This document discusses benefit-cost analysis for public sector projects. It defines key terms like costs, benefits, and dis-benefits. It explains that the conventional B/C ratio compares benefits minus dis-benefits to costs. A modified B/C ratio includes maintenance and operation costs in the numerator. It provides examples of calculating B/C ratios for single projects and using the incremental B/C method to select between alternatives. Engineers must consider ethical issues when involved in public policy making and planning projects.

1. Benefit/Cost Analysis
LO4a
EGN 3203 Engineering Economics
LO3 – a

2. LEARNING OUTCOMES
9-2
1. Explain difference in public vs. private sector projects
2. Calculate B/C ratio for single project
3. Select better of two alternatives using B/C method

3. 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
9-3

4. • 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
9-4
Introduction

5. 9-5
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

6. 9-6
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

7. • 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.
9-7
Benefit/Cost Analysis

8. 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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9. • The conventional B/C ratio, probably the most widely used,
• Dis-benefits are subtracted from benefits, not added to costs.
9-9
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:

10. • 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 is
PW 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.
9-10
Benefit/Cost Analysis

11. B/C Relations : summary
cost
Benefit (B) -- Advantages to the public
Disbenefit (D) -- Disadvantages to the public
Cost (C) -- Expenditures by the government
Note: Savings to government are subtracted from costs
Conventional B/C ratio = (B–D) / C
Modified 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 FW
Note 2 : Do not use minus sign ahead of costs
9-11
Must identify each cash flow as either benefit, dis-benefit, or cost

12. 9-12
Benefit/cost analysis
If B/C ≥ 1.0, project is economically justified at
discount rate applied
If 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

13. 9-13
Conventional B/C ratio =
B - D
C
Modified B/C ratio = B – D – M&O
C
If B/C ≥ 1.0,
accept project;
otherwise, reject
PI =
PW of initial investment
If PI ≥ 1.0,
accept project;
otherwise, reject
PW of NCFt
Denominator is
initial investment

14. 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 the
project be undertaken?
Solution: Express all values inAW terms and find B/C ratio
B = $175,000
D = $25,000
C = 1,400,000(A/P,10,%6)+40,000$ = 230,218$
B/C= (175,000 – 25,000) / 230,218
= 0.65 < 1.0
Do not build project
9-14
Example: B/C Analysis – Single Project
Annual – use AW

15. 9-15
Example: B/C Analysis – Single Project
Example Conventional & Modified B/C
B
D
A
P

16. 9-16
Example: B/C Analysis – Single Project
Conventional B/C
Modified B/C
Example Conventional & Modified B/C

17. 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
9-17
Example: B/C Analysis – Single Project
Example Conventional B/C

18. 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
B = 900,000(1.5) – 900,000 = $450,000
C = 300,000 + 25,000(P/A,6%,20)
= 300,000 + 25,000(11.4699)
= $586,748
B/C = 450,000/586,748 = 0.77
9-18
Example: B/C Analysis – Single Project
Example Conventional B/C

19. 9-19
Example: B/C Analysis – Single Project
Example profitability index (PI),

20. 9-20
Example: B/C Analysis – Single Project
Example profitability index (PI),

21. Defender, Challenger and Do NothingAlternatives
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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22. 9-22
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

23. 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

24. Example: Incremental B/C Analysis
Compare 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 Y
X vs. DN: (B-D)/C = (110,000 – 20,000) / 97,080 = 0.93
Alternative X Y
First cost, $ 320,000 540,000
M&O costs, $/year 45,000 35,000
Benefits, $/year 110,000 150,000
Disbenefits, $/year 20,000 45,000
Life, years 10 20

25. 9-25
Example: ∆B/C Analysis;

26. 9-26
Example: ∆B/C Analysis;

27. 9-27
Example: ∆B/C Analysis;

28. Solution
East vs. DN: (B-D)East = 990,000 – 120,000 = $870,000 per year
CEast = 11,000,000(0.06) + 100,000 = $760,000 per year
(B-D)/C = 870,000/760,000
= 1.14
Eliminate DN
West 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 = $950,000
ΔB/C = 1,430,000/950,000
= 1.51
Select 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.
9-28

29. Example: ∆B/C Analysis; Selection Required
Must 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 X
AW 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, $ 320,000 540,000
M&O costs, $/year 45,000 35,000
Benefits, $/year 110,000 150,000
Disbenefits, $/year 20,000 45,000
Life, years 10 20

30. 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 Ethics
9-30