life of 20 years, use one spreadsheet to determine if the high-way should be constructed at an interest rate of 6% per year by applying (a) the B - C method, (b) the B/C method, and (e) the modified B/C method. (Additionally. if the instructor requests it: Set up the spreadsheet for sensitivity analysis and use the Excel IF operator to make the build-don't build decision in each part of the problem.)

9.20 The U.S. Bureau of Reclamation is considering a project to extend irrigation canals into a desert area. The initial cost of the project is expected to be S1.5 million, with annual maintenance costs of $25,000 per year. (a) If agricultural revenue is expected to be $175,000 per year, do a B/C analysis to determine whether the project should be undertaken, using a 20-year study period and a discount rate of 6% per year. (b) Rework the problem, using the modified B/C ratio.

9.21 (a) Set up the spreadsheet and (b) use hand calculations to calculate the B/C ratio for Problem 9.20 if the canal must be dredged every 3 years at a cost of $60,000 and there is a $15,000 per year disbenefit associated with the project.

Alternative Comparison

9.22 Apply incremental B/C analysis at an interest rate of 8% per year to determine which alternative should be selected. Use a 20-year study period, and assume the damage costs might occur in year 6 of the study period.

	Alternative A	Alternative B
Initial cost, $	600,000	800,000
Annual M&O costs, $/year	50,000	70,000
Potential damage costs, $	950,000	250,000

 

9.23 Two routes are under consideration for a new interstate highway segment. The long route would be 25 kilometers and would have an initial cost of $21 million. The short Trans mountain route would span 10 kilometers and would have an initial cost of $45 million. Maintenance costs are estimated at $40,000 per year for the long route and $15,000 per year for the short route. Additionally, a major overhaul and resurfacing will be required every 10 years at a cost of 10% of the first cost of each route. Regardless of which mute is selected, the volume of traffic is expected to be 400,000 vehicles per year. If the vehicle operating expense is assumed to be $0.35 per kilometer and the value of reduced travel time for the short route is estimated at $900.000 per year, determine which route should be selected, using a conventional B/C analysis. Assume an infinite life for each road, an interest rate of 6% per year, and that one of the roads will he built.

9.24 A city engineer and economic development director of Buffalo are evaluating two sites for construction of a multipurpose sports arena. At the downtown site, the city already owns enough land for the arena. However, the land for construction of a parking garage will cost $1 million. The west side site is 30 kilometers from downtown, but the land will be donated by a developer who knows that an arena at this site will increase the value of the remainder of his land holdings by many times. The downtown site will have extra construction costs of about $10 million because of infrastructure relocations, the parking garage, and drainage improvements. However, because of its centralized location, there will be greater attendance at most of the events held there. This will result in more revenue to vendors and local merchants in the amount of $350.000 per year. Additionally the average attendee will not have to travel as far, resulting in annual benefits of $400,000 per year. All other costs and revenues are expected to be the same at either site. If the city uses a discount rate of 8% per year, where should the arena be constructed? One of the two sites must be selected.

9.25 A country with rapid economic expansion has contracted for an economic evaluation of possibly building a new container port to augment the current port. The west coast site has deeper water so the dredging cost is lower than that for the east coast site. Also, the redredging of the west site will be required only every 6 years while the east site must be reworked each 4 years. Redredging, which is expected to increase in cost by 10% each time, will not take place in the last year of a port's commercial life. Disbenefit estimates vary from west revenue loss) to east (fishing and resort revenue losses). Fees to shippers per 20-foot STD equivalent are expected to be higher at the west site due to greater difficulty in handling ships be-cause of the ocean currents present in the area and a higher cost of labor in this area of the country. All estimates are summarized below in $1 million, except annual revenue and life. Use spreadsheet analysis and a dis-count rate of 4% per year to determine if either port should be constructed. It is not necessary that the country build either port since one is already operating successfully.

