# Fundamentals of Engineering Economics

## Quiz 8 :Benefitcost Analysis

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A city that operates automobile parking facilities is evaluating a proposal to erect and operate a structure for parking in its downtown area. Three designs for a facility to be built on available sites have been identified as follows, where all dollar figures are in thousands: At the end of the estimated service life, the selected facility would be torn down and the land would be sold. It is estimated that the proceeds from the resale of the land will be equal to the cost of clearing the site. If the city's interest rate is known to be 10%, which design alternative would be selected on the basis of the benefit-cost criterion?
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Given information: Present net revenue:
Present net revenue can be obtained by using the following formula: …… (1)Where,
P = Present worth
A = Annual equivalent cash flow
i = Interest rate
N = Number of years
C = Annual revenue or annual cost
Benefit-cost ratio is can be obtained using the following formula: …… (2)Present worth of annual revenue for design A:
Equation (1) is used to obtain present worth of annual revenue of Design a. Present worth of annual revenue of design A is .
Present worth of annual cost for design A:
Equation (1) is used to obtain present worth of annual cost of Design a. Present worth of annual cost of design A is .
Present worth of annual revenue for design B:
Equation (1) is used to obtain present worth of annual revenue of Design b. Present worth of annual revenue of design B is .
Present worth of annual cost for design B:
Equation (1) is used to obtain present worth of annual cost of Design b. Present worth of annual cost of design B is .
Present worth of annual revenue for design C:
Equation (1) is used to obtain present worth of annual revenue of Design c. Present worth of annual revenue of design C is .
Present worth of annual cost for design C:
Equation (1) is used to obtain present worth of annual cost of Design c. Present worth of annual cost of design C is .
Benefit cost ratio for design A:
Substitute the respective values in Equation (2) to calculate benefit cost ratio of design a. Cost benefit ratio for design A is .
Benefit cost ratio for design B:
Substitute the respective values in Equation (2) to calculate benefit cost ratio of design b. Cost benefit ratio for design B is .
Benefit cost ratio for design C:
Substitute the respective values in Equation (2) to calculate benefit cost ratio of design c. Cost benefit ratio for design C is . Since design B's cost benefit ratio is higher than other two designs, design B should be selected.

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A city government is considering increasing the capacity of the current wastewater treatment plant. The estimated financial data for the project are as follows: What would be the benefit-cost ratio for this expansion project? (a) 3.26 (b) 3.12 (c) 1.30 (d) 2.23
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Given information: Present equivalent worth of the annual cash flow can be obtained by using the following formula: …… (1)Where,
P = Present equivalent worth
A = Annual cash flow
i = Interest rate
N = Number of years
Present equivalent worth of the future worth can be obtained by using the following formula: …… (2)Where,
F = Future worth
Present equivalent worth:
To obtain the cost benefit ratio, equalize the present equivalent revenue of the project with its present equivalent cost.
Equation (1) and (2) is used to convert the present worth of the project. Benefit-cost ratio:
Benefit-cost ratio is calculated as follows: The benefit-cost ratio for the expansion of the project is .
Hence, option (a) is chosen.

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Two different routes are under consideration for a new interstate highway: For either route, the volume of traffic will be 400,000 cars per year. These cars are assumed to operate at $0.25 per mile. Assuming a 40-year life for each road and an interest rate of 10%, determine which route should be selected. Free Essay Answer: Answer: Given information: Per mile expenses of a car is$0.25.
Annual worth of user benefit for long route :
Each year 400,000 cars travel in either route; hence, the annual cash flow of user benefit of long route travel can be calculated as follows: Thus, long route user benefit is $2,200,000. Annual worth of user benefit for long route : Each year 400,000 cars travel in either route; hence, the annual cash flow of user benefit of shortcut route travel can be calculated as follows: Thus, short route user benefit is$1,000,000.
Annual worth for the benefits, initial investment and the annual cost is calculated as follows for each of the two available alternative routes:
For Long Route ( j ): For Short Route ( k ) Compute the incremental benefit cost ratio using the following formula: Therefore, the incremental benefit-cost ratio is The incremental ratio between long route and shortcut route is . Since the incremental ratio is less than 1, select the lower cost alternative which is the long route.

