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Lectures in Engineering Economy
Prof. Corrado lo Storto
DIEG, Dept. of Economics and Engineering Management
School of Engineering, University of Naples Federico II
email: [email protected]
phone: 081-768.2932
Major issues
 Framework of benefit-cost analysis
 Valuation of benefits and costs
 Benefit-cost ratios
 Incremental B-C analysis
Engineering Economy/public activities/ 2005 /prof. corrado lo storto
Benefit-Cost analysis



The Benefit-cost analysis is commonly used to evaluate public projects.
Benefits of a non-monetary nature need to be quantified in dollar
terms as much as possible and factored into the analysis.
A broad range of project users distinct from the sponsor should be
considered—benefits and dis-benefits to all these users can (and
should) be taken into account.
Engineering Economy/public activities/ 2005 /prof. corrado lo storto
Framework of Benefit-Cost Analysis
 Identifying all the users and sponsors of the project.
 Identifying all the benefits and dis-benefits of the project.
 Quantifying all benefits and dis-benefits in some unit of money
measure.
 Selecting an appropriate interest rate at which to discount benefits and
costs to a present value.
Engineering Economy/public activities/ 2005 /prof. corrado lo storto
Analyses for Government Agencies and Public Utilities
 The government (public sector) analyst has usually greater difficulties
when he/she tries to measure benefits than does the private sector
analyst because the government sector analyst should include the
social benefits and cost of the project;
 Economic studies for government agencies are made easier because
such agencies are not subject to income tax. While funds for many
such agencies are obtained through income taxes none of the agencies
pays income taxes to others.
Engineering Economy/public activities/ 2005 /prof. corrado lo storto
Criteria for judging acceptability of government projects
Analyses of capital expenditures for independent projects can take many
forms, such as:
1. Maximization of the ratio of benefits to costs on an annual or present
equivalent basis;
2. Minimization of combined annual cost to the public user and the
agency supplier of the facility when benefits are fixed;
3. Minimization of the present value sacrificed if the project were cut.
Engineering Economy/public activities/ 2005 /prof. corrado lo storto
Major difficulties
What is perceived to be in the best interest of the public may vary sharply
over time:
1. It depends on changes in such conditions as the state of the
economy, foreign relations, public health, environmental degradation,
and public services;
2. Intangibles or irreducibles are generally more important in public
works than they are in private enterprises.
Engineering Economy/public activities/ 2005 /prof. corrado lo storto
Major difficulties
Analysts who perform economic studies for a government agency
sometimes fall into the trap of making the study based on just the
disbursements and receipts for that particular agency or government body
it represents.
For example, a state or local government might rationalize that a
particular project is justified if the federal government pays most of the
cost, even though the project may be unjustified based on total costs and
benefits.
Engineering Economy/public activities/ 2005 /prof. corrado lo storto
Example
Classification of benefits and costs related to the completion of a new toll
road through a rural area having as a major goal to shorten the distance
between two large communities:
Benefits to Public
- Reduced vehicle operating costs
- Reduced commercial and non commercial travel time
- Increased safety
- Increased accessibility between communities
- Ease of driving
- Appreciation of land values
Engineering Economy/public activities/ 2005 /prof. corrado lo storto
Example
Disbenefits to Public
- Land removed from agrucultural production
- Damages resulting from changes of water flow
- Decreased movement of livestock across highway
- Increased air pollution and litter
Cost to State
- Construction costs
- Maintenance costs
- Administrative costs
Savings to State
- Toll revenues
- Increased taxes due to appreciated land and increased business activity
Engineering Economy/public activities/ 2005 /prof. corrado lo storto
Example : Problem 1
A county is considering installing a water treatment system that is
expected to cause environmental and direct benefits of $ 1,000,000 per
year for its inhabitants. The system would require an investment of $
9,000,000 and have operating and maintenance costs of $ 300,000 per
year for an expected life of 20 years, after which it would have no value.
If money for this type of project costs the county 6%, is the project
justified on an economic basis? Suppose the state government is willing to
pay $ 4,000,000 of the investment. Now is it justified?
Engineering Economy/public activities/ 2005 /prof. corrado lo storto
Example: Solution to problem 1
Using the net present worth method based on total benefits and costs, we
get
Net PW = ($ 1,000,000 - $ 300,000)(P/A, 6%, 20) - $ 9,000,000 =
= - $ 971,000 < $ 0
Thus, it is not justified in total.
Based only on benefit and costs to the county:
Net PW = ($ 1,000,000 - $ 300,000)(P/A, 6%, 20)
- ($ 9,000,000 - $ 4,000,000) = $ 3,029,000 > $ 0
Thus, it is apparently justified to the county.
It would be common for county decision makers to consider only the net
PW = $ 3,029,000 on the county investment and conclude that the
project must be worthwhile, never seriously considering that the net PW
on the total investment is < $ 0.
Engineering Economy/public activities/ 2005 /prof. corrado lo storto
Example: Solution to problem 1
This is the equivalent of considering the state’s money as free, which is
sometimes rationalized on the basis that “… we ought to get it, bacause if
we don’t some other agency or organization will.”
Nevertheless, one should consider – in principle – the total benefits and
costs to determine if the investment of state as well as county fund is
justified.
Engineering Economy/public activities/ 2005 /prof. corrado lo storto
Benefit-Cost Ratio Criterion
Equivalent Users' Net Benefits
Benefit-Cost Ratio=
Equivalent Sponsor's Net Cost
If this BC ratio exceeds 1, the project can be justified
Engineering Economy/public activities/ 2005 /prof. corrado lo storto
Definition of Benefit-Cost Ratio
B
N
n
b
(1

