UNITED STATES ENVIRONMENTAL PROTECTION AGENCY
WASHINGTON, D.C. 20460
DEC 29
OF
SOLID WASTE AND EMERGENCY RESPONSE
MEMORANDUM
SUBJECT: Part Three of OSWER's System Life Cycle
Management Guidance - Directive No^^^GS.O
FROM: Asa R. Frost Jr., Director
Information Management Staf
TO: Addressees
OSWER Directive 9028.00 states that every information
management project which supports the Agency's hazardous waste
program must comply with OSWER's Information System Life Cycle
Management Guidance. A Practice Paper on Benefit-Cost Analysis
has been completed and is now being issued as an addition to the
Directive, as No. 9028.OOb. The Benefit-Cost Analysis Practice
Paper is available in Room M2416 of Headquarters, or by mail by
calling FTS 475-6760. In addition, the Practice Paper is being
distributed to those who have already received Parts 1, 2 and 3
of the Guidance.
The Benefit-Cost Analysis Paper describes the
benefit-cost analysis noted in Parts 1 and 2 of the Guidance,
in the context of the OSWER program and information management
environment. Topics addressed include lists of quantifiable
and non-quantifiable benefits and costs, risk assessment of
alternatives, comparison of alternatives and an explanation
of net present value.
In general, the Guidance serves to promote better management
of information activities by presenting a structured approach for
solving problems and for selecting and using the methods, tools
and technology appropriate fee each project. ._^
Parts 1 and 2 of the Guidan§& were distributed initially
in 1988. Part 3 is reserved fo£ Practice Papers which describe
a particular tQgie in depth, reflecting changes in technologf°|o;|
organizational structures. Six Practice Papers were distribute;!
in March 1989, covering topics such as project review and --&£!
approval, data management, and expert systelnsi
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- 2 -
If you have any questions concerning the Guidance, or
the Practice Papers, please call me or Mary Lou Melley at FTS
475-6760.
Attachment
Addressees: (without Attachment)
OSWER Information Management Steering Committee Members
OSWER Division Directors
OSWER Program Management'Staff Directors
OSWER Staff Directors, Office of Resource Management Staff
Headquarters SIRMOS
Inspector General
Assistarft Regional Administrators
Regional SIRMOS
ORD Headquarters and Laboratory Managers
OSWER Contractors
OIRM Contractors
Addressees; (with Attachment)
OSWER information Management Coordinators
OIRM Division Directors
National Data Processing Division Directors
Regional Waste Management Division Directors
Regional IRM Branch Chiefs
Individual recipients of OSWER's Life Cycle Management Guidance,
(Parts 1 and 2)
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Mgency
Washington. DC 20460
OSWER Directive Initiation Request
1. Directive Number
9028.OOb
2. Originator Information
of Contact Person
ASA R. FROST, JR.
Mail Code
OS-110
Office
OPMT/IMS
Telephone Code
475-6760
3. Title
OSWER'S SYSTEM LIFE CYCLE MANAGEMENT GUIDANCE: PART THREE - PRACTICE PAPER
BENEFIT - COST ANALYSIS
4. Summary of Directive (include brief statement of purpose)
The Guidance for information systems provides a structured approach for the solution of
information management problems, particularly those that require consideration of
automated systems. The Guidance explains the importance of life cycle management and
describes the progression of the life cycle in terms of the activities and products
required for each phase of the life cycle.
5. Keywords Analytic Methods, Automation, baseline information standards, cost management
data, data management guidance '
6a. Does This Directive Supersede Previous Directive^?
b. Does It Supplement Previous Directive(s)?
X No
No
Yes What directive (number, title)
Yes What directive (number, title) 9028. 00
OSWER'S System Life Cycle Mgmt. Guid.
7. Draft Level :
A-SignedbyAA'DAA
B - Signed by Office Director
i C - For Review & Comment
D -- In Development
8. Document to be distributed to States by Headquarters?
Yes
X
No
LThis Request Meets OSWER Directives System Format Standards.
f
i. Signature of Lead Office Directives Coordinator
Date
-°tC,
10. Name and i itle of Approving'^) fficial
Date
EPA Form 1315-17 (Rev. 5-87) Preyfpos editions are obsolete.
OSWER OSWER OSWER O
'E DIRECTIVE DIRECTIVE DIRECTIVE
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OFFICE OF SOLID WASTE
AND EMERGENCY
RESPONSE
(OSWER)
SYSTEM LIFE CYCLE
MANAGEMENT
GUIDANCE
Part 3: Practice Paper
Benefit-Cost Analysis
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OSWER Directive # 9028.OOb
Table of Contents
1. Practice Paper Purpose 1
2. Overview of Benefit-Cost Analysis 2
2.1. Benefit-Cost Analysis Defined : 2
2.2. Appropriate Depth of Analysis 2
2.3. Uses of Benefit-Cost Analysis Throughout the System
Life Cycle 3
2.4. Secondary Uses of Benefit-Cost Analysis ..... 6
2.5. Limitations 7
2.6. Steps in the Benefit-Cost Analysis Process .7
3. Analysis of Benefits 10
3.1. Identifying Benefits 10
3.2; Quantifiable Benefits (Source: DOE) 16
3.3. Estimating Non-Quantifiable Benefits (Source: DOE) . 19
4 . Analysis of Costs '. 24
4.1. Non-Recurring Costs 24
4.2. Recurring Costs .".... 26
4.3. Sunk Costs (Source: DLA) : . . . . 26
4.4. Opportunity Costs 26
4.5. Cost Accounting Problems (Source: DOE) 27
4.6. Estimating Costs 27
4.7. Cost Elements 28
4.8. Other Considerations (Source: DOE) 28
5. Analysis of Risks . . . 29
5.1. Overview of .Risk Analysis 29
5.2. Volatility of Requirements 30
5.3. Project Scope (Organization and Operations) 31
5.4. Project Management Ability 31
5.5. Project Staffing Levels and Skills (Government Staff
and Contractor Support) 32
5.6. Technology Experience and Degree of Innovation ..... 33
5.7. Availability of Funding 34
5.8. Senior Management Support 35
5.9. Number and Types of Procurement 36
6. How to Compare Alternatives 37
6.1. Comparing Quantitative and Non-quantitative Benefits
and Costs 37
6.2. Comparing Budget-related Benefits and Costs:
Financial Analysis 41
7. How to Refine the Analysis, Sensitivity Analysis 52
4
8. Outline for Presenting Benefit-Cost Analysis 55
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OSWER Directive # 9028.OOb
Appendices
Table of Contents
A. Economic Life and Project Life (Source: DLA) I
B. The Notion of Present Value (Source: DLA) 5
C. Basic Discounting Techniques (Source: DLA) 12
D. Inflation (Source: DLA) 17
E. Terminal Value (Source: DLA) . . . . : 23
F. Unequal Economic Lives - Uniform Annual Cost
(Source: DLA) 27
G. Break-Even Analysis (Source: DLA) 34
H. Savings/Investment Ratio (Source: DLA) 41
I. Payback (Source: DLA) . . 44
J. Sensitivity Analysis (Source: DLA). 50
K. Benefit-Cost Analysis Review Checklist (Source: DLA) .... 55
L. Project Year Discount Factors (Source: DLA) 57
M. Glossary of Terms (Source: DLA) 58
11
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OSWER Directive # 9028.OOb
Exhibits
2-1 The Steps in the Benefit-Cost Analysis Process 9
3-1 Approach to Avoid Double-counting Benefits and Costs .... 11
3-2 Potential Categories of Benefits For System Concept
Alternatives 13
3-3 Typical Quantifiable Benefits 17
4-1 Typical Quantifiable Costs 25
6-1 Alternatives vs. Criteria Matrix with Focus on Each
Alternative 39
6-2 Alternatives vs. Criteria Matrix with Focus on Each
Criterion 40
6-3 Break-Even Chart 4 43
6-4 Break-Even Chart Classical Case 44
6-5 Discount Factors Based on a 10 Percent Discount Rate .... 46
6-6 Present Value Analysis: Alternative X, Summary of
Alternative Benefits and Costs 48
6-7 Graphic Representation of NPV Line Chart 50
6-8 Graphic Representation of NPV Bar Chart 50
7-1 Sensitivity Analysis: NPV of Alternatives Under Varying
Assumptions 54
iii
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OSWER Directive # 9028.OOb
1 . Practice Paper Purpose
This practice paper constitutes a section of Part 3 of the
Office of Solid Waste and Emergency Response (OSWER) System Life
Cycle Management Guidance. This paper describes the benefit-cost
analysis noted in Guidance Parts 1 and 2 in the context of the
OSWER program and information management environment. This paper
also complements Chapter 3: Options Analysis, of the EPA Systems
Design and Development Guidance. Volume Ef issued by the Office of
Information Research Management (OIRM).
The topics addressed in this practice paper include:
The structure and content, of the benefit-cost analysis
document
Developing a list of quantifiable and non-quantifiable
benefits.
Developing a list of quantifiable and non-quantifiable
costs.
Assessing the risk of each alternative
Comparing the benefit, cost, and risk profile of each
alternative
Preparing net present value calculations
This practice paper is intended for use by information
technology personnel with little or no previous experience in the
analysis of benefits and costs. It describes the essential
concepts and procedures necessary to conduct a benefit-cost
analysis. It explains the use of benefit-cost analyses to support
decisions related to information resource management (IRM).
We would like to acknowledge our debt to the Department of
Energy and the Department of Defense for their guidances on
benefit-cost analysis. We have used the Department of Energy's
"Analysis of Benefits and Costs (ABC's) Guideline"1 and the
Department of Defense's "Economic Analysis"2 as the basis for
several sections of this paper, and in many cases used material
directly with only minor editing.
1U.S. Department of Energy, Assistant Secretary, Management
and Administration, Directorate of Administration, Office of ADP
Management, "Analysis of Benefits and Costs (ABC's) Guideline:
Volume 2: An Analysts's Handbook for Analysis of Benefits and
Costs", June 1988.
Department of Defense, Defense Logistics Agency, "Economic
Analysis", DLAM 7041.1, May 1985.
