Presentazione di PowerPoint

Lectures in Engineering Economy

Prof. Corrado lo Storto

DIEG, Dept. of Economics and Engineering Management

School of Engineering, University of Naples Federico II email: corrado.lostorto@unina.it

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.


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.


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.


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.


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.


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.


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


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


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?


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.


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.


Benefit-Cost Ratio Criterion

Benefit-Cost Ratio=

Equivalent Users' Net Benefits

Equivalent Sponsor's Net Cost

If this BC ratio exceeds 1, the project can be justified


Definition of Benefit-Cost Ratio

B 

N



C 

N



 n

 n b n

=Benefit at the end of period n , c n

=Expense at the end of period n , b n c n



0



0

A n

= b n

– c n

N = Project life i =Sponsor’s interest rate (discount rate)


Breakdown of the Sponsor’s Cost

I 

K

  n

C ' 

N

  n

BC(i) 

B

C



B

I C '

, I C '  0

Equivalent capital investment at n = 0

Equivalent O&M costs at n = 0


Example of B-C Analysis

K = 1

N = 5

$20

$30 $30

Benefits ( b n

)

$20

$10 $10

Investment ( c n

)

$5 $5 $8 $8

Recurring costs ( c n

)


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

BC(10%)

= $18.3



71.98




Relationship between B/C Ratio and NPW

B

 1

B > ( I + C ’’)

B – ( I + C ’’) > 0

PW( i ) = B – C’ > 0


Incremental Analysis Based on

BC

(

i

)

  B k

 B j

  I k

 I

J

 C '  C ' k

 C ' j

BC(i) 

 B

I C '


Example 2: Incremental Benefit-Cost Ratios

I

B

C ’

PW( i )

A1

$5,000

12,000

4,000

$3,000

A2

$20,000

35,000

8,000

$7,000


A3

$14,000

21,000

1,000

$6,000

Solution

BC ( i )

Ranking Base

I + C ’

A1

1.33

A1

$9,000

A2

1.25

A3

$15,000

A3

1.40

A2

$28,000

BC(i) 

 1.5 1, select A2.

BC(i) 




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


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.


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.


Comparing alternatives using benefit-cost analysis when receipts and disbursements are known: an example

First cost

Life

Salvage value

Annual receipts

Annual disbursements

Minimum attractive rate of return=8%

Study period=10 yr

A

$ 10,000

5 yr

$ 2,000

$ 5,000

$ 2,200

Lathe

B

$ 15,000

10 yr

$ 0

$ 7,000

$ 4,300

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.


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


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

$ 72

= -1.39 < 1

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.


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

$ 1,000 $ 1,500 $ 2,500 $ 4,000 $ 5,000 $ 7,000 Investment

Annual savings in cash disbursements

Salvage value

MARR = 18%

$ 150 $ 375 $ 500 $ 925 $ 1,125

$ 1,000 $ 1,500 $ 2,500 $ 4,000 $ 5,000


$ 1,425

$ 7,000

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;


Summary

 The B/C ratio is defined as:

BC(i) 

B

C



B

I C '

The decision rule is if BC( i ) > 1, the project is acceptable.

 The net B/C ratio is defined as

B / C(i) 

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.


Presentazione di PowerPoint

Lectures in Engineering Economy

Framework of Benefit-Cost Analysis

BC

i

Related documents

Products

Support

Presentazione di PowerPoint

Lectures in Engineering Economy

Framework of Benefit-Cost Analysis

BC

i

Related documents

Add this document to collection(s)

Add this document to saved

Suggest us how to improve StudyLib