	West Coast Site	East Coast Site
Initial cost, $
Year 0	21	8
Year 1	0	8
Dredging cost, $ year 0	5	12
Annual M&O, $/year	1.5	0.8
Recurring dredging cost, $	2 each 6 years with increase of 10% each time	1.2 each 4 years with increase of 10% each time
Annual disbenefits, $/year	4	7
Annual fees: number of 20 foot.	5 million/year at $2.50 each	8 million/year at $2 each
STD at $/container
Commercial life, years	20	12

 

9.26 A privately owned utility is considering two cash rebate programs to achieve water conservation. Program 1, which is expected to cost an average of $60 per household, would involve a rebate of 75% of the purchase and installation costs of an ultralow-flush toilet. This program is projected to achieve a 5% reduction in overall household water use over a 5-year evaluation period. This will benefit the citizenry to the extent of $1.25 per household per month. Program 2 would involve grass re-placement with desert landscaping. This is expected to cost $500 per household, but it will result in reduced water cost at an estimated $8 per household per month (on average). At a discount rate of 0.5% per month, which program. if either, should the utility undertake? Use the B/C method.

9.27 Solar and conventional alternatives are available for providing energy at a remote space research site. The costs associated with each alternative are shown below. Use the B/C method to determine which should be selected at a discount rate of 0.75% per month over a 6-year study period.

	Conventional	Solar
initial cost, $	2,000,000	4,500,000
M&O cost, $/month	50,000	10,000
Salvage value, $	0	150,000

 

9.28 The California Forest Service is considering two locations for a new state park. Location E would require an investment of $3 million and $50,000 per year in maintenance. Location W would cost $7 million to construct, but the Forest Service would receive an additional $25,000 per year in park use fees. The operating cost of location W will be $65,000 per year. The revenue to park concessionaires will be $500,000 per year at location E and $700,000 per year at location W. The disbenefits associated with each location are $30,000 per year for location E and $40,000 per year for location W. Use (a) the B/C method and (b) the modified B/C method to determine which location, if either, should be selected, using an interest rate of 12% per year. Assume that the park will be maintained indefinitely.

9.29 Three engineers made the estimates shown below for two optional methods by which new construction technology would be implemented at a site for public housing. Either one of the two options or the current method may be selected. Set up a spreadsheet tor B/C sensitivity analysis, and determine if option 1, option 2, or the do-nothing option is selected by each of the three engineers. Use a life of 5 years and a discount rate of 10% per year for all analyses.

	Engineer Bob		Engineer Judy		Engineer Chen
	Option 1	Option 2	Option 1	Option 2	Option 1	Option 2
Initial cost, $	50,000	90,000	75,000	90,000	60,000	70,000
Cost, $/year	3,000	4,000	3,800	3000	6,000	3,000
Benefits, $/year	20,000	29,000	30,000	35,000	30,000	35,000
Disbenefits, $/year	500	1,500	1,000	0	5,000	1,000

 

Multiple Alternatives

9.30 One of four new techniques, or the current method, can be used to control mildly irritating chemical fume leakage into the surrounding air from a mixing machine. The estimated costs and benefits (in the form of reduced employee health costs) are given below for each method. Assuming that all methods have a 10-year life with zero salvage value, determine which one should be selected, using a MARR of 15% per year and the B/C method.

 

	Technique
	1	2	3	4
Installed cost, $	15,000	19,000	25,000	33,000
AOC, $/year	10,000	12,000	9,000	11,000
Benefits, S/year	15,000	20,000	19,000	22,000

 

9.31 Use a spreadsheet to perform a B/C analysis for the techniques in Problem 9.30, assuming they are independent projects. The benefits are cumulative if more than one technique is used in addition to the current method.

9.32 The Water Service Authority of Dubay is considering tour sizes of pipe for a new water line. The costs per kilometer ($/km) for each size are given in the table. Assuming that all pipes will last 15 years and the MARR is 8% per year, which size pipe should be purchased based on a B/C analysis? Installation cost is considered a part of the initial cost.