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OSWER Directive # 9028.OOb
2. Overview of Benefit-Cost Analysis
2.1. Benefit-Cost Analysis Defined
A benefit-cost analysis is a systematic approach for
comparing alternative ways to satisfy an objective. Benefit-cost
analyses provide a structured framework for identifying
alternatives, organizing data, and making decisions. The
benefit-cost analysis process includes:
Defining objectives.
Formulating assumptions.
Identifying all reasonable alternatives for satisfying
stated objectives. (A reasonable alternative is both
technically and operationally feasible.)
Identifying benefits and costs of each alternative, over
the project life cycle. Determining when benefits and
costs will occur.
Identifying risks of each alternative, over the project
life cycle.
Comparing alternatives.
Conducting sensitivity analysis on assumptions.
Presenting results.
The structured framework benefit-cost analyses provide is
useful in a variety of different situations. Benefit-cost
analyses provide a tool by which factors affecting a decision are
enumerated and quantified to aid decision makers. Benerit-cost
analyses also include evaluating qualitative information for its
impact on the decision. While benefit-cost analyses do not remove
all uncertainty, they help clarify the impact of choosing among
alternatives, based on their benefits, costs, and associated
risks.
2.2. Appropriate Depth of Analysis
A complete benefit-cost analysis of even a fairly limited
project can become very involved and expensive. The approach
presented in this paper should be tailored by the project team to
fit individual projects. The manner in which it should be applied
depends on the level of the project.
Formal In Depth Analysis is required within OSWER for a Level
I project, if the designation of Level I results from the
estimated high cost of the system.
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OSWER Directive # 9028.OOb.
Less Formal Analysis is appropriate for all other Level I
projects and Level II projects. For these projects the
approach should be tailored to fit the scope and complexity
of the project.
For a complete definition of Level I and Level II projects,
refer to the System Life Cycle Reviews and Approvals practice
paper in Part 3 of the guidance.
2.3. Uses of Benefit-Cost Analysis Throughout the System Life
Cycle
. Benefit-cost analyses provide input to a series of decisions
made throughout a project's life cycle.
Benefit-cost analyses, or modified versions of them, will aid
decision making in all five phases of the life cycle:
Initiation Phase: The initial decision to proceed to
solve an information management problem.
Concept Phase: The selection among alternative
approaches for solving the information management
problem, and the decision to proceed with the system
project.
Definition and Design Phase: The' decision to continue
the system project.
Development and Implementation Phase: The decision to
continue the system project.
Operation Phase: Post-implementation monitoring and
evaluation, and the decision to continue, replace or
terminate a system.
The first decision point, during the Initiation phase, is
whether or not a system project should be conducted (Go/No-Go
Decision). A first cut, high level benefit-cost analysis is
important at this stage in determining the economic feasibility of
a project. Often, its primary purpose is to compare the present
system (status quo) to a proposed change.
Benefit-cost analysis is broad, not deep. (Numbers are
very rough estimates rather than absolute figures)
Solution to the information management problem may not
require automation
Benefit-cost analysis is often used by an organization
to determine the need to study a project in more detail
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OSWER Directive # 9028.OOb
Benefit-cost analysis often serves as an initial
indicator of feasibility and helps determine the
appropriate scope of the project
The second decision point, during the Concept phaser
determines which alternative solution is most desirable, or
whether no solution is acceptable. This decision depends on a
defined set of requirements. It then requires a comparison among
alternatives to determine which solution is most advantageous,
considering all benefits, costs and potential risks. At this
stage, the benefit-cost analysis requires a different focus than
the initial go/no-go decision. The definition and analysis of
different alternatives must be more precise. For many projects,
the differences in benefits among possible alternatives are quite
small since they all meet the same requirements. Therefore, the
major focus should be defining the associated costs as precisely
as possible.
Refined, formal benefit-cost analysis
Full range of solutions explored
Highly detailed
Initial projections on return on investment
Used for justification purposes
Within OSWER and EPA
For outside groups such as GSA and OMB
For benefit-cost analysis required by section 43.2
(c) of OMB Circular A-ll
Required by FIRMR 201-30.009(a)
A third set of decision points occurs during the remainder .of
the life cycle; during the Definition and Design phase and the
Development and Implementation phase. These decisions determine
whether or not to continue with the project, or make major changes
in direction. The exact nature of the benefits, costs and risks
will become clearer as the project moves through its life cycle.
As more accurate information and projections become available, the
benefit-cost analysis should be adjusted to reflect these changes.
At the end of each stage in the life cycle, a decision must be
made whether to proceed with the project, stop the project
altogether, modify the current approach, or choose another
alternative to solve the problem facing the organization. The
decision maker, usually an OSWER program manager, will find the
benefit-cost analysis crucial in making this decision.
The last decision point, at the Operation phase, is reviewing
whether the project accomplished its intended results. A
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OSWER Directive t 9028.0'Ob
comparison of actual benefits and costs, to those projected in
prior benefit-cost analyses, helps managers evaluate whether the
initiative has met its goals, and whether additional work on the
initiative., is needed. Benefit-cost analyses used for post-
implementation reviews can help identify patterns that may require
changes in the assumptions of future benefit-cost analyses. This
information when shared throughout the organization, will improve
future benefit-cost analyses and decisions. A benefit-cost
analysis at these points provides information to decision makers
to help evaluate new requirements and potential system changes.
Provides most accurate of all analyses
Identifies problem areas
Used for future guidance and justification
Used to validate projected costs and benefits over life
of system
Used to validate projections of return on investment
The following illustration shows how a benefit-cost analysis
is used at each point of the project life cycle.
Suppose an organization has responsibility for collecting and
updating a certain type of information. The information is
currently gathered and updated manually. The manager believes it
would be more efficient to develop an automated data base to
manage this information. A benefit-cost analysis would compare
the cost of collecting and maintaining the information manually in
the present system (status quo) versus the cost of automating
collection and maintenance. Costs for automating the data base
would be rough estimates based on OSWER experience.- Benefits
derived from automating may include savings in personnel costs due
to increased productivity.
If the initial benefit-cost analysis shows the present system
(status quo) is the cost-beneficial alternative, no change is
warranted. If the benefit-cost analysis shows that automation
might prove cost-beneficial, further analysis is appropriate. In
this case, the benefit-cost analysis supports a decision to
conduct further research and move to the Concept phase.
During the Concept phase, an analysis to identify the needs
of the organization (i.e., a requirements analysis) is performed.
Various alternatives, which meet these needs, are defined and
evaluated. These alternatives might specify different technical
solutions, such as levels of automation, to meet the requirements.
Different types of hardware and software might also be specified
as alternatives. In any case, all technologically and
operationally feasible alternatives are considered.
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OSWER Directive # 9028.OOb
Moreover, alternatives need to be analyzed in as much detail
as warranted by their level and cost (see 2.2. Appropriate Depth
of Analysis). This will assure the manager has all the pertinent
information regarding the effect of choosing one alternative over
the others. Particular attention is paid to the evaluation of
benefits which are not easily quantified. If no method is found
to quantify benefits, then a narrative explanation is prepared.
The more information available about each alternative, the more
likely the decision maker will select the best alternative.
After selecting an alternative, the project team can use the
benefit-cost analysis updated in subsequent life cycle stages to
evaluate whether the project should be continued. For example,
the project sponsor may discontinue the current project in order
to develop another alternative project which takes advantage of a
previously unanticipated breakthrough in technology. Also, in a
volatile legislative environment, at the time the project is about
to enter the Implementation phase the requirement that the project
set out to satisfy may no longer exist. In this case the project
sponsor may decide to cancel the project to avoid incurring
additional costs.
Finally, after a project is implemented, a benefit-cost
analysis can help measure the results. If benefits/costs are
significantly higher/lower than projected, the sponsor may inquire
whether a change in the system would bring actual results closer
to projections. If the gap between estimated and actual benefits
and/or costs is consistently inaccurate, a component of the
benefit-cost analysis process may need examination. In the
benefit-cost analysis, changes are identified in assumptions or
estimating techniques that will help make future benefit-cost
analyses more accurate.
2.4. Secondary Uses of BenefitCost: Analysis-"
While the primary purpose of benefit-cost analysis is to aid
the decision maker in choosing a course of action among
alternatives, it can also serve other purposes. For example:
1. The benefit-cost analysis can serve as a benchmark for
future program evaluations.
2. Benefit-cost analyses can be useful to the budgeter in
determining future funding requirements. However, care must be
exercised in this area for several reasons: estimates in the
benefit-cost analysis are made in constant dollars; estimates
include allowances for funded as well as unfunded fringe benefits;
estimates may include opportunity costs/benefits; and the actual
timing of costs and savings may be at variance with the
assumptions.
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OSWER Directive # 9028.OOb
3. The benefit-cost analysis serves as visible evidence to
higher echelons of review and approval that economic factors
bearing on the recommended decision have been duly considered.
Thus, it also plays a project documentation role.
2.5. Limitations
Benefit-cost analysis is subject to a number of limitations.
First, in benefit-cost analysis, priorities among various
goals and objectives are not established - the analysis is
performed to determine the most cost-effective means of satisfying
a given objective. In certain specialized contexts, however,
benefit-cost analysis can be used to help establish priorities for
competing projects (see Appendix I - Payback).
Second, even in choosing the most preferred means of meeting
an objective, benefit-cost analysis is not itself a decision
making process; it is only an input to a decision making process.
The decision maker typically must weigh the results of the
analysis against other factors, such as safety, health, morale,
environmental impact, political considerations, and national
priorities. In short, benefit-cost analysis is not a substitute
for sound judgement. Rather, by systematically quantifying what
is quantifiable, and fully describing other factors, it allows the
decision maker to focus his/her judgement more, sharply on those
areas where it is more vitally needed.
Finally, after a system is implemented, a benefit-cost
analysis cannot provide results which are more valid than the
available data. Judicious formulation of assumptions and careful
estimation of costs and benefits are therefore critical to the
benefit-cost analysis process.
