Benefit/Cost AnalysisLO4a

EGN 3203 Engineering EconomicsLO3 – a

LEARNING OUTCOMES

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1. Explain difference in public vs. private sector projects

2. Calculate B/C ratio for single project3. Select better of two alternatives using B/C

method

Introduction • Evaluation methods of previous LO are usually applied to alternatives

in the private sector.• This LO introduces economic consideration for the public sector. • In the case of public projects, the owners and users (beneficiaries)

are the citizens and residents of a government unit—city, county, state, province or nation. • Government units provide the mechanisms to raise capital and

operating funds.• This chapter also introduces service sector projects and discusses

how their economic evaluation is different from that for other projects

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• A public sector project is a product, service, or system used, financed, and owned by the citizens of any government level. The primary purpose is to provide service to the citizenry for the public good at no profit. Areas such as public health, criminal justice, safety, transportation, welfare, and utilities are all publically owned and require economic evaluation.

Some public sector examples:• Hospitals and clinics• Parks and recreation• Utilities: water, electricity, gas, sewer, sanitation• Schools: primary, secondary, community• colleges, universities

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Introduction

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Life Longer (30 – 50+ years) Shorter (2 – 25 years)

Annual CF No profit Profit-driven

Funding Taxes, fees, bonds, etc.

Stocks, bonds, loans, etc.

Interest rate Lower Higher

Selection criteria Multiple criteria Primarily ROR

Environment of evaluation Politically inclined Economic

Characteristic Public Private

Size of Investment Large Small, medium, large

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Contractors does not share project risk Fixed price - lump-sum payment Cost reimbursable - Cost plus, as

negotiated

Contractor shares in project risk Public-private partnerships (PPP), such as:

Design-build projects - Contractor responsible from design stage to operations stage

Design-build-operate-maintain-finance (DBOMF) projects - Turnkey project with contractor managing financing (manage cash flow); government obtains funding for project

• To perform a benefit/cost economic analysis of public alternatives, the costs (initial and annual), the benefits, and the dis-benefits, if considered, must be estimated as accurately as possible in monetary units.• Costs—estimated expenditures to the government entity for

construction, operation, and maintenance of the project, less any expected salvage value.• Benefits—advantages to be experienced by the owners, the

public.• Dis-benefits—expected undesirable or negative consequences to

the owners if the alternative is implemented. Dis-benefits may be indirect economic disadvantages of the alternative.

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Benefit/Cost Analysis

Benefit/Cost Analysis• The benefit/cost ratio is relied upon as a fundamental analysis method

for public sector projects. • All cost and benefit estimates must be converted to a common

equivalent monetary unit (PW, AW, or FW) at the discount rate (interest rate). The B/C ratio is then calculated using one of these relations:

• Present worth and annual worth equivalencies are preferred to future worth values. • The sign convention for B/C analysis is positive signs; costs are preceded

by a + sign. • Salvage values and additional revenues to the government, when they

are estimated, are subtracted from costs in the denominator. • Dis-benefits are considered in different ways depending upon the model

used.

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• The conventional B/C ratio, probably the most widely used, • Dis-benefits are subtracted from benefits, not added to costs.

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Benefit/Cost Analysis

• The modified B/C ratio includes all the estimates associated with the project such as maintenance and operation. (M&O) costs are placed in the numerator and treated as dis-benefits. The denominator includes only the initial investment. • all amounts are expressed in PW, AW, or FW terms, the modified B/C

ratio is calculated as

Two types of analyses:

• It is possible to develop a direct formula connection between the B/C of a public sector and B/C of a private sector project that is a revenue alternative ; both revenues and costs are estimated.• the PW for project cash flows isPW of project = PW of revenue - PW of costs

• This relation can be slightly rewritten to form the profitability index (PI), which can be used to evaluate revenue projects in the public or private sector.

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Benefit/Cost Analysis

B/C Relations : summary

cost

Benefit (B) -- Advantages to the public Disbenefit (D) -- Disadvantages to the public Cost (C) -- Expenditures by the governmentNote: Savings to government are subtracted from costs

Conventional B/C ratio = (B–D) / CModified B/C ratio = [(B–D) – C] / Initial Investment Profitability Index = NCF / Initial Investment

Note 1 : All terms must be expressed in same units, i.e., PW, AW, or FWNote 2 : Do not use minus sign ahead of costs

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Must identify each cash flow as either benefit, dis-benefit, or cost

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Benefit/cost analysisIf B/C ≥ 1.0, project is economically justified at

discount rate appliedIf B/C < 1.0, project is not economically acceptable

Profitability index analysis of revenue projects

If PI ≥ 1.0, project is economically justified at discount rate applied

If PI < 1.0, project is not economically acceptable

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Conventional B/C ratio = B - DC

Modified B/C ratio = B – D – M&OC

If B/C ≥ 1.0, accept project; otherwise, reject

PI =PW of initial investment

If PI ≥ 1.0,accept project; otherwise, reject

PW of NCFtDenominator is initial investment

A flood control project will have a first cost of $1.4 million with an annual maintenance cost of $40,000 and a 10 year life. Reduced flood damage is expected to amount to $175,000 per year. Lost income to farmers is estimated to be $25,000 per year. At an interest rate of 6% per year, should theproject be undertaken?