	Pipe Size, Millimeters
	130	150	200	230
Initial equipment cost, $/km	9180	10510	13180	15850
Installation cost, $/km	600	800	1400	1500
Usage cost, $/km per year	6000	5800	5200	4900

 

9.33 The federal government is considering three sites in the National Wildlife Pre-serve for mineral extraction. The cash flows (in millions) associated with each site are given below. Use the B/C method to determine which site, if any, is best. if the extraction period is limited to 5 years and the interest rate is 10% per year.

	Site A	Site B	Site C
Initial cost, $	50	90	200
Annual cost, $/year	3	4	6
Annual benefits, $/year	20	29	61
Annual disbenefits, $/year	0.5	1.5	2.1

 

9.34 Over the last several months, seven different toll bridge designs have been proposed and estimates made to connect a resort is-land to the mainland of an Asian country.

Location	Construction Cost, $ Millions	Annual Excess Fees Over Expenses, $100,000
A	14	4.0
B	8	6.1
C	22	10.8
D	9	8.0
E	12	7.5
F	6	3.9
G	18	9.3

 

A public-private partnership has been formed, and the national bank will be pro-viding funding at a rate of 4% per year. Each bridge is expected to have a very long useful life. Use B/C analysis to answer the following. Solution by spreadsheet or by hand is acceptable.

(a) If one bridge design must be selected determine which one is the best economically.

(b) An international bank has offered to fund as many as two additional bridges, since it is estimated that the traffic and trade between the island and mainland will increase significantly. Determine which the three best designs are economically. If there is no budget restraint for the purpose of this analysis.

9.35 Three alternatives identified as X, Y, and Z were evaluated by the B/C method. The analyst, Joyce, calculated project B/C values of 0.92, 1.34, and 1.29. The alternatives are listed in order of increasing total equivalent costs. She isn't sure whether an incremental analysis is needed.

(a) What do you think? If no incremental analysis is needed, why not; if so, which alternatives must be compared incrementally?

(b) For what type of projects is incremental analysis never necessary? If X, Y, and Z are all this type of project, which alternatives are selected for the B/C values calculated?

9.36 The four mutually exclusive alternatives below are being compared using the B/C method. What alternative, if any, should be selected?

Alternative	Initial Investment, $millions	B/C Ratio	Incremental B/C when Compared with Alternative
			J	K	L	M
J	20	1.10	-
K	25	0.96	0.40	-
L	33	1.22	1.42	2.14	-
M	45	0.89	0.72	0.80	0.08	-

 

9.37 The city of Ocean View, California, is considering various proposals regarding the disposal of used tires. All the proposals involve shredding, but the charges for the service and handling of the tire shreds differ in each plan. An incremental B/C analysis was initiated, but the engineer conducting the study left recently. (a) Fill in the blanks in the incremental B/C portion of the table. (b) What alternative should be selected?

Alternative	Initial Investment, $millions	B/C Ratio	Incremental B/C when Compared with Alternative
			P	Q	R	S
P	10	1.1	-	2.83
Q	40	2.4	2.83	-
R	50	1.4			-
S	80	1.5	0.72			-

 

FE REVIEW PROBLEMS

9.38 When a B/C analysis is conducted,

(a) The benefits and costs must be ex-pressed in terms of their present worths.

(b) The benefits and costs must be ex-pressed ill icons of their annual worths.

(c) The benefits and costs must be ex-pressed in terms of their future worths.

(d) The benefits and costs can be ex-pressed in terms of PW, AW, or FW.

9.39 In a conventional B/C ratio,

(a) Disbenefits and M&O costs are subtracted from benefits.

(b) Disbenefits are subtracted from benefits, and M&O costs are added to costs.

(c) Disbenefits and M&O costs are added to costs.

(d) Disbenefits are added to costs, and M&O costs are subtracted from benefits.