Yet no matter how much care is exercised during these stages,
uncertainty cannot be eliminated completely. Benefit-cost
analysis necessarily involves assumptions, projections, or
estimates of future events whose outcomes cannot be known with
certainty until they occur. There are, however, systematic
techniques for assessing the impact of uncertainty on analysis
results; these techniques are examined in Appendix J - Sensitivity
Analysis.
2.6. Steps in the Benefit-Cost Analysis Process
The benefit-cost analysis process consists of nine basic
steps. They are:
Define Objectives
Formulate Assumptions
Identify Alternatives
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OSWER Directive # 9028.OOb
-Estimate Benefits and Costs*
Conduct Risk Analysis*
Compare Alternatives
Conduct Sensitivity Analysis*
Present Results*
Select Alternative and Recommend Course of Action*
These are depicted graphically in Exhibit 2-1. Note that
this is the process during the Concept phase. The analysis is
updated and refined in subsequent phases, particularly for all the
steps marked with an asterisk (*).
The remaining chapters of this paper explain the major steps
in the benefit-cost analysis process.- The first three steps of
the benefit-cost analysis process, Define Objectives, Formulate
Assumptions, and Identify Alternatives, are activities that are
integral to other analyses of the Concept phase, and are described
in Part 2 of the Guidance. This paper will focus on the remaining
steps. Chapter 3, Analysis of Benefits, and Chapter 4, Analysis
of Costs, provide advice on how to estimate the benefits and costs
of a system project. Chapter 5, Analysis of Risks, outlines risks
common to system projects, and provides a framework for assessing
the risks of each alternative. Chapter 6, How to Compare
Alternatives, introduces the concept of present value analysis and
the net present value.and benefit-cost ratio comparison
techniques, as well as providing advice on comparing non-monetary
benefits and costs. Chapter 7, How to Refine the Analysis,
describes how to conduct a sensitivity analysis. The final step
of the benefit-cost analysis is to present the results and make a
recommendation to the decision maker. Chapter 8, Outline for
Presenting Benefit-Cost Analysis, provides an outline for
presenting the results of the analysis to the decision makers.
This practice paper will assist the project team in
conducting a benefit-cost analysis (i.e., how to conduct the
analysis and present results). However, the project team should
determine the best way to analyze a project to meet the needs of
the decision makers.
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OSWER Directive * 9028.OOb
Exhibit 2-1 The Steps in the Benefit-Cost Analysis Process
The Benefit-Cost Analysis Process
Define Objectives |
Formulate Assumptions |
Identify Alternatives |
V
Determine Benefits* | | Determine Costs* | Determine Risks* |
I
Compare Alternatives |
I
Conduct Sensitivity
Analysis*
I
Present Results*
Select Alternative and
Recommend Course
of Action*
* Updated and refined throughout life cycle
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OSWER Directive # 9028.OOb
3. Analysis of Benefits
3.1. Identifying Benefits
3.1.1. Introduction
In this paper, the term "benefits" signifies two types of
benefits: program benefits and system benefits. "Program"
benefits represent benefits that improve the efficiency and
effectiveness of carrying out the mission of OSWER. That is to
say that these benefits are related to functions and activities
which represent uses and applications of systems and data (e.g.,
permitting, oversight, compliance monitoring, etc.). An example
of a programmatic benefit for a system is a reduction of twenty
FTEs to accomplish a programmatic function or activity.
"System" benefits relate to advantages or improvements of a
system or potential system approach, other than cost improvements.
Some examples of this type of benefit are system adaptability,
compatibility, and security. There may be projected resource
savings associated with system-related activities such as a
reduction in resources (e.g., FTE, contract dollars) needed to
maintain the data within the system. These "savings" are
accounted for in the analysis of costs, rather than in the
analysis of benefits. In general, all resources for system-
related activities are accounted for in the analysis of costs, as
described in Chapter 4 of this Practice Paper. Exhibit 3-1
summarizes the approach used in this practice paper to avoid
double counting resource related benefits and costs.
Double counting of resource related factors at times
inadvertently occurs in benefit-cost analyses because cost savings
and avoidances could be considered as either a reduction in costs
or as a benefit. For OSWER, a specific approach is prescribed to
account for resource, or budget related factors, as well as for
other factors. For example, in an analysis for replacing an
existing information system, the software maintenance costs may be
lower for a new system alternative than for the present system
(status quo). The benefit-cost analysis should account for these
lower costs in the cost analysis, and not in the analysis of
benefits.
The first step in an analysis of benefits is to list the
benefits for each alternative. The project team should describe
all expected benefits whether or not they can be quantified.
Descriptions of benefits should relate to organizational goals,
objectives, missions, functions, and operating environment.
One method to identify benefits is to form a group of users,
managers, and professionals with knowledge of the project being
analyzed. This group can brainstorm to identify the possible
benefits of the project. They can then identify the extent to
10
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OSWER Directive # 9028.OOb
Exhibit 3-1
Approach to Avoid Doublecounting Benefits and
Costs
How to Account for Benefits and Costs
Program Related System Related
Factors Factors
Quantifiable
Budgeted Factors
(i.e. Dollar, FTE)
Quantifiable
Non-budgeted
Factors
(e.g. Efficiency, Reliability)
Non-Quantifiable
Factors
(e.g., Decision making,
System Security)
State as Benefits
State as Benefits
State as Benefits
State as Costs
State as Benefits
State as Benefits
11
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OSWER Directive * 9028.OOb
which each alternative provides the different benefits. The more
input, the greater likelihood that the analysis will include all
important benefits. In addition, group analysis is helpful in
understanding the significance or insignificance of non-
quantifiable benefits.
The result is a list of all benefits to use in evaluating the
alternatives. The list should define each benefit, if possible,
in quantitative terms. The benefits for any alternative may fall
into one of many categories. Exhibit 3-2 .provides a list of
categories which may help to identify benefits. This list is not
all inclusive; it is only illustrative of benefit categories.that
could be applicable to system projects.
12
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OSWER Directive # 9028.OOb
Exhibit 3-2 potential Categories of Benefits For System Concept
Alternatives
Acceptability - How well does the alternative meet the needs
of the primary user(s)? How well does the alternative
contribute to the operation of parallel or higher "level
organizations? How well does it improve quality of
information for decision makers?
Accessibility - How well does the alternative meet
requirements for the physical or electronic distribution of
data? How well does the alternative ensure that users will
have the means to gain access to the data from various
locations?
Accuracy - How well does the alternative decrease error rates
or improve the correctness of information?
Adaptability - How well does the alternative's software for
the system allow differing system constraints and user needs
to be satisfied? How can the alternative's hardware be used
for other tasks for which the organization is responsible?
Availability - How well does the alternative ensure that the
required information can be obtained when required?
Compatibility - How will existing operations, facilities,
equipment, and data requirements be affected by the
alternative? How much initial training will be required?
How will work methods/procedures have to be altered?
Data.Quality - How well does the alternative improve the
accuracy, reliability, and completeness of the data? To what
extent does the alternative meet documented requirements?
Ecology - HOW well does the alternative improve the ecology?
How well does it meet current legislative requirements?
Economic - How well does the alternative meet the needs
established by employment benefits, EPA small business
obligations/ economically depressed area relationships,
legislative requirements?
Efficiency - To what extent will the alternative perform its
intended mission/functions with a minimum consumption of
resources? How quickly will it process the required data or
calculations?
Integratibility - HOW well will the alternative interface
with existing or planned systems? To what extent will
modifications to other systems be required? How will the
work load and product of the organization be affected by the
changes necessitated in modification of existing facilities
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OSWER Directive # 9028. OOb
or equipment, technical data requirements, and initial
personnel training? .
Maintainability - How much will the alternative's
implementation increase the maintainability of a functional
unit? Does this level of maintainability, satisfy documented
requirements ?
ii-y - HOW will the alternative impact the
involvement /need for supervisors or quality inspections?
Will the alternative require a different type of worker than
currently used? Are trained workers available? If not, are
they readily trainable?
Morale - How well will the alternative contribute to . a
positive employee attitude towards work?
Performance - How well will the alternative's computer system
and/or its subsystems perform their required functions (e.g.,
with adequate throughput, response times, and/or number of
transactions) ?
Portability - How easily can the. software of the alternative
be transferred from one computer system or environment to
another?
Productivity - How will the rate of production (e.g., records
entered per hour, etc.) increase if the alternative is
selected? Will the alternative decrease the number of staff
resources previously needed to produce the -same product, or
will the alternative allow more items to be produced with
existing staff resources? Does the rate of productivity
satisfy the documented requirements? '
Program Effectiveness - How will progralft operations and
impact be improved, in terms such as: improved timeliness of
products or services, increased service levels, and improved
targeting of services to the highest priority areas?
Quality - To what extent will a better product be produced by
the alternative? Will better service be provided? How will
the quality of products be more consistent?
Reliability - For software: how well will the alternative's
software be able to perform its required functions under
stated conditions for a stated time period? For hardware:
is the alternative's hardware projected failure rate (mean
time between failure/service calls per year) acceptable
(i.e., does it meet the requirements of the project)?
Reutilization - To what extent will the hardware and/or
software potentially be usable for other future projects?
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OSWER Directive f 9028.OOb
Residual Value - What value will the hardware and/or software
have when it is no longer needed for the project?
Safety - To what extent will the software and/or hardware of
the alternative promote safety in the work place?
Security - How will the alternative's system (hardware and/or
software) decrease the chance of fraud, misuse of Government
resources, theft, unauthorized disclosure, etc.? Will the
system result in fewer precautions being needed? If so, what.
are they? If the system must handle classified/sensitive
unclassified data, is there an alternative which provides
better security at a "better" cost?
Service Life - How well will the alternative's hardware
and/or software be able to support the stated requirements
for the projects estimated system life? Does the alternative
have a service life which will eliminate the need for
replacement hardware and/or software during the estimated
system life of the project?
Software Quality - How well will the composite character-
istics of the alternative's software to be used meet the
needs/expectations of the primary user(s)?
Useability - To what extent will the alternative provide the
user with a user friendly interface? To what extent will the
alternative improve the presentation of the information?
Upgradability - To what extent will the alternative's
software be usable on newer or larger hardware?