Solution: Express all values in AW terms and find B/C ratio

B = $175,000 D = $25,000

C = 1,400,000(A/P, 10 ,% 6 ) + 4 0, 0 0 0 $ = 2 3 0 ,2 1 8 $ B/C= (175,000 – 25,000) / 230,218

= 0.65

< 1.0

Do not build project

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Example: B/C Analysis – Single Project

Annual – use AW

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Example: B/C Analysis – Single ProjectExample Conventional & Modified B/C

BD

A

P

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Example: B/C Analysis – Single Project

Conventional B/C

Modified B/C

Example Conventional & Modified B/C

The cost of grading and spreading gravel on a short rural road is expected to be $300,000. The road will have to be maintained at a cost of $25,000 per year. Even though the new road is not very smooth, it allows access to an area that previously could only be reached with off-road vehicles. The improved accessibility has led to a 150% increase in the property values along the road. If the previous market value of a property was $900,000, calculate the B/C ratio using an interest rate of 6% per year and a 20-year study period.

Solution

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Example: B/C Analysis – Single ProjectExample Conventional B/C

The cost of grading and spreading gravel on a short rural road is expected to be $300,000. The road will have to be maintained at a cost of $25,000 per year. Even though the new road is not very smooth, it allows access to an area that previously could only be reached with off-road vehicles. The improved accessibility has led to a 150% increase in the property values along the road. If the previous market value of a property was $900,000, calculate the B/C ratio using an interest rate of 6% per year and a 20-year study period.

SolutionB = 900,000(1.5) – 900,000 = $450,000C = 300,000 + 25,000(P/A,6%,20)= 300,000 + 25,000(11.4699)= $586,748B/C = 450,000/586,748 = 0.77

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Example: B/C Analysis – Single ProjectExample Conventional B/C

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Example: B/C Analysis – Single ProjectExample profitability index (PI),

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Example: B/C Analysis – Single ProjectExample profitability index (PI),

Defender, Challenger and Do Nothing Alternatives

When selecting from two or more ME alternatives, there is a: Defender – in-place system or currently selected alternative Challenger – Alternative challenging the defender Do-nothing option – Status quo system

General approach for incremental B/C analysis of two ME alternatives:

Lower total cost alternative is first compared to Do-nothing (DN) If B/C for the lower cost alternative is < 1.0, the DN option is compared to

∆B/C of the higher-cost alternative If both alternatives lose out to DN option, DN prevails, unless

overriding needs requires selection of one of the alternatives

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Procedure similar to ROR analysis for multiple alternatives

(1) Determine equivalent total cost for each alternative(2) Order alternatives by increasing total cost(3) Identify B and D for each alternative, if given, or go to step 5(4) Calculate B/C for each alternative and eliminate all with B/C < 1.0(5) Determine incremental costs and benefits for first two

alternatives(6) Calculate ∆B/C; if >1.0, higher cost alternative becomes defender(7) Repeat steps 5 and 6 until only one alternative remains

Select higher cost alternative

B/C Analysis of Independent Projects

Independent projects comparison does not require incremental analysis

Compare each alternative’s overall B/C with DN option

+ No budget limit: Accept all alternatives with B/C ≥ 1.0

+ Budget limit specified: capital budgeting problem; selection follows different procedure (discussed in chapter 12)

9-23© 2012 by McGraw-Hill All Rights Reserved

Example: Incremental B/C AnalysisCompare two alternatives using i = 10% and B/C ratio

Eliminate X Eliminate DNY vs. DN: (150,000 – 45,000) / 98,428 = 1.07

9-24© 2012 by McGraw-Hill All Rights Reserved

Solution: First, calculate equivalent total cost AW of costsX = 320,000(A/P,10%,10) + 45,000 = $97,080 AW of costsY = 540,000(A/P,10%,20) + 35,000 = $98,428

Order of analysis is X, then YX vs. DN: (B-D)/C = (110,000 – 20,000) / 97,080 = 0.93

Alternative X YFirst cost, $ 320,000 540,000M&O costs, $/year 45,000 35,000Benefits, $/year 110,000 150,000Disbenefits, $/year 20,000 45,000Life, years 10 20

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Example: ∆B/C Analysis;

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Example: ∆B/C Analysis;

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Example: ∆B/C Analysis;

SolutionEast vs. DN: (B-D)East = 990,000 – 120,000 = $870,000 per yearCEast = 11,000,000(0.06) + 100,000 = $760,000 per year(B-D)/C = 870,000/760,000= 1.14Eliminate DNWest vs. East: Δ(B-D) = (2,400,000 – 100,000) – (990,000 – 120,000) = $1,430,000 ΔC = [27,000,000(0.06) + 90,000] – 760,000 = $950,000ΔB/C = 1,430,000/950,000= 1.51Select West location

9.31 The estimates shown are for a bridge under consideration for a river crossing in Wheeling, West Virginia. Use the B/C ratio method at an interest rate of 6% per year to determine which bridge, if either, should be built.

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Example: ∆B/C Analysis; Selection RequiredMust select one of two alternatives using i = 10% and ∆B/C ratio

Alternative X Y

Solution: Must select X or Y; DN not an option, compare Y to XAW of costsX = $97,080 AW of costsY = $98,428

Incremental values: ∆B = 150,000 – 110,000 = $40,000

Y vs. X: (∆B - ∆D) / ∆C = (40,000 – 25,000) / 1,348 = 11.1 Eliminate X

9-29© 2012 by McGraw-Hill All Rights Reserved

∆D = 45,000 – 20,000 = $25,000∆C = 98,428 – 97,080 = $1,348

First cost, $ 320,000 540,000M&O costs, $/year 45,000 35,000Benefits, $/year 110,000 150,000Disbenefits, $/year 20,000 45,000Life, years 10 20

Ethical Considerations

Engineers are routinely involved in two areas where ethics may be compromised:

Public policy making – Development of strategy, e.g., water system management (supply/demand strategy; ground vs. surface sources)

Public planning - Development of projects, e.g., water operations (distribution, rates, sales to outlying areas)

Engineers must maintain integrity and impartiality and

always adhere to Code of Ethics9-30