i)
 n
n0
C
N
 cn (1  i)n
n0
bn=Benefit at the end of period n, bn  0
cn=Expense at the end of period n, cn  0
An= bn – cn
N = Project life
i =Sponsor’s interest rate (discount rate)
Engineering Economy/public activities/ 2005 /prof. corrado lo storto
Breakdown of the Sponsor’s Cost
K
I   c n (1  i) n
n0
N
C '   c n (1  i) n
n  K 1
BC(i) 
Equivalent capital investment
at n = 0
Equivalent O&M costs
at n = 0
B
B

, I  C'  0
C I  C'
Engineering Economy/public activities/ 2005 /prof. corrado lo storto
Example of B-C Analysis
$30
K=1
N=5
$10
$20
$20
$5
$10
Benefits (bn)
$30
$5
$8
$8
Recurring costs (cn)
Investment (cn)
Engineering Economy/public activities/ 2005 /prof. corrado lo storto
Solution
B = $20(P/F, 10%, 2) + $30(P/F, 1%, 3)
+$30(P/F, 10%, 4) + $20(P/F, 10%, 5)
= $71.98
C = $10 + $10(P/F, 10%, 1) + $5(P/F, 10%, 2) + $5(P/F, 10%, 3)
+ $8(P/F, 10%, 4)+ $8(P/F, 10%, 5)
=$37.41
I = $10 + $10(P/F, 10%, 1)
= $19.09
C’ = C – I
= $18.3
71.98
BC(10%) 
 1.92  1, Accept the project.
$19.09  $18.32
Engineering Economy/public activities/ 2005 /prof. corrado lo storto
Relationship between B/C Ratio and NPW
B
1
I  C'
B > (I + C’’)
B – (I+ C’’) > 0
PW(i) = B – C’ > 0
Engineering Economy/public activities/ 2005 /prof. corrado lo storto
Incremental Analysis Based on BC(i)
B  B k  B j
I  Ik  I J
C '  C 'k  C ' j
BC(i)k  j
B

I  C '
Engineering Economy/public activities/ 2005 /prof. corrado lo storto
Example 2: Incremental Benefit-Cost Ratios
A1
A2
A3
I
$5,000
$20,000
$14,000
B
12,000
35,000
21,000
C’
4,000
8,000
1,000
PW(i)
$3,000
$7,000
$6,000
Engineering Economy/public activities/ 2005 /prof. corrado lo storto
Solution
A1
A2
A3
BC(i)
1.33
1.25
1.40
Ranking Base
A1
A3
A2
I +C’
$9,000
$15,000
$28,000
BC(i)3 1 
$21, 000  $12, 000
($14, 000  $5, 000)  ($1, 000  $4, 000)
 1.5  1, select A2.
BC(i)2 3
$35, 000  $21, 000