Versatility - To what extent will the alternative' «* software
or hardware provide additional capacity/capability beyond
that required for the system? If additional capacity or
capability is provided, is it needed and/or is there an
additional cost(s) for the additional capacity/capability not
needed by the project?
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Directive *
3.2. Quantifiable Benefits (Source: DOE)
*
Dollar values are assigned to benefits which are either one-
time (non-recurring) or occur over the life of the project
(recurring). Benefits result from increased program efficiency or
improved program effectiveness.
Benefits can also result from an increase in services to the
organization or the organization's clients (e.g., more timely
response to inquiries). These benefits are usually service
improvements not provided by the present system (status quo).
Exhibit 3-3 provides a sample of quantifiable benefits typically
associated with system initiatives.
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OSWER Directive # 9028.OOb
Exhibit 3~3 Typical Quantifiable Benefit.5
Program Related Benefits
Program Efficiency
Improved operating efficiency
Improved resources utilization
Reduced Full Time Equivalents (FTEs) needed to carry out
functions that alternative supports
Reduced travel and training needed to carry out
functions that alternative supports
Reduced space necessary to carry out functions that
alternative supports
Reduced supplies, and utilities to carry out functions
that alternative supports
Decreased overhead - Reduction in overhead activities
and costs attributable .to the alternative
Program Effectiveness
Improved service, oversight or monitoring
Improved administrative and operational effectiveness
Improved timeliness of program delivery
Expanded capacity or capability
Improved security and privacy
System Related Benefits
Increased efficiency of processing
Improved reliability of equipment and/or services
Increased service life of equipment and software
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OSWER Directive # 9028.OOb
3.2.1. Measuring Quantifiable Benefits .
The project team can directly measure many benefits in
monetary terms. For example, projects for modernization or
replacement of existing equipment can generate cost savings
relative to the programmatic functions supported by the system.
This benefit is quantifiable in direct monetary terms.
Replacing a particular task, function, or piece of equipment
is another common information resource benefit. For example, an
expert system may reduce the number of staff needed to perform a
programmatic function.
Benefits which are not specifically monetary can often be
converted into equivalent monetary values with varying degrees of
difficulty. They include benefits such as labor savings and error
reduction in carrying out a programmatic function. An efficiency/
productivity increase, typically expressed in person-years, is a
benefit whose value includes all decreases in direct and indirect
labor costs. Direct labor costs are salaries or hourly wages,
while indirect labor costs -include personnel leave and fringe.
benefits to reflect the full cost of providing a person-year of
labor.
One value enhancement that is important for system
initiatives is the avoidance of future costs. Cost avoidance
represents future costs that will not be incurred by selecting a
proposed alternative, but would be if the present system (status
quo) remained. For example, consider a manual process with an
increasing work load. Automating the process would avoid the cost
of hiring additional staff required by the manual process to
handle the increased work load.
3.2.2. Measuring and Quantifying Personnel Resources
Personnel resources are often the principal and most costly
ingredient of many system initiatives. Like equipment,
facilities, and utilities personnel resources can be measured.
There are many methods available to estimate, sample, or
accurately measure personnel effort in any system. Some are
extremely accurate, yet costly and time consuming. Others are
relatively easy to perform yet have a greater margin of error.
There are four categories of estimating techniques:
Estimation - This technique consists of asking the
judgment of supervisors or senior workers and averaging
them to lessen bias. This technique is quick and easy,
but there is a large potential for error.
Simulation - This technique relies on a flow chart of
.the proposed system environment. Industrial engineers
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OSWER Directive # 9028.OOb
make projections of how long each task will take and how
many people will be required.
Comparison - This technique relies on identifying
similar jobs elsewhere in the organization. The time
required to do three similar jobs is used as a baseline
for estimating the new system requirements.
Observation - This technique consists of having an
analyst measure the time required to perform the tasks
by observing and recording the actual time spent. This
is valuable when a pilot study approach is used.
Many books-on work measurement provide an explanation of
these techniques.- The choice .of which technique to use will
depend on the level and scope of the benefit-cost analysis.
3.3. Estimating Non-Quantifiable Benefits (Source: DOE)
Non-quantifiable (also called intangible) benefits can have a
major impact on a benefit-cost analysis and the decisions it
supports. Non-quantifiable benefits often associated with
information resources include but are not limited to:
Acceptability - Improved decision making,
fulfillment of functional and data requirements;
Data Quality - Better management information;
Versatility - Greater versatility or flexibility
Useability - Better presentation of information;
Availability - Improved report generation
.(timeliness) ; ~°
Morale - Improved staff morale.
In many benefit-cost analyses, the analysis of quantifiable
benefits may not be sufficient to distinguish a preferable
alternative. In these cases/ decisions require the evaluation of
both quantifiable and non-quantifiable benefits. The goal in the
analysi»-'of non-quantifiable benefits is to improve the overall
usefulness of the benefit-cost analysis.
There are a number of accepted procedures for analyzing non-
quantifiable benefits in a benefit-cost analysis. Many benefits
not readily converted to a dollar figure can be expressed in a
common unit of measure (such as percentage satisfaction with
services provided, etc.). The project team can compare
alternatives when similar benefits are expressed in a common
measure.
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OSWER Directive # 9028.OOb
The procedure used to evaluate non-quantifiable benefits
depends on the purpose, scope, and size of the system project.
For many projects, enumeration and ordinal ranking is sufficient.
For larger projects, more complex techniques may be necessary to
provide decision makers with complete information. The discussion
below describes several techniques to use in evaluating non-
quantifiable benefits.
3.3.1. Simple Techniques for Evaluating Non-Quantifiable
Benefits (Source: DOE)
Enumeration is a "simple listing" of non-quantifiable
benefits associated with each alternative. This allows decision
makers to compare non-quantifiable benefits associated with each
alternative.
Ranking non-quantifiable benefits by their relative
importance to the goals and objectives of the initiative provides
a more useful piece of information. . Such a ranking describes the
degree to which each alternative achieves a given objective. The
ranking does not imply a strict quantification of the non-
quantifiable benefits. However, it provides the decision maker a
description of all benefits and how each contributes to the
project's goals. This analysis is by nature rather subjective and
requires a consensus on the relative importance of the non-
quantifiable benefits. In many cases, this is as far as the
analysis can go to include certain non-quantifiable benefits "in
the benefit-cost analysis. However, the ranking explicitly
identifies the differences among alternatives for the decision
maker.
An additional step that can supplement ranking is scoring
each alternative on-how it contributes to the non-quant?fiable
benefit. These scores are subjective estimates derived from a
meeting of users, managers, and professionals with knowledge of
the system, or simply the project team's judgment. Scoring the
alternative provides the decision maker with a means to compare
across alternatives on individual non-quantifiable factors.
3.3.2. A Technique for Evaluating Non-Quantifiable Benefits
A third technique1, which we will refer to as the Phillips
technique in this paper, is useful for larger projects and builds
on a modified version of the ranking procedures described above.
This technique seeks to overcome the deficiency in traditional
ranking schemes. In the traditional approach, the project team
identifies a large number of criteria and assigns a numerical
iThis technique is derived from work done by Lawrence D.
Phillips, "Introduction to Decision Theory", Tutorial Paper 79-1,
Decision Analysis Unit, London School of Economics and Political
Science, University of London, 1979.
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OSWER Directive # 9028.OOb
weight to each to signify its importance to the analysis. A
numerical rating is assigned for how well each alternative meets
each criterion. The ratings and weights are multiplied together
and are tallied to derive a score for each alternative. The best
score wins.
The failure of such an approach is two-fold. The Phillips
technique addresses these failures. The first is the manner in
which weights for the various criteria are derived. For example,
the project sponsor may feel that cost is the most significant
criteria, and thus assign a large weight to this factor. In the
Phillips technique, the decision-makers should give the criteria
with the greatest disparity between the worst and best alter-
native., as they perceive it, the greatest weight. In this manner,
the most discriminating factor gets the greatest weight. To
understand why this is correct, imagine choosing between two cars.
One is significantly more comfortable than the other, yet cost
only a few dollars more. If cost is of primary importance to you,
and comfort of secondary importance, then if you follow the
traditional approach strictly and. weight the cost high enough you
might make a counter intuitive decision. You would choose the
cheaper, less comfortable car when actually you might have
preferred to pay the few dollars more to get the car with the
extra comfort. By weighting the criteria in terms of disparity,
the decision-maker avoids making the incorrect decision.
The second error of the traditional approach is that it fails
to address the sensitivity of the results to the assumptions. For
example, what happens if the estimated benefits are off by 25
percent? The best choice may be the alternative that minimizes
the downside exposure, not the one that offers the most benefits
if everything works perfectly. Thus the Phillips technique
includes a sensitivity analysis component to counteract this
deficiency.
The Phillips technique is outlined below.
First, before scoring each alternative against a set of
factors or criteria, the decision-makers, with the aid of the
project team, must determine which criteria distinguish
alternatives. In order to do this the technique of triads is
used. Using triads, the decision-makers randomly select three
alternatives and then determine what distinguishes any two of the
alternatives from the remaining third alternative. For example
two of the alternatives may have a much faster processing time
then the third. In another iteration two other alternatives may
provide much less information then a third. The decision-makers
repeat this process until they are reasonably certain that they
have documented all of the pertinent criteria. This list of
criteria will be all of the quantifiable and non-quantifiable
benefits and costs that distinguish one-alternative from another.
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OSWER Directive # 9028.OOb
Once the decision-makers have a complete list of these
distinguishing criteria, they should score each alternative
against each criterion, scoring all alternatives against a single
criterion before proceeding with the next criterion. This is done
using a separate 0 to 100 scale for each criterion, first
assigning a 100 to the alternative which ranks the highest on the
criterion under examination, then assigning a 0 to the alternative
which ranks the lowest on the criterion, and then ranking each of
the remaining alternatives along the scale from 0 to 100. Keep in
mind that just because an alternative ranks a 0 on the scale, it
does not"mean that it is devoid of that criterion. In fact, an
alternative that ranks a 0 on a specific criterion may still be
quite satisfactory in terms of that criterion. An important
feature of these scales is that they portray the relative
desirability of each alternative against each other, not against
an absolute standard.