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Three public investment alternatives are available: A1, A2, and A3. Their respective total benefits, costs, and first costs are given in present worth as follows: These alternatives have the same service life. Assuming that there is no do-nothing alternative, which project would you select, calculating on the basis of the benefit-cost ratio on incremental investment (BC(i))?
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The U.S. government is considering building apartments for its employees working in a foreign country and currently living in locally owned housing. A comparison of two possible buildings indicates the following: Assume the salvage or sale value of the apartments to be 60% of the first investment. Use 10% and a 20-year study period to compute the B/C ratio on incremental investment, and make a recommendation as to the best option. (Do not assume a do-nothing alternative.)
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The city of Jefferson is reviewing the benefits and costs of a potential universal water-metering program. Two options are considered: Option 1: Treated Surface Water Only Benefits of Deferring/Downsizing Water and Sewer Projects-$28.1 million Costs of Metering-$9.3 million Benefit-Cost Ratio-3.02 Option 2: Treated Surface Water Supplemented By 40 ML/Day Groundwater Benefits of Deferring/Downsizing Water and Sewer Projects-$38.9 million Costs of Metering (and groundwater development)-$14.7 million Benefit-Cost Ratio-2.65 Which option should the city implement, assuming that the city has enough money to fund either project? (a) Option 1. (b) Option 2. (c) Neither. (d) Both options.
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A city government is considering two types of town-dump sanitary systems. Design A requires an initial outlay of $400,000 with annual operating and maintenance costs of$50,000 for the next 15 years; design B calls for an investment of $300,000 with annual operating and maintenance costs of$80,000 per year for the next 15 years. Fee collections from the residents would be $85,000 per year. The interest rate is 8%, and no salvage value is associated with either system. (a) By the benefit-cost ratio (BC( i )), which system should be selected? (b) If a new design (design C ), which requires an initial outlay of$350,000 and annual operating and maintenance costs of $65,000, is proposed, would your answer to (a) change? Essay Answer: Tags Choose question tag Auburn Recreation and Parks Department is considering two mutually exclusive proposals for a new softball complex on a city-owned lot. The complex will be useful for 30 years and has no appreciable salvage value (regardless of seating capacity). Assuming an 8% discount rate, which of the following statements is incorrect ? (a) Select A1 because it has the largest B/C ratio. (b) Select A1 because it has the most benefits per seating capacity. (c) Select A1 because it has the largest PW. (d) Select A1 because the incremental benefits generated from A2 are not large enough to offset the additional investment ($200,000 more than A1).
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A local government is considering four possible countermeasures to reduce crimes in the municipal park. Since each option has a different program length of duration, all benefits and costs are expressed in terms of equivalent annual values. Because of a limited budget, only one countermeasure will be implemented. Which countermeasure would you recommend based on the B/C analysis?
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Consider the following two mutually exclusive projects: (a) Which project has the higher profitability index at i = 7%? (b) Which project would you choose if you can raise an unlimited amount of funds in financing either project at 7%? Use the profitability index rule.
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The Ulrich Corporation is trying to choose between the following two mutually exclusive design projects. If the required rate of return is 10%, which of the following statements is correct? (a) Select A2 because it has a higher PI. (b) Select A2 because it has a higher ROR. (c) Select A1 because its incremental PI exceeds 1. (d) Not enough information to decide.
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A regional airport is considering installing a new baggage handling system. Two different vendors submitted bids on the system. The airport is to replace its current system. The cash flows that describe each baggage handling system with respect to the current system are given below. Which of the following statements is correct? (a) Vendor B is preferred as long as the airport's interest rate is less than or equal to 15.73% (b) Vendor B is preferred as long as the airport's interest rate is more than 5%. (c) Vendor B is preferred as long as the airport's interest rate is less than 7%. (d) Vendor A is preferred if the airport's interest rate is more than 15.73%.
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A city is trying to decide whether to build a parking garage. An engineering plan calculates that the building will cost $2 million with costs of$200,000 per year to operate. Our analysis of operating revenue determines that the garage will start to earn revenues of $500,000 per year in the second year. The city is interested in knowing whether this project will be profitable over the next eight years at 6%. The project's B/C ratio is closest to (a) 1 (b) 0.87 (c) 1.33 (d) 2.50 Multiple Choice Answer: Tags Choose question tag A city government is considering increasing the capacity of the current wastewater treatment plant. The estimated financial data for the project are as follows: Calculate the benefit-cost ratio for this capacity expansion project. Essay Answer: Tags Choose question tag A local government is considering promoting tourism in the city. It will cost$5,000 to develop a plan. The anticipated annual benefits and costs are as follows: Annual benefits: Increased local income and tax collections $117,400 Annual support service: Parking lot expansion, rest room, patrol car, and street repair$48,830 If the city government uses a discount rate of 6% and a study period of five years, is this tourism project justifiable according to the benefit-cost analysis?
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The federal government is planning a hydroelectric project for a river basin. In addition to producing electric power, this project will provide flood control, irrigation, and recreational benefits. The estimated benefits and costs expected to be derived from the three alternatives under consideration are listed as follows: The interest rate is 10%, and the life of each project is estimated to be 50 years. (a) Find the benefit-cost ratio for each alternative. (b) Select the best alternative, according to BC(i).
