This document discusses benefit-cost analysis for public sector projects. It covers analyzing single projects and multiple alternatives. For single projects, the benefit-cost ratio is calculated by dividing the present worth of benefits by the present worth of costs. A ratio of 1 or greater means the project is justified. For multiple alternatives, alternatives are ordered by increasing cost and incremental benefit-cost ratios are calculated to determine which alternative is selected at each step. Direct benefits are compared to a do-nothing option first before being compared to each other. The document provides examples of applying these techniques.

1. © 2014, McGraw-Hill Education All rights reserved7 - 1
Slides to accompany Blank and Tarquin
Basics of Engineering Economy, 2nd
ed.
Basics of Engineering Economy
by
Leland Blank and Anthony Tarquin
Slides to accompanySlides to accompany
Chapter 7
Benefit/Cost Analysis
and Public Sector Projects

2. Chapter 7 – Benefit/Cost Analysis
PURPOSE
Learn about
and perform a benefit/cost
analysis
TOPICS
B/C analysis of single project
B/C analysis of 2 or more
alternatives
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3. Sec 7.1 – Public Sector Project Estimates
Analysis requires estimates as accurate as possible for costs, benefits, and
dis-benefits.
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Description
Costs: expenditures to the
government to build,
maintain, & operate
project; salvage/sales
value possible
Benefits: advantages to
public; income and
savings
Examples
• Bridge construction cost
• Annual cost of drug
abusers’ treatment
program
• New jobs and salary
money
• Reduced property taxes
• Lower transportation
costs; less gas used

4. Sec 7.1 – Public Sector Project Estimates
Disbenefits: Expected undesirable, negative
consequences of project to owners – the public; usually
these are economic disadvantages estimable in
monetary units
Disbenefits are not always included in the analysis; subject to
political and special interest challenges
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Examples
 $150M school bond issue -- Increased property taxes
 Tourist amusement park -- Higher local car insurance
premiums based on increased traffic accidents
 New state prison – Reduced property values for houses
in adjacent subdivisions

5. Sec 7.2 – B/C Analysis – Single Project
Convert all estimates to
PW, AW or FW values at
discount rate i%. Using PW
PW of benefits
PW of costs
Same formula for AW or FW
All + signs, costs included
exceptexcept
Salvage has – sign; it is
subtracted from costs
If disbenefits are estimated,
subtract from benefits
Use PW, AW or FW for B/C
If D is added to costs in
denominator, the B/C value
changes, but economic
decision is the same
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6. Sec 7.2 – B/C Analysis – Single Project
Guideline for economic justification
If B/C ≥ 1.0 project justified
If B/C < 1.0 project not acceptable
Example: P = $15 M A = $500 K per year
B = $1,500 K per year D = $200 K per year
i = 6% n = 10 years
AW equivalent of P = 15M(A/P,6%,10) = $2,038 K
B/C = = 0.51
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7 - 6

7. Sec 7.2 – B/C Analysis – Single Project
TWO ALTERNATE B/C MEASURES
►Determine PW, AW or FW equivalent; denominator is only
initial investment with any salvage estimate
Same selection guideline: accept if Modified B/C ≥ 1.0
►If difference relation is desired, subtract net costs from net
benefits, once equivalence is determined
B-C Difference = B – C
Selection guideline: accept if B-C Difference ≥ 0
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8. Sec 7.3 – B/C Analysis for ≥ 2 Alternatives
• Technique similar to incremental ROR evaluation using ∆i* for ME
alternatives
• Find equivalent PW, AW or FW; calculate incremental B/C measure,
that is, ∆B/C
• Comparison is always between 2 alternatives at a time
Selection guideline
If ∆B/C ≥ 1.0 → select larger-cost alternative
Otherwise → select lower-cost alternative
• Decision is based on incrementally justified
total alternative cost, not incremental initial investment
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9. Sec 7.3 – B/C Analysis for ≥ 2 Alternatives
To perform the ∆B/C analysis correctly
 Order alternatives by increasing equivalent total cost
Note: If this is not done, a larger-cost alternatives that is
actually justifiable may be rejected because ∆B/C < 1 results
 Equal service requirement is necessary. If lives are
short, use LCM method
Note: Public projects usually have long lives (> 25 or 30 years),
so lives are equal, or long enough to use capitalized cost
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10. Sec 7.3 – B/C Analysis for ≥ 2 Alternatives
Two types of benefits
They require different treatment during ∆B/C analysis
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USAGE COST ESTIMATES
DEFINITION
Implied benefits are based
on difference in cost
estimates of alternatives
TREATMENT
Comparison of alternatives
is against each other only
DIRECT BENEFIT ESTIMATES
DEFINITION
Benefits are actually
estimated for each alternative
TREATMENT
Comparison of alternatives is
against DN first, then each
other (Similar to revenue alternatives
in ROR analysis)