The next step is to weight the criteria. Weighting of the
various criteria plays a vital role in the decision process as
already seen in the introduction to this section. By this stage
each of the criterion has a 0 to 100 scale upon which each of the
alternatives has been given a value. What should be clear is that
the units are not the same from one scale to the next. In effect,
the decision-makers wish to determine which scales have the
largest units, and put a higher weight on that criterion. To get
a first-cut at the weights, the decision-makers may wish to
determine which criterion scale has the smallest increments and
thus should exert the least influence on the decision. In other
words, the decision-makers determine which of the criterion has
the smallest variance from the best to the worst alternative. The
decision-makers then proceed to rank order the criterion, from the
criterion with the least difference from best to worst, to the
criterion with the greatest difference from best to worst. Once
the criteria are rank ordered, a weight is assigned to each
criterion according to its relation to the other criteria.
Once the decision-makers have assigned values to the
criteria, the project team should calculate a single number for
each alternative. The calculations that follow, though simple,
only hold if the each criterion scale is utility independent. A
scale is utility independent of other scales if locations of the
alternatives on the scale do not depend on their location on other
scales.1 Given this condition, to calculate a value for each
alternative, simply multiply the score of the alternative on each
criterion scale by the appropriate weight of each criterion.
Once a value has been assigned to each alternative, the
decision-makers should compare these values. As stated above one
of the major deficiencies of traditional weighting schemes is that
the analysis stops at this point. However, it is important at
1 Keeney, R. and Raiffa, H., Decisions with Multiple
Objectives. New York: Wiley, 1976.
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OSWER Directive # 9028.OOb
this point to test the underlying assumptions of the model by
using sensitivity analysis until the decision-makers are satisfied
with the results of the decision. Sensitivity analysis is
discussed more fully in Chapter 7, so only a cursory discussion is
included here. To perform sensitivity analysis, the decision-
makers simply change any scores and weights that they are not
fully convinced of, to determine if the alternative with the
highest score changes. Sensitivity analysis is a great tool for
gaining consensus on a particular course of action. With
sensitivity analysis, different decision-makers may not agree on
the weights and scores, but if they see that these weighting
preferences do not affect the outcome, they will agree on the
course of action.
For major investments in technology or systems, the Phillips
technique allows decision makers to analyze large quantities of
information. A major advantage of this technique is that several
microcomputer software programs can perform the complex
calculations required, including the sensitivity analysis where
rapid calculations facilitate the decision process.
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OSWER Directive # 9028. OOb
4. Analysis of Costs
An important component of a benefit-cost analysis is
identifying and estimating costs. Costs are the dollar value of
input used or expended in developing, acquiring, or operating an
information resource. Costs are incurred throughout the life of- a
project. The project team must consider the cost of acquisition
and operation of an alternative over its full life cycle. The
timing of costs in an alternative's life cycle is important
because the net total cost of an alternative depends on when the
costs occur. (Chapter 6 discusses the time value of money.) There
are two broad categories of costs: non-recurring and recurring
costs.
In identifying costs, it is important to. note the specific
organizations that are projected to incur each costs, and the
magnitude of cost for these organizations. Some costs may pertain
to a relatively small group of people in one organization, whereas
others may pertain to a large number of organizations and people
(e.g., all Regional Waste Management Divisions or state waste
management agencies). This organizational perspective of costs
will prove useful when comparing the benefits and costs of the
projects.
4.1. Non-Recurring Costs
Non-recurring costs are one-time expenses incurred under any
alternative, such as site/facility construction, system design and
programming, system testing, equipment or software purchase, and
system documentation. Listed below in Exhibit 4-1 are the
one-time costs that should be considered in an analysis.
Because of the diversity of problems encountered, cost
elements will vary from analysis to analysis. The list in the
exhibit is broad and therefore should be considered as a checklist
against which each alternative should be measured. In those
instances when the list is not broad enough to meet the
requirements of certain analyses, the project team should feel
free to augment it as necessary.
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OSWER Directive # 9028.OOb
Exhibit 4-1
Typical Quantifiable Costs
Non-recurring Costs
Recurring Costs
Hardware Investments
- ADP Equipment
- Data Communications
- Security and Privacy Equipment
Software Investments
- Database
Software Purchase
Research and Development (R&D) Costs
.. Database Development
~ Database Preparation
- Reviews and Other Technical Management
Overhead
Software Development
- Studies
-- System Test
Conversion Costs
ADP Software Conversion
Conversion/Parallel Operations
-- Data Conversion
Personnel Costs (Used only for personnel assigned
to project development)
-- Direct Support Services (Inter-Agency Services)
- Fringe Benefits
Involuntary Retirement and Severance
Overtime
Recruitment
- Relocation Costs
- Salaries
- Training
-- Travel
Pre-Existing Investments
- Terminal/Residual Value
- Value of Existing Assets Employed
- Value of Existing Assets Replaced
- Working Capital
Site Investments
- Demolition and Site Restoration
- Environmental Conditioning Equipment
Land Acquisition or Easement
New Construction
- Plant Rearrangement and Tooling
-- Rehabilitation or Modification
- Relocation Costs (Including power and
communication lines)
- Site Preparation
Overhead Include overhead costs that represent
additional or incremental costs attributable to the
alternative.
Contractual, Interagency, or Other Direct Support
Services
-- Incremental or Additional Overhead Costs
-- Procurement Process
Hardware Costs
- Data Communications Lease, Rental, and
Maintenance
Equipment Lease, Rental, and Maintenance
- Equipment Repair
Software Costs
- Software Lease, Rental, and Maintenance
Operation
- Materials, Supplies, Utilities and Other Services
- Operating Costs
-- Security and Privacy
Timesharing
Personnel Costs (Used only for personnel covered
in project management plan)
Direct Support Services (Inter-Agency Services)
Fringe Benefits
Overtime
- Salaries
- Training
-- Travel
Site Costs
Building Maintenance
Building Rental or Lease
Office Furniture
- Utilities (Heating, Air conditioning. Power)
Overhead Include overhead costs that represent
additional or incremental costs attributable to the
alternative.
- Incremental or Additional Overhead Costs
-- Supplies and Utilities
Contractor Support
Contractor Services
-- Contractual and Interagency Services (e.g., ADP
services, data communications, software, technic
and other support)
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OSWER Directive f 9028.OOb
4.2. Recurring Costs
Recurring costs are incurred on a regular basis throughout
the project or system life cycle. Recurring costs are similar to
the annual operating expenses of a business. Recurring costs
include system operations and maintenance, telecommunications,
supplies, equipment lease and maintenance, and salaries for
personnel involved in system, activities.
Again, because of the diversity of problems encountered, cost
elements will vary from analysis to analysis. The list of
recurring costs in Exhibit 4-1 is broad and therefore should be
considered as a checklist against which each alternative should be
measured. In those instances when the list is not broad enough to
meet the requirements of certain analyses, the project team should
feel free to augment it as necessary.
4.3. Sunk Costs (Source: DLA)
V .
Sunk costs is a term used to describe expenditures that
already have been made. They are considered irrelevant in an
benefit-cost analysis. The consequences of any decision regarding
a course of action for the future cannot possibly start before the
moment of decision. What has happened up-to-date cannot be
changed by any choice among alternatives for. the future. It is
only the prospective differences among alternatives that is
significant in making a choice.
To demonstrate this concept, assume for example that $100,000
has been sunk in research and development of a new project. In
order to get this project underway, an additional investment of
$50,000 is required. For decision-making purposes, the relevant
investment figure is $50,000. The original $100,000 may be
regretted, but it cannot be recouped.
Although sunk costs should not be included as part of the
cost analysis, a narrative account of such costs is generally made
to provide additional background information.
4.4. Opportunity Costs
Implicit in the discussion of relevant costs is an
alternative use concept. The value of the alternative use is
often referred to as the "opportunity cost" of employing the
resources. Opportunity cost can be described as the sacrificed
benefits that could have been realized by another alternative with
the same time, effort, and resources expended.
For example, suppose OSWER plans to develop a system that
could run on an OSWER-owned microcomputer that would need to be
dedicated to this system. Since this microcomputer is owned by
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OSWER Directive # 90.28. OOb
OSWER and is paid for, the microcomputer would be treated as a
free resource. As long as there are alternative uses for the
microcomputer, those uses represent potential opportunity costs.
Such costs are often overlooked, but should be considered in the
cost analysis.
4.5. ''Cost Accounting Problems (Source: DOE)
There are two main problems in cost accounting when computing
system life cycle costs cost omissions and hidden costs.
Omitting costs is most common when dealing with overhead
costs. Examples of easily overlooked costs include charges for
space, electricity, and change-overs when upgrading equipment.
Omitting these costs may seriously distort the analysis.
Hidden costs are usually indirect costs or support activities
which are allocated to a project. They exist elsewhere in the
organization, typically in a staff or service unit. Frequently,
these costs are charged at a standard rate by an internal billing
system. However, these charges are not always directly charged to.
the initiative. For example, excluding the costs of analysts and
programmers, which work on the project, but were hired by an in-
house service organization, makes salary costs for data processing
appear lower than they really are. Any support activity should be
identified and its cost appropriately allocated to the initiative.
4.6. Estimating Costs
4.6.1. The Work Breakdown (Bottom-up) Approach
The traditional method of developing cost estimates is to add
detailed work level data. This process, known as the bottom-up
approach, separates the total product into discrete components.
The project team then establishes costs for each component.
A project team charts the activities and tasks required to
develop a system alternative using a work breakdown structure or
process flow chart. Each task contains sub-tasks which require
time and resources. The "bottom-up" approach costs the entire
process by adding the costs of each sub-task. The result is a
consolidation of many individual sub-task estimates into a total
project cost.
This "bottom-up" approach requires considerable time and
effort because it is so detailed. However, this approach yields
the most accurate results. It is also easy to modify with new
information or a revision to the alternative.