9.40 In a modified B/C ratio analysis,

(a) Disbenefits and M&O costs are subtracted from benefits. (b) Disbenefits are subtracted from benefits, and M&O costs are added to costs.

(c) Disbenefits and M&O costs are added to costs.

(d) Disbenefits are added to costs, and M&O costs are subtracted from benefits.

9.41 An alternative has the following cash flows: benefits = $60,000 per year, disbenefits = $17,000 and costs = $35,000 per year. The B/C ratio is closest to

(a) 0.92 (b) 0.96 (c) 1.23 (d) 2.00

9.42 In evaluating three mutually exclusive alternatives by the B/C method, the alternatives were ranked in terms of increasing total equivalent cost (A, B, and C, respectively), and the following results were obtained for the project B/C ratios: 1.1, 0.9, and 1.3. On the basis of these results, you should

(a) Select A. (b) Select C. (c) Select A and C. (d) Compare A and C incrementally.

9.43 Four independent projects are evaluated, using B/C ratios. The ratios are as follows:

Project	A	B	C	D
B/C Ratio	0.71	1.29	1.07	2.03

 

On the basis of these results, you should (a) Reject B and D. (b) Select D only. (c) Reject A only. (d) Compare B. C and D incrementally.

9.44 If two mutually exclusive alternatives have B/C ratios of 1.5 and 1.4 for the lower first-cost and higher first-cost alter-natives, respectively,

(a) The B/C ratio on the increment be-tween them is less than 1.4.

(b) The B/C ratio on the increment between them is between 1.4 and 1.5.

(c) The B/C ratio on the increment between them is greater than 1.4.

(d) The lower-cost alternative is the better one.

 

Extended Exercise

COSTS TO PROVIDE LADDER TRUCK SERVICE FOR FIRE PROTECTION

For many years, the city of Medford has paid a neighboring city (Brewster) for the use of its ladder truck when needed. The charges for the last few years have been $1000 per event when the ladder truck is only dispatched to a site in Medford, and $3000 each time the truck is activated. There has been no annual fee charged. With the approval of the Brewster city manager, the newly hired fire chief has presented a substantially higher cost to the Medford tire chief for the use of the ladder truck:

Annual flat fee $30,000 with 5 years fees paid up front (now)     

Dispatch fee     $3000 per event

Activation fee   $8000 per event

The Medford chief has developed an alternative to purchase a ladder truck, with the following cost estimates for the truck and the fire station addition to house it:

Truck:

Initial cost $850,000

Life 15 years

Cost per dispatch $2000 per event

Cost per activation $7000 per event

Building:

Initial cost $500,000

Life 50 years

The chief has also taken data from a study completed last year and updated it. The study estimated the insurance premium and property loss reductions that the citizenry experienced by having a ladder truck available. The past savings and current estimates, if Medford had its own truck for more rapid response, are as follows:

	Past Average	Estimate if Truck is Owned
Insurance premium reduction, $/year	100,000	200,000
Property loss reduction, $/year	300,000	400,000

 

Additionally, the Medford chief obtained the average number of events for the last 3 years and estimated the future use of the ladder truck. He believes there has been a reluctance to call for the truck from Brewster in the past.

	Past Average	Estimate if Truck is Owned
Number of dispatches per year	10	15
Number of activations per year	3	5

 

Either the new cost structure must be accepted, or a truck must be purchased. The option to have no ladder truck service is not acceptable. Medford has a good rating for its bonds; a discount rate of 6% per year is used for all proposals.

Questions

 Use a spreadsheet to do the following.

1   Perform an incremental B/C evaluation to determine if Medford should purchase a ladder truck.

2   Several of the new city council members are "up in arms" over the new annual fee and cost structure. However, they do not want to build more fire station capacity or own a ladder truck that will be used an average of only 20 times per year. They believe that Brewster can be convinced to reduce or remove the annual $30,000 fee. How much must the annual fee be reduced for the alternative to purchase the ladder truck to be rejected?