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Consider the following two projects: (a) Calculate the profitability index for A1 and A2 at an interest rate of 6%. (b) Determine which project(s) you should accept (1) if you have enough money to undertake both and (2) if you could take only one due to a budget limit.
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The government is considering undertaking one of the four projects A1, A2, A3, and A4. These projects are mutually exclusive, and the estimated present values of their costs and of their benefits are shown in millions of dollars as follows: All of the projects have the same duration. Assuming that there is no do nothing alternative, which alternative would you select? Justify your choice by using a benefit-cost ratio on incremental investment (BC(i)).
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The Texas Department of Transportation is considering in improving accident prevention countermeasures on the state's accident-prone public highways and bridges. The following set of projects has been recommended for evaluation at three different locations and assumes the budget is $20 million. All alternatives are mutually independent projects. Determine the best combination of projects within the budget constraint. (a) II-B and III-B only (b) I-A, II-A, and III-B (c) I-B, III-A, and III-B (d) II-B and III-B Multiple Choice Answer: Tags Choose question tag The city of Portland Sanitation Department is responsible for the collection and disposal of all solid waste within the city limits. The city must collect and dispose of an average of 300 tons of garbage each day. The city is considering ways to improve the current solid-waste collection and disposal system: The present collection and disposal system uses Dempster Dumpmaster front-end loaders for collection and disposal. Each collecting vehicle has a load capacity of 10 tons, or 24 cubic yards, and dumping is automatic. The incinerator in use was manufactured in 1962. It was designed to incinerate 150 tons every 24 hours. A natural gas afterburner has been added in an effort to reduce air pollution; however, the incinerator still does not meet state air-pollution requirements. Prison-farm labor is used for the operation of the incinerator. Because the capacity of the incinerator is relatively low, some trash is not incinerated but is taken to the city landfill instead. The trash landfill and the incinerator are located approximately 11 miles and 5 miles, respectively, from the center of the city. The mileage and costs in person-hours for delivery to the disposal sites are excessive; a high percentage of empty vehicle miles and person-hours are required because separate methods of disposal are used and the destination sites are remote from the collection areas. The operating cost for the present system is$905,400. This figure includes $624,635 to operate the prison-farm incinerator,$222,928 to operate the existing landfill, and $57,837 to maintain the current incinerator. The proposed system calls for a number of portable incinerators, each with 100-ton-per-day capacity for the collection and disposal of refuse waste from three designated areas within the city. Collection vehicles will also be staged at these incineration disposal sites with the necessary plant and support facilities for incinerator operation and collection-vehicle fueling and washing, and with support building for stores as well as shower and locker rooms for collection and site personnel. The pickup and collection procedure remains essentially the same as in the existing system. The disposal-staging sites, however, are located strategically in the city according to the volume and location of wastes collected; thus, long hauls are eliminated and the number of miles the collection vehicles must travel from pickup to disposal site and back is reduced. Four variations of the proposed system are being considered, containing one, two, three, and four incinerator-staging areas, respectively. The type of incinerator used in each variation is a modular prepackaged unit, which can be installed at several sites in the city. All of the four units meet state and federal standards on exhaust emissions. The city of Portland needs 24 units, each with a rated capacity of 8.5 tons of garbage per 24 hours. The price per unit is$137,600, which means a capital investment of about $3,302,000. The estimated plant facilities, such as housing and foundation, are estimated to cost$200,000 per facility. This figure is based on a plan incorporating four incinerator plants strategically located around the city. Each plant would house eight units and would be capable of handling 100 tons of garbage per day. Additional plant features, such as landscaping, are estimated to cost $60,000 per plant. The annual operating cost of the proposed system would vary according to the type of system configuration. It takes about 1.5 to 1.7 MCF of fuel to incinerate 1 ton of garbage. The conservative 1.7 MCF figure was used for total cost, resulting in a fuel cost of$4.25 per ton of garbage at a cost of $2.50 per MCF. Electric requirements at each plant will be 230 kW per day. For a plant operating at full capacity, that requirement means a$0.48-per-ton cost for electricity. Two workers can easily operate one plant, but safety factors dictate that there will be three operators at a cost of $7.14 per hour per operator. This translates to a cost of$1.72 per ton. The maintenance cost of each plant is estimated to be $1.19 per ton. Since the proposal for three plants will require fewer transportation miles, it is necessary to consider the savings accruing from this operating advantage. For example, the configuration with three plant locations will save 6.14 miles per truck per day on average. At an estimated$0.30-per-mile cost, this would mean that an annual savings of $15,300 would be realized from minimum trips to the landfill. Labor savings are also realized because the shorter routes would permit more pickups per day. This plan thus offers an annual labor savings of$103,500 for three incinerators. The following table summarizes all costs, in thousands of dollars, associated with the present and proposed systems. A bond will be issued to provide the necessary capital investment at an interest rate of 8% with a maturity date 20 years. The proposed systems are expected to last 20 years with negligible salvage values. If the current system is to be retained, the annual O M costs would be expected to increase at an annual rate of 10%. The city will use the bond interest rate as the interest rate for any public-project evaluation. (a) Determine the operating cost of the current system in terms of dollars per ton of solid waste. (b) Determine the economics of each solid-waste disposal alternative in terms of dollars per ton of solid waste. (c) Select the best alternative based on the benefit-cost ratio.