4.6.2. The Parametric Costing (Top-down) Approach
The "top-down" approach does not require the detail of the
"bottom-up" approach. The project team can reach an estimate of
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total costs with little or no difficulty. Using this approach,
the project team relates activities conducted in the alternative
to similar activities with known costs. The project team uses the
actual cost for similar activities as a basis for estimating the
costs for activities in the system under analysis. The data
developed relies upon historical costs of a comparable but not
necessarily identical activity. The prime advantage of this
approach is that it does not rely on complete detailing of the
work actions, and takes less effort.
The "top-down" approach is also useful in obtaining the cost
of the present system if one exists. Normally, managers know the
total cost of an operation or activity. The project team may then
apportion the costs of the major functions.
4.7. Cost Elements
The following is a list of cost elements used within OSWER to
plan and budget project resources. These elements correspond
roughly with resource "purpose" as the term is used in IRM
planning and the OSWER Five Year IRM Information System (FIRMIS).
People
EPA FTE
Contractor Support
Other External Organization
Hardware
Software
Supplies
Data
Site Preparation
Time Sharing
Maintenance Support (e.g., PC maintenance contracts)
This structure may be useful for summarizing the costs of a
system or a system alternative in order to develop or update the
budget request for the project.
4.8. Other Considerations (Source: DOE)
Estimates of benefits and costs for each year of the analysis
period should be expressed in current year dollars. Estimates
should not include any factors to account for inflation.
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OSWER Directive #.9028.00b
5. Analysis of Risks
One factor which may play an important role in any decision
is risk. With -any project there is a certain element of risk
involved, risk that costs may exceed expectations, that benefits
will not materialize as expected, etc. Benefit-cost analysis
helps reduce risk by requiring explicit definition of expected
benefits, costs, and risks. However, some risk always remain. If
there is a high probability that benefits may not materialize from
a project, the project should not proceed unless its expected
benefits"are substantially greater than its costs. Similarly, if
costs and benefits are almost assuredly known, the project may be
viable even at a lower benefit-cost ratio or lower rate-of-return.
The risk factors should be evaluated in any decision concerning
the project.
5.1. Overview of Risk Analysis
Risk is an often overlooked, yet vital part of the
benefit-cost analysis. Sound business judgement dictates the
assessment of benefits and costs with an explicit consideration of
risks. An organization does not merely consider the benefits and
costs of an investment, it also assesses the probability of
success. If the benefits less costs do not outweigh the risks,
the organization seeks another investment. One hardly walks
outdoors without at least informally assessing the probability of
rain against the cost (or burden) of 'carrying an umbrella and the
benefit of the use of the umbrella. Insurance companies routinely
analyze risks before quoting premiums. Without analyzing risk, an
individual does not have all the information necessary to make an
intelligent decision.
Risk analysis is used in comparing alternatives in- a
decision. Given equivalent benefits and cost*, the rational
individual prefers the alternative with the least risk. If one
alternative has a greater risk, then a greater benefit is
expected. For example, an insurance company will charge a higher
premium (i.e. receive greater benefits) for insuring an
individual with a higher risk profile. So when choosing one
alternative from a set of competing alternatives, the alternative
with the most favorable relationship between benefits, costs, and
risks is selected. Risk analysis also is used to determine
whether the most "favorable" alternative carries an acceptable
level of risk, or whether new alternatives need to be explored
including cancelling the project.
There are eight major risk factors that may distinguish one
system alternative from another:
1) Volatility of Requirements
2) Project Scope (Organization and Operations)
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3) Project Management Ability
4) Project Staffing Levels and Skills (Government Staff and
Contractor Support)
5) . Technology Experience and Degree of Innovation
6) Availability of Funding
7) Senior Management Support
8) Number and Types of Procurement
All factors should be included in the risk assessment, even
if a particular risk factor is the same for all the alternatives
being considered. This allows the decision maker the full range
of information about the decision at hand, including the risks
that are unavoidable and are intrinsic in the nature of the
requirement or problem that all alternatives seek to meet.
. When assessing risks in the benefit-cost analysis it is wiser
to be pragmatic, not optimistic. There will be a temptation to
understate the risks involved to push through a favored project,
but this is ill-advised.
Explanations of the eight different risk factors follow.
5.2. Volatility of Requirements
The success of a project depends on how well the resulting
system meets the actual requirements. The requirements can, in
some cases, be very volatile.
Some of the factors that contribute to volatile requirements
include:
Upcoming legislative initiatives and reauthorization
Potential reductions in budget and personnel levels
Increased or decreased activity (e.g., service levels,
case loads)
Uncertain program implementation strategies (e.g., state
delegation)
Turnover of senior program managers, project sponsor
New program organization and/or operations
Significant probability that program organization and/or
operations will change
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Program policies unclear, poorly documented, and/or
likely to change
5.3. Project Scope (Organization and Operations)
It is more important that an alternative have a high real
probability of success than that it provides in theory the maximum
potential benefits. Very ambitious projects may carry with them
an unacceptably high risk of failure. OSWER must be realistic
when sizing projects to match its capabilities as well as its
needs. Defining the scope of the project should be a process in
which deliberate tradeoffs are made between potential benefits and
risk. Also, explicit actions should be incorporated in the
project strategy and plan to mitigate risk.
Factors positively correlated with risk include:
Extent of decentralization of programmatic operations -
involvement of Regions
Impact on personnel levels and day-to-day operations
Scale of operations
Number of organizations involved
Number of programs involved
Extent of integration of existing systems
5.4. Project Management Ability
Leadership is a key ingredient in successful prbjects. Each
project must be led by a manager with the appropriate skills,
experience, availability, and authority. The ability of the
project manager is one of the most important factors in a project,
and thus a potential risk if there is not a proper match between
project and available project manager.
Risk decreases when the project manager has the:
Full control of key personnel
Authority to make day-to-day technical decisions
Control of expenditures and input to the budgetary
process
Direct access to senior OSWER management
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OSWER Directive # 9028.OOb
Confidence of the IRM, programmatic and procurement
communities
Project managers need to be skilledr experienced and proficient
in:
Planning
Managing personnel
Managing contracts
Developing and adhering to schedules
Monitoring financial status and use of funds
Quality assurance
Issue identification and resolution
Applying chosen methodology
Applying chosen technology
Life cycle management
Benefit-Cost analysis
Data management
Managing projects of similar size, scope, and type
s
Federal budgetary and political environment
Understanding and working with oversight organizations
Understanding and working within the OSWER programmatic
environment
5.5. Project Staffing Levels and Skills (Government Staff and
Contractor Support)
A broad range of skills must be embodied in the project team,
be it government staff or contractor support. Some members of the
team must have knowledge of the programmatic and organizational
environment in which the project is implemented, while others must
have knowledge in the technologies which are to be applied.
Managers and staff must be dedicated to these projects - "pick-up
teams" are not effective. An alternative that demands staffing or
skills beyond what is available increases the risk that the system
wilj. not be completed on time or at all. There is always the risk
that key individuals will leave, and if the project is dependent
on such an individual or individuals it should be,noted.
32
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OSWER Directive # 9028.OOb
Skills to look for in a project group, which can then be
assessed against the requirements of the alternatives in question,
include experience, knowledge and proficiency in:
OSWER programs and policies
Organizational processes and dynamics
Liaison with Federal oversight and advisory
organizations
Large scale technology procurement and contract
administration
Contemporary information technology
Large scale project management
Specific skills necessary to complete tasks
5.6. Technology Experience and Degree of Innovation
The risk of an alternative increases in direct proportion to
the extent that it deviates from OSWER's technical experience
base. Unproven or unfamiliar technologies increase the risks
.involved. A highly innovative or state-of-the-art approach
generally brings with it the promise of great benefits. If risks
are not considered, all other factors being equal, the innovative
approach will be chosen every time. Thus, the benefits must be
measured against the risks in order to make a rational decision.
There has been increasing use of new methodologies,
productivity tools and technical approaches'for executing a wide
range of projects. These include strategic systems'planning
methodologies, analysts' and designers' workbenches, system's
development and documentation standards, integrated data
dictionaries, and similar products and procedures. The objective
is to increase the success rates of such projects by making them
more systematic and efficient, and less dependent on a handful of
key in-house and contractor personnel. Unfortunately, these
tools, methodologies and approaches do not offer a panacea if
not properly selected they may severely handicap a project. The
selection of methodologies, tools and approaches must be
considered a very high leverage decision and subject to rigorous
analysis by senior management and technical staff. It is critical
that a burden of evidence in favor of specific methodologies and
tools be established.
Risk decreases if the methodologies selected are:
33
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OSWER Directive # 9028.OOb
Tailored to the Federal environment not strictly
commercial
Successful on projects of similar scale and complexity
Documented, vendor-independent and fully supportable
' Consistent with available in-house expertise
Risk decreases if the tools selected:
Are useful throughout the systems life-cycle
Offer proven productivity improvements
Are capable of providing quality control benefits
Are fully supported by a vendor known for product
integrity
Are easy to use and possess industry-wide experience
base
Risk decreases if the technology base.. selected is:
. Proven on projects with similar requirements
.Capable of processing data at required speeds
Readily available
Highly reliable and dependable
Fully supportable
' Able to communicate freely with OSWER's existing
technology base
Consistent with OSWER professionals' expertise
5.7. Availability of Funding
The risk of an alternative rises in proportion to the
likelihood that funds will not be available when needed. Funding
availability is dependent on the budgetary process; if the
required funding for the proposed project is not in the budget,
the project cannot proceed. The project team must assess the
probability that the necessary funding will be included in the
appropriate budgets. Commitment from senior level management is
needed to insure full funding throughout the life cycle of the
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OSWER Directive # 9028.OOb
project. Funding risk is also contingent on the likelihood that
funding may be decreased in subsequent years. The budget may be
cut in across-the-board cuts or on a project by project basis. In
either case, if the project team anticipates a budget cut in the
coming years, this may affect the alternative selected. Also, an
alternative will have higher funding risk if it is more difficult
to predict the timing of required funds, relative to other
projects.
Funding risk increases if the alternative selected:
Has funding-level requirements which are difficult to
predict
Has funding-timing requirements which are difficult to
predict
Does not have sufficient senior management commitment to
keep it fully budgeted throughout life cycle
Is not currently supported by budget
5.8. Senior Management Support
Project risk decreases as senior management support
increases. A certain alternative may be the logical choice, and
yet even if this alternative is chosen it may run a- significant
risk if senior management is not willing to actively support it.