3   Another council member is willing to pay the annual fee, but wants to know how much the building cost can change from $500,000 to make the alter-natives equally attractive. Find this first cost for the building.

4   Finally, a compromise proposal offered by the Medford mayor might be acceptable to Brewster. Reduce the annual fee by 50%, and reduce the per event charges to the same amount that the Medford fire chief estimates it will cost if the truck is owned. Then Medford will possibly adjust (if it seems reasonable) the sum of the insurance premium reduction and property loss reduction estimates to just make the arrangement with Brewster more attractive than owning the truck. Find this sum (for the estimates of premium reduction and property loss reduction). Does this new sum seem reasonable relative to the previous estimates?

CASE STUDY

FREEWAY LIGHTING

Introduction

A number of studies have shown that a disproportionate number of freeway traffic accidents occur at night. There are a number of possible explanations for this, one of which might be poor visibility. In an effort to determine whether freeway lighting was economically beneficial for reducing nighttime accidents, data were collected regarding accident frequency rates on lighted and unlighted sections of certain freeways. This case study is an analysis of part of those data.

Background

The Federal Highway Administration (FHWA) places value on accidents depending on the severity of the crash. There are a number of crash categories, the most severe of which is fatal. The cost of a fatal acci-dent is placed at $2.8 million. The most common type of accident is not fatal or injurious and involves only property damage. The cost of this type of accident is placed at $4500. The ideal way to determine whether lights reduce traffic accidents is through before-and-after studies on a given section of free-way. However, this type of information is not readily available, so other methods must be used. One such method compares night to day accident rates (or lighted and unlighted freeways. If lights are beneficial, the ratio of night to day accidents will be lower on the lighted section than on the unlighted one. If there is a difference, the reduced accident rate can be translated into benefits which can be compared to the cost of lighting to determine its economic feasibility. This technique is used in the following analysis.

Economic Analysis

The results of one particular study conducted over a 5-year period are presented in the table below. For illustrative purposes, only the property damage category will be considered. 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 the 839 if there had not been lights on the freeway. This is a difference of 247 accidents. At a cost of $4500 per accident, this results in a net benefit of

B = (247)($4500) = $1.111.500

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 (54.5 miles) of lighted freeway, the installed cost of the lighting is

Installation cost = $3500(87.8/0.067)

= 3500(1310.4) = $4,586,400

The annual power cost based on 1310 poles is Annual power cost

 = 1310 poles(2 bulbs/pole)(0.4 kilowatts/bulb) X (12 hours/day)(365 days/year) x ($0.08/kilowatt-hour) = $367,219 per year

These data were collected over a 5-year period. There-fore, the annualized cost C at i = 6% per year is Total annual cost = $4,586,400(A/P,6%,5) + 367,219 = $1,456,030

 

Freeway Accident Rates, Lighted and Unlighted
	Unlighted		Lighted
Accident Type	Day	Night	Day	Night
Fatal	3	5	4	7
Incapaciting	10	6	28	22
Evident	58	20	207	118
Possible	90	35	384	161
Property damage	379	199	2069	839
Totals	540	265	2697	1147

 

 

The B/C ratio is

B/C = $1,111,500/$1,456,030 = 0.76

 

Since B/C < 1, the lighting is not justified on the basis of property damage alone. To make a final determination about the economic viability of the lighting, the benefits associated with the other accident categories would obviously also have to be considered.

Case Study Exercises

I. What would the B/C ratio be if the light poles were twice as far apart as assumed above?

2. What is the ratio of night to day accidents for fatalities?

3. What would the B/C ratio be if the installation cost were only $2500 per pole?

4. How many accidents would be prevented on the unlighted portion of freeway if it category Consider the property damage category only.

5. Using only the category of property damage, what would the lighted night-to-day accident ratio have to be for the lighting to be economically justified?