($20, 000  $14, 000)  ($8, 000  $1, 000)
 1.08  1, select A2.
Engineering Economy/public activities/ 2005 /prof. corrado lo storto
Interest rate for government projects
Three main choices for the interest rate to use in government economic
studies are as follows:
1. borrowing rate
2. the opportunity cost to the governmental agency
3. the opportunity cost to the taxpayer
Engineering Economy/public activities/ 2005 /prof. corrado lo storto
The borrowing rate
In general, it is appropriate to use the borrowing rate only for cases in
which money is borrowed specifically for the project under analysis and
where use of that money will not cause other worthy projects to be
foregone.
Engineering Economy/public activities/ 2005 /prof. corrado lo storto
The opportunity cost
It is the interest rate on the best investment opportunity foregone.
If projects are chosen so that the return rate on alla accepted projects is
higher than the return on any of the rejected projects, then the interest
rate for use in the economic analysis is equal to the opportunity cost.
If this is done for all projects and investment capital available within a
government agency, then the result is a government opportunity cost. If,
on the other hand, one considers the best opportunity available to the
taxpayers if the money were not obtained through taxes for use by the
government agency, the result is a taxpayers’ opportunity cost.
Engineering Economy/public activities/ 2005 /prof. corrado lo storto
Comparing alternatives using benefit-cost analysis when
receipts and disbursements are known: an example
Lathe
A
B
$ 10,000
$ 15,000
5 yr
10 yr
Salvage value
$ 2,000
$0
Annual receipts
$ 5,000
$ 7,000
Annual disbursements
$ 2,200
$ 4,300
First cost
Life
Minimum attractive rate of return=8%
Study period=10 yr
Two alternatives lathes are considered in the analysis. Annual receipts are treated
as annual benefits, while annual disbursements are treated as annual operating
and maintenance costs.
Engineering Economy/public activities/ 2005 /prof. corrado lo storto
Comparing alternatives using benefit-cost analysis when
receipts and disbursements are known: solution to the
example
It is assumed that after 5 years lathe A will be replaced with another
lathe having an identical cash flow profile. Hence, annual worths for
individual life cycles can be used in computing the benefit-cost ratio.
The first increment of investment (the $ 10,000 for lathe A) has a B/C of
1.294 > 1.
Hence, the increment of investment in lathe A is justified.
The next step is to determine if the second increment of investment is
justified. The simplest approach is to divide the difference in the annual
worths of net annual benefits by the differences in capital recovery costs.
For lathe B,
CR= $ 15,000(A/P, 8%, 10) = $ 2,235
Engineering Economy/public activities/ 2005 /prof. corrado lo storto
Comparing alternatives using benefit-cost analysis when
receipts and disbursements are known: solution to the
example
For the second increment of investment,
B/C =
$ 7,000 - $ 4,300   $ 5,000-$ 2,200 
$ 2,235 - $ 2,163

$ 2,700 - $ 2,800
$ 2,235 - $ 2,163
=
- $ 100
= -1.39 < 1
$ 72
Since the modified B/C ratio for the increment of investment from lathe A to
lathe B has a value less than 1, the increment cannot be justified and thus lathe
A is recommended.
Engineering Economy/public activities/ 2005 /prof. corrado lo storto
Comparing numerous alternatives using benefit-cost
analysis when receipts and disbursements are known:
example
The following example shows 6 investment alternatives. Each alternative has a
salvage value equal to the investment and there is no depretiation cost, and the
incremental capital recovery cost equals the product of the MARR and the
incremental investment:
Alternatives
A
B
C
D
E
F
Investment
$ 1,000
$ 1,500
$ 2,500 $ 4,000 $ 5,000
$ 7,000
Annual savings in cash
disbursements
$ 150
$ 375
$ 500
$ 1,125
$ 1,425
Salvage value
$ 1,000
$ 1,500
$ 2,500 $ 4,000 $ 5,000
$ 7,000
$ 925
MARR = 18%
Engineering Economy/public activities/ 2005 /prof. corrado lo storto
Summary
 A benefit-cost analysis is commonly used to evaluate public
projects;
 Difficulties involved in public project analysis include the
following:
1) Identifying all the users who can benefit from the project;
2) Identifying all the benefits and disbenefits of the project;
3) Quantifying all benefits and disbenefits in some money unit
of measure;
4) Selecting an appropriate interest rate at which to discount
benefits and costs to a present value;
Engineering Economy/public activities/ 2005 /prof. corrado lo storto
Summary
 The B/C ratio is defined as:
BC(i) 
B
B

,I  C '  0
C I  C'
The decision rule is if BC(i) > 1, the project is acceptable.
 The net B/C ratio is defined as
B  C' B'
B / C(i) 
 ,I  0
I
I'
The net B/C ratio expresses the net benefit expected per dollar
invested. The same decision rule applies as for the B/C ratio.
Engineering Economy/public activities/ 2005 /prof. corrado lo storto