If the project runs into difficulties, the support will not be
there to provide needed direction. This is a particularly
difficult risk to assess.
.
Senior OSWER executives are generally the sponsors and
proponents of major projects; therefore, it is importanr that they
show strong support for the programs and the teams responsible for
them. Senior management must set the general direction for the
program, mobilize required resources, neutralize parochial
interests of existing organizational units and manage the
political environment and budget process. Of particular
importance, senior management must establish the project as a high
priority of OSWER and overcome skepticism about the value and
likely success of such projects.
Risk decreases as senior management increases its involvement
in:
Budget processes
Meetings with project team
Periodic project reviews
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OSWER Directive # 9028.OOb
""High leverage" decision-making processes
5.9. Number and Types of Procurement
As the number and types of procurement of an alternative
increases so does the risk of the alternative. Major procurements
are integral to large-scale projects. Industry is increasingly
relied upon to execute large-scale projects providing the
technological base, developing and installing new application
systems, and providing a range of services. However, at the same
time, OSWER must navigate through an increasingly complex
acquisition environment. Project teams running major procurements
require an unprecedented level of sophistication with respect to
both technology and Federal'procurement processes.
The stakes are high. Poor procurements can sap OSWER's
budget for years without providing needed capabilities. Even
delays in the procurement process - now very common as the
frequency of protests increases - can set back a major project for
more than one year. Key elements of successful procurements are
sophisticated procurement strategies, teams experienced with large
scale information technology acquisition, and specifications that
reliably represent the needs of OSWER.
Risk of procurement related delays increase when the
following have not been explicitly addressed.
Scope technological components and services
Roles and responsibilities of acquisition team
Acquisition schedule
Contract form and business strategy
Protest vulnerability and preventative measures
Ensuring integrity of offerers
Contract administration substantive and financial
control
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OSWER Directive # 9028.OOb
6. How to Compare Alternatives.
During the initial steps of the benefit-cost analysis, the
project team identifies alternatives and estimates their benefits
and costs. The later steps require the project team to compare
the benefits and costs of different alternatives. This chapter
describes the techniques that permit comparison of alternatives.
6.1. Comparing Quantitative and Non-quantitative Benefits and
Costs
There are four key steps to comparing benefits, costs, and
risks. These steps are:
1) Develop common set of criteria to evaluate alternatives
2) Clearly articulate the benefits, costs, and risks of
each alternative
3) Evaluate each alternative against the common criteria.
4) Identify the criteria that discriminate most sharply
among the alternatives
Following a discussion of the defects that benefit-cost
analyses typically contain, this section describes a recommended
strategy for performing the analysis.
6.1.1. The Usual Approaches
Often, benefit-cost analysis are carried out using a
straightforward three-step, approach:-
1) Define the alternatives
2) Describe the benefits and costs of each alternative
3) Draw conclusions and present a recommendation
X
This approach has a serious defect which derives from the
failure to explicitly define the evaluation criteria (i.e. the
benefits and costs). When the project team focuses only on the
highlights for each alternative, the decision maker may be left
with the uncomfortable feeling that some important issue has
either been omitted or given short shrift. The conclusions may
sound like a comparison of apples and oranges, and they are
usually expressed in vague, unquantified terms.
This strategy is subject to yet another deficiency. It fails
to address the sensitivity of the results to the assumptions. For
example, what happens if the estimated benefits are off by 25
percent? The best choice may be the alternative that minimizes
the downside exposure, not the one that offers the most benefits
if everything works perfectly.
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OSWER Directive # 9028.OOb
6.1.2. The Goal of Benefit-Cost Analysis
The goal of a benefit-cost analysis is not necessarily a
single answer. Oftentimes the individual that prepares the
benefit-cost analysis is not the person who has to make the
decision. The goal of the benefit-cost analysis is to provide the
decision maker with a sound basis for making the decision. The
analysis is successful if the decision maker understands the
trade-offs among the most attractive alternatives - what is gained
and what is lost when the decision is implemented.
An example of this is what one typically finds in an issue of
Consumer Reports. A graphical representation of. all the relevant
data is presented, with little or no assumptions made as to the
relative importance of the criteria. Each potential buyer of a
car may have a different set of values. To one potential car
buyer seating capacity may be the discriminating factor, to
another the cost of purchase, and to another the risk of major
repairs within the first five years.
Similarly, in a benefit-cost analysis, it is the decision
maker who must ultimately decide whether the set of benefits,
costs, and risk of one alternative make that alternative more
attractive than any other. In order to enable the decision maker
to make a rational choice, the project team must make certain
that:
There is not yet another alternative with an even better
cost/benefit/risk profile
All the costs, key benefits, and risks are represented
accurately
6.1.3. Develop Common Set of Criteria to Evaluate Alternatives
Define clear and unambiguous criteria for evaluating the
alternatives. To keep the rest of the analysis manageable, a
general rule of thumb is to include no more than five to seven
major criteria. If there are many more than this, group the
criteria into categories. For example, in a DBMS evaluation there
may be a dozen or more specific questions related to
restart/recovery and concurrent update; group them into a category
called "Data Integrity". Besides simplifying the analysis and the
presentation, this approach helps to confirm the completeness of
the-criteria. It is difficult to demonstrate that an unclustered
set of dozens of individual criteria defines the goal of the
decision.
Include as criteria the factors that will influence the
decision. If a factor will not influence the decision, leave it
out of the analysis. For example, although "number of current
users" is often a factor in a software package evaluation, who
38
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OSWER Directive # 9028.OOb
really makes such a decision based on this criteria? Vendor
credibility and stability are real concerns, however, and may be
valid benefits.
Do not try to assign weights to the benefit/cost/risk
criteria, even subjectively. Just write them down and define them
as precisely as possible, then proceed to the next step.
6.1.4. Clearly Articulate the Benefits.
Each Alternative
Costs, and Risks of
Having identified a set of viable alternatives and
significant benefits, costs, and risks, it is appropriate to
describe the alternatives on the basis of each criteria. It is
useful to think of the' analysis in terms of a matrix -
alternatives vs. criteria. This phase focuses on the columns.
Alternatives
1234
Criteria
Exhibit 6-1
Alternatives vs
Alternative
Criteria Matrix with Focus on Each
Do not compare alternatives at this point. The purpose of
this stage is to describe each alternative as objectively as
possible in terms of the criteria. Write down all the important
facts for each "cell" in the matrix.
Do not hesitate to iterate the previous step. If a missing
or superfluous criterion is discovered, go back and revise the
list of criteria. If an alternative proves infeasible, or a new
option is identified, revise the list of alternatives.
6.1.5.
Evaluate Each Alternative Aaainst the Common Criteria
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OSWER Directive # 9028,0Gb
The goal of this step is to identify the relative strengths
and weaknesses of the alternatives for each of the criteria. In
terms of the- matrix, this section addresses each row separately.
Alternatives
1234
Criteria
Exhibit 6-2
Alternat ives
Criterion
vs. Criteria Matrix with Focus on Each
If the previous step was done thoroughly, the alternatives
are now fully described and it will be easy to compare them. If
not, it may be necessary to do some further research to gather
missing data.
Quantify the merit of the alternatives against "the criteria
whenever possible. Sometimes the previous step results directly
in a value - for example, costs ($), speed (MIPS), service life
(years). More often the evaluation is subjective, leading no
scores like "excellent", "good", "fair", and "poor".
If the alternatives differ very little, it will be hard to
distinguish them using such a scoring scheme. In this case, focus
on the differences to develop scores such as "best", "middle",
"worst". This allows the comparison of alternatives, even though
all might rate "fair" on an absolute scale. Do not, however, .
exaggerate minor differences among perfectly satisfactory
alternatives so that the worst alternative appears to be awful.
The discussion of discriminators in the next section will clarify
when to use differences and when not to.
If appropriate, a very rigorous scoring method can be used.
See Section 3.3.2. 'which describes the Phillips technique.
6.1.6. Identify the Criteria that Discriminate Most
Among the Alternatives
Sharplv
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OSWER Directive # 9028.OOb
Recall that it was advised not to assign weights to criteria
in the traditional manner (See 3.3.2). This is the reason.
Perhaps surprisingly, the importance of each criterion depends on
the results of the analysis. If a criterion does not discriminate
among the alternatives, it is not important to the decision even
though it may be critical to the success of the project. For
example, although data integrity is crucial in most DBMS
applications, it will not affect the selection decision if all the
alternatives satisfy all the data integrity objectives.
Similarly, if all the costs of the alternatives a-re nearly
identical, the cost., though important, will not enter into the
decision of deciding between alternatives.
The decision will be based on the discriminators - the
benefits, costs and risks that most sharply differentiate the
alternatives. In this phase of the analysis the goal is to
identify t'he discriminators and to review the descriptions of the
alternatives to make certain that each discriminator is fully
discussed.
If there are truly no discriminators, do not fabricate one.
"No difference" is a valid conclusion for the analysis of any
single criterion. More often, discriminators between alternatives
will exist and will provide a basis for making an insightful
choice.
At the conclusion of this step, the project team is left with
a set of clearly defined benefits, costs and risks for each
alternative. These will be used as the basis for choosing among
alternatives. In the next step, sensitivity analysis (Chapter 7),
the project team will have the opportunity to test their estimates
and assumptions before presenting their recommendations.
6.2. Comparing Budgetrelated Benefits and Costs: Financial
Analys is
There are four major computational techniques for comparing
alternatives: Payback, Break Even Analysis, Net Present Value, and
Benefit/Cost Ratio. These techniques may be used independently or
in combination, as appropriate, to compare the financial viability
of alternative projects.
6.2.1. Payback (Source: DLA)
Probably the most widely understood method for comparing
alternatives (or for evaluating a single project) is "payback"
analysis. Most simply defined, payback is the period of time
required for a project's total accumulated benefits to offset
investment (i.e. non-recurring) costs. Thus, if one were to
consider a project costing $100, yielding a $25 annual benefit,
its undiscounted payback perio'd would be 4 years.
41
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OSWER Directive # 9028.OOb
Note that the economic connotation of payback is not affected
by the duration of the project's life. (For example, a 4.5-year
payback means the same thing whether the economic life is 10 years
or 25 years.) Thus, the payback method can be used to establish
priorities for competing projects. Projects having quick payoffs
are generally preferred.
There are two major shortcomings to undiscounted payback.
Undiscounted payback ignores the "time value of money" and it -
ignores the cash flows beyond the payback period.
In the example above, the 4-year payback represents an
undiscounted payback. By failing to distinguish the timing of
cash flows within a project payoff period, undiscounted payback
ignores an important element, the "time value of money." For
example, a project costing $350,000 that will return $50,000 per
year for 10 years appears to be a good investment. The return
will be $500,000. Thus, it appears that the project will amortize
itself in 7 years. However, application of the 10% discount
factor over the full 10 years yields a present val-ue of only
$322,350. Thus, such a return would not adequately cover the
initial $350,000 non-recurring cost.
A second weakness of the example lies in its failure to
address cash flows beyond a period necessary to recover initial
investment or non-recurring costs. If significant one-time costs
(e.g., major repair or overhaul costs, or terminal site
restoration costs) are to occur after the estimated point of
payback, the economic attractiveness of the proposed project will
be overstated.
There is a more'useful method to apply the payback technique.
By incorporating a."time value" element and including all future
cash flows, the concept can be modified to determine the
"discounted payback" period. Thus, payback would be achieved when
total accumulated present value benefits are sufficient to offset
(i.e., amortize) the total present value costs of a proposed
alternative. The payback period is simply the total elapsed time
between the point of initial investment and the point at which
payback will occur.
A more detailed explanation can be found in Appendix I -
Payback.
6.2.2. Break-even Analysis (Source: DLA)
Break-even analysis is an important analytical technique used
to study the relationship between alternative cost patterns.
Here, the analysis focuses on finding the value of the variable
(the "break-even point") at which the manager is indifferent
regarding two possible courses of action. At the break-even
42
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OSWER Directive # 9028.OOb
point, the economic desirability of the two alternatives is equal.
To either side of the point one alternative or the other has the
economic advantage.
Break-even analysis is usually carried out with the use of
so-called break-even charts. Exhibit 6-3 is an example. Such a
chart serves as a convenient and effective means for communicating
with the decision maker, and is readily acceptable and easily
understood.
In Exhibit 6-3, the horizontal axis is scaled to measure time
in yearly intervals. However, any other convenient and meaningful
measurementcould be used, such as the number of units produced or
hours of machine operation. The vertical axis is scaled off in
dollars. Accordingly, the chart depicts the cost patterns
(cumulative total cost over time) for each alternative. The
intersection of the two cost curves determines the break-even
point. In this case it occurs during Year 4.
Costs
($)
400
300
200
100
0
Alt 1
Alt 2
Break-even
point
End of
Years
Exhibit 6-3
Break-Even Chart
To the left of the point for the example presented in Exhibit
6-3, the cumulative cost for Alternative 1 is less than the cost
for Alternative 2. At the break-even point the two alternatives
are equal. To the right of the point, the cumulative cost for.
Alternative 1 is greater than for Alternative 2. Thus, as
demonstrated in Exhibit 6-3, graphical break-even analysis
provides a quick, visible means of comparing alternative cost
patterns.
When comparing two alternatives, the project team generally
performs a break-even analysis of their life cycle cost patterns.
Cumulative discounted costs for each alternative are compared over
43
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OSWER Directive # 9028.OOb
time, and the point at which the alternatives are equal is
determined.
When an alternative is compared against its status quo, the
break-even point determines the exact point when annual net
benefits will begin to accrue. The following example demonstrates
this use of break-even analysis. '
In this example, break-even analysis is used to graphically
compare a proposed investment with the status quo. Cumulative
discounted costs for each alternative were computed from the
following cost data and are graphed in Exhibit 6-4.. The status
quo has an annual cost of $80, while the proposal had a non-
recurring investment of $200 and an annual cost of $20.
Cumulative discounted costs are:
Year Status Quo
0 $0
1 76
2 146
3 209
4 266
5 318
6 366
7 409
8 448
Proposal
$200
219
236
252
266
280
291
302
312
Cumulative
Discount Costs
($)
500 '
400
300
200
100
0
Status
Quo
Proposal
Break-even
point
End of
Years
Exhibit 6-4
Break-Even Chart -- Classical Case
Note that all numerals on the horizontal graph represent the end
of years. Thus, the chart -shows a break-even point at the end of
Year 4, i.e., when cumulative discounted costs for both
alternatives are $266.
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OSWER Directive # 9028.OOb
For a more detailed explanation of break-even analysis refer
to Appendix G - Break-Even Analysis.
6.2.3. Net Present Value (Source: DOE)
It is necessary to express the benefits and costs of
different alternatives in terms of their present value. The
benefits and costs of each alternative are likely to occur at
different points in the analysis period. How does a decision
maker compare different benefits and costs when they occur at
different intervals? Present value analysis allows a project team
to convert benefits and costs occurring at different times to
their current (i.e., present) value.
Present Value Analysis is based on two principles:
Benefits accruing in the future are worth less than the
same level of benefits that accrue now; and
Costs that occur in the future are less burdensome than
costs that occur now.
Present value analysis assumes that a dollar received today
is worth more than a dollar received tomorrow. A dollar invested
today begins to earn interest immediately. A dollar received in
the future cannot earn interest until it is invested. The
difference in present value is the amount or interest earned by
the dollar invested today before the future dollar can be
invested.
The current year (year 0) establishes the time reference
point for present value calculations. This is known as the
baseline year. The present value analysis atiows the value of
future years benefits and costs to be calculated as if they all
occurred in this year.
Calculating the present value of benefits and costs is called
discounting. This calculation multiplies the benefits and costs
by a factor referred to as the discount rate, or opportunity cost
of capital. A discount factor is a predetermined factor based on
the established discount rate and time period. Discount factors
used by OSWER incorporate the 10 percent discount rate specified
by the Office of Management and Budget in their Circular A-94.
Exhibit 6-5 shows the discount factors based on a 10 percent
discount rate. Column 2 shows the "end-of-year" factors. These
factors are used when benefits and costs are incurred toward the
end of each year.
It is common for benefits and costs to occur, more evenly
throughout the year. A good example is monthly time-sharing
charges. It is also common for major cost elements to occur at
the beginning or middle of the year. Thus a more realistic.
45
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OSWER Directive # 9028.OOb
discount factor would be an average factor for the year. Column 3
of Exhibit 6-5 shows average discount factors.
Choosing which factors to use depends on the project being
analyzed. Use the average factor if benefits or costs occur
evenly throughout a year. Use the end-of-year factor if the
timing of benefits and costs cannot be specified or if they occur
in the later part of a year.
The illustration shown in Exhibit 6-6 is a sample report
which shows how to present a present value analysis. The one-time
costs plus the recurring costs .equal the total costs for the
proposed alternative. In this illustration, costs and benefits
occurred in the later part of each year. Thus, the project team
used the end-of-year discount factors. Discounted costs were
entered into the "Discounted Costs" column. The "Expected Yearly
Benefit" column represents the discounted benefits associated with
the proposed system.
Reducing all quantifiable benefits and costs to present value
allows a comparison of the various alternatives. The most
straight forward comparison is net present value (NPV).
NPV is the difference between the present value of the
benefits and the present value of the costs, or:
NPV = PV (benefits) - PV (costs)
In the illustration in Exhibit 6-6, the present value of
benefits is $1,646,719, and the present value of cost is
$1,519,682. The NPV is $127,037 (i.e. $1,646,719 - $1,519,682)
over the eight year period.
In other words, the quantifiable benefits for this
alternative exceed costs (i.e., it makes a net contribution to
value). Using NPV assists in selecting the most economical
alternative (i.e.,'the alternative with the highest NPV).
However, non-quantifiable benefits may show that an alternative
with a lower NPV may be more desirable (i.e., quantifiable
benefits may not be the sole criterion for choosing the best
alternative). Mitigating factors such as different non-
quantifiable benefits among the alternatives, large initial cash
outlays, budgetary constraints, manpower restrictions, etc., may
require selection of an alternative that does not have the highest
NPV.
Exhibit 6-5 Discount Factors Based on a 10 Percent Discoutit
Rate
Average
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OSWER Directive # 9028.OOb
End of Year Discount
Project Year Discount Factor Factor
0 1.000 1.000
1 .909 .954
2 .826 .867
3 .751 .788
4 .683 .717
5 .621 .651
6 .564 . .592
7 .513 . .538
8 .467 .489
9 .424 .445
10 .386 .405
A discussion of the formulas for calculating the discount
factors can be found in many texts on managerial economics. These
books usually .contain tables with the discount factors for a range
of discount rates.
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OSWER Directive # 9028.OOb
Exhibit 6-6
Present Value Analysis: Alternative Xr
Alternative Benefits and Costs
Summary of
Organisation -
Date -
Project Title -
Year Expected Yearly Cost
Sine* One-Tim* Co*t« Recurring Cost* - Total Coiti
Initiation (Propoied System) (Proposed System)
0
1
2
3
4
5
«
7
I
Total
100,000
173,150
9,000
0
0
0
0
0
0
0
235,300
23S.300
235,300
235,300
235.300
235,300
235,300
235,300
100,000
401,450
244,300
235.300
235,300
235,300
235.300
235,300
235,300
Expected Yearly
Benefit
(Total of
Current System)
0
306,730
309,200
309.200
309,200
309,200
309,200
309,200
309,200
Discount
Factor
(10%)
1.000
0.909
0.126
0.751
0.613
0.621
0.564
0.513
0.467
Present
value Costs
(Discounted
Costs)
100.000
371.211
201.792
176,710
160,710
146,121
132,709
120,709
109,650
1,519,612
Present
value Benefits
(Discounted
Savings)»
0
278,111
255.399
232.209
211,114
192,013
174,389
151,620
144,017
1,646,719
NPV - SI,646