11. Sec 7.3-B/C Analysis for ≥ 2 ME Alternatives
PROCEDURE FOR ∆B/C OF MUTUALLY EXCLUSIVE ALTERNATIVES
1. Determine equivalent value for costs, benefits (and
disbenefits, if estimated)
2. Order alternatives by increasing total equivalent cost (for
direct benefit alternatives, add DN first)
3. For each pair of alternatives (call them 2 and 1), determine
incremental C and B over LCM. For usage cost alternative,
∆B = usage cost2 – usage cost1
4. Determine ∆B/C or ∆(B-D)/C
5. If ∆B/C ≥ 1.0, B is survivor; otherwise, A is survivor
6. Compare survivor with next alternative; continue steps (3) –
(5) until only 1 alternative remains
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12. Sec 7.3 – B/C Analysis – Example 1
Equal 30-year life; i = 5%; direct benefit alternatives
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Step 1. No disbenefits; use equivalent AW of costs
AW1 = 10 M(A/P,5%,30) + 35,000 = $685,500
AW2 = 15 M(A/P,5%,30) + 55,000 = $1,030,750
Step 2. Add DN option with C = $0 and B = $0;
comparison order is DN, 1, 2
Step 3. Compare 1-to-DN over 30 years
cont →

13. Sec 7.3 – B/C Analysis – Example 1
Step 4. ∆B/C = 800,000/685,500 = 1.17
Step 5. 1.17 > 1, eliminate DN; 1 is survivor
Step 6. Compare 2-to-1 (back to step 3)
Step 3. Compare 2-to-1
∆B = 1,050,000 – 800,000 = $250,000
∆C = 1,030,750 – 685,500 = $345,250
Step 4. ∆B/C = 250,000/345,250 = 0.72
Step 5. 0.72 < 1, eliminate 2; 1 is survivor
Step 6. Select design 1
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14. Sec 7.3 – B/C Analysis – Example 2
8-year study period; i = 7%; usage cost alternatives
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cont →
Step 1. Total cost is sum of two incentives. Determine AW
over 8 years. For proposal 1
AW1 = 250,000(A/P,7%,8) + 25,000 = $66,867

15. Sec 7.3 – B/C Analysis – Example 2
Step 2. Order alternatives by increasing AW of total costs
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cont →
Step 3. Compare 2-to-1 over 8 years; ∆usage costs for ∆B
∆B = entrance fee decrease + sales tax receipt increase
= 50,000 + 10,000 = $60,000
∆C = 93,614 – 66,867 = $26,747
Step 4. ∆B/C = 60,000/26,747 = 2.24
Step 5. 2.24 > 1.0; eliminate 1; 2 survives

16. Sec 7.3 – B/C Analysis – Example 2
Step 6.Compare 3-to-2 (back to step 3)
Table below completes the analysis
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cont →

17. Sec 7.3 – B/C Analysis – Example 2
Results of comparisons
•Compare 3-to-2: ∆B/C = 25,000/40,120 = 0.62
Proposal 2 survives
•Compare 4-to-2: ∆B/C = 220,000/120,360 = 1.83
Proposal 2 eliminated; 4 survives
Conclusion: Select Proposal 4
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18. Sec 7.3 - B/C Analysis-Additional Comments
 Long lives (considered infinite for analysis purposes)
 Use capitalized cost to determine PW or AW. Incremental
analysis is performed after using the equivalency relations
AW = PW(i) or PW = AW/i
 Independent Projects (with no budget limitation)
 No incremental analysis needed
 Compare each project to DN option
 Select all projects with B/C ratio ≥ 1.0
 Example 7.5 illustrates both of these situations
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