Matakuliah
Tahun
: D0762 – Ekonomi Teknik
: 2009
Benefit Cost Ratio
Course Outline 8
Outline
•
•
•
•
Definition
Benefit Cost Ratio for Single Project
Alternative Selection
B/C selection from multiple alternatives
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Definition
• Benefit Cost Ratio is a method for selecting alternatives
for public works project.
• B/C method of analysis is based on the ratio of the
benefits to costs associated with a particular project
• First steps : determine which of the elements are
benefits, disbenefits, and costs
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What is Public Project?
• Public Sector is owned by the citizens
• Public Sector Projects provide needed services at ‘no
profit’
• Facts…
• Generally large investment size
• Long life span (30-50 years)
• Revenues are used to cover future cost
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Terminology
• Costs: estimated expenditures for operations,
maintenance, and construction -- Government
• Benefits: economic advantages experienced by the
owners -- Public
• Disbenefits: expected undesirable consequences to
the owners -- Public
• Note: defining the benefit and disbenefit are not as
easy as one two three for some public sectors
• Discount rate: interest rate for public sector projects
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Be Consistent!
• Select a viewpoint prior determining costs, benefits, and disbenefits
and stick with one only!
• The Do-Nothing option!
• Several viewpoints:
• Citizen
• Economic development
• Job creation/retention, etc
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Conventional B/C Ratio - Single Project
• Calculated as follows
B/C =benefits –disbenefits
B-D=
C
Costs
B/C = PW(B-D) = AW(B-D) =
FW(B-D)
PW(C)
AW(C)
FW(C)
• Decision Criteria
• If B/C ≥ 1, then … accept the alternative at the discounted rate
• Otherwise, … not acceptable however it can still be funded for
other reasons…
NOTE
• In B/C analyses, costs are not preceded by a minus sign
• Salvage values are subtracted from costs
• Disbenefits are generally subtracted from benefits
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Modified B/C For Single Project
• Conventional B/C
• Modified B/C
benefits - disbenefits
B-D
B/C =
=
costs
C
benefits - disbenefits - M&O costs
initial investment
• Benefit and Cost difference measure of worth
B – C, if (B-C) ≥ 0, accept the project and vice versa
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Alternative Selection: B/C Incremental Analysis
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•
Given: ≥ 2 mutually exclusive alternatives
Steps…
•
•
•
Estimate total equivalent costs for all alternatives
Rank the alternatives from low to high based upon total costs
in the denominator of the ratio
Calculate the incremental cost (ΔC) for the larger-cost
alternative
Calculate the total benefits and disbenefits for both
benefits - disbenefits
B-D
alternatives – incremental benefits
B / C = (ΔB) for the larger-cost
=
costs
C
alternative  Δ(B-D)
Calculate ΔB/C ratio
•
Accept the higher cost alternative if ΔB/C ≥1
•
•
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B/C Incremental Analysis for Multiple Alternatives
• Given ≥ 3 mutually exclusive alternatives, must
select one
• Conduct pairwise ΔB/C
• Selection rule: choose the largest-cost alternative
after justfied by incremental B/C ≥1
• Note: any alternatives that have an overall B/C <1.0
can be eliminated immediately and no need not to
be considered in the incremental analysis
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Independent Projects
• As long as the budget is unlimited,
• Compare each alternative with DN
• Choose all that have B/C ≥ 1
• If the budget is limited,
• Use optimization methodology (capital budgeting)
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Example …
(Example 9.1) The Wartol Foundation, a nonprofit educational research
organization, is contemplating an investment of $1.5 million in grants to
develop new ways to teach people the rudiments of a profession. The grants
will extend over a 10-year period and will create an estimated savings of
$500,000 per year in faculty salaries, student tuition and fees, and other
expenses. The foundation uses a rate of return of 6% per year on all grant
awards.
Since the new program will be in addition to ongoing activities, an estimated
$200,000 per year will be removed from other program funding to support
this educational research. To make this program successful, a $50,000-peryear operating expense will be incurred by the foundation from its regular
M&O budget.
Use the following analysis methods to determine if the program is justified
over a 10-year period: (a) conventional B/C, (b) modified B/C, (c) (B-C)
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Analysis
Example …(Cont’d)
• AW, PW, or FW?
Use the one with…
• Conventional B/C
B/C = (500k – 200k)/(203,805+50k) = 1.18, thus…
• Modified B/C
B/C = (500k – 200k – 50k)/203,805 = 1.23, thus…
• Benefit and Cost Difference
B-C = (500k – 200k) – (203,805+50k) = $46,195, thus…
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Another One…
(Example 9.3) Two routes are under consideration for a new interstate
highway segment. The northerly route N would be located about 5 km from
the central business district and would require longer travel distances by
local commuter traffic. The southerly route S would pass directly through the
downtown area, and, although its construction cost would be higher, it would
reduce the travel time and distance for local commuters. Assume that the
costs for the two routes are as follows:
Route N
Route S
Initial cost, $
10,000,000
15,000,000
Maintenance cost/year, $
35,000
55,000
Road-user cost/year, $
450,000
200,000
If the roads are assumed to last 30 years with no salvage value, which route
should be selected on the basis of B/C analysis using an interest rate of 5%/
year?
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Another One…(Cont’d)
• AW, PW, or FW?
Use the one with…
• AWN = $685,500 and AWS = $1,030,750
Incremental cost value = $345,250/year
Incremental benefit = $250,000/year
B/C ratio = $250,000/$345,250 = .724
thus…
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Example
(Example 9.4) Consider the four mutually exclusive
alternatives, apply incremental B/C analysis to select the
best alternative for a MARR = 10% per year. Use a PW
analysis
Location
A
B
C
D
Building cost, $
-200,000
-275,000
-190,000
-350,000
Annual cash flow, $
22,000
35,000
19,500
42,000
Life, years
30
30
30
30
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Example
• Find the PW of the cash flows …
• Eliminate those with B/C <1, why?
• Start performing incremental analysis …
• B to A
Incremental cost = 75,000
Incremental benefit = 122,551  incremental B/C ratio = 1.63
Choose?
• D to B
Incremental cost = 75,000
Incremental benefit = 65,989  incremental B/C ratio = .88
Choose?
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(Example 9.6)
Six different sites are into consideration as possible location
to construct a dam. If MARR of 6% per year is required and
dam life is infinite for analysis purposes, select the one best
location using the B/C method
Site
Choose E
Construction Cost, $ (millions)
Annual Income, $
A
6
350k
B
8
420k
C
3
125k
D
10
400k
E
5
350k
F
11
700k
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Spreadsheet Example
• Alternative routes are being considered by the local
highway district for a new bypass. Route A, costing
$4000,000 to local business. Route B, costing
$6,000000 can provide $1000,000 in annual benefits.
The annual cost of maintenance is $200000 for A and
$120000 for B. If the life of each road is 20 years and an
interest rate of 8% per year is used, which alternative
should be selected on the basis of a conventional B/C
analysis?
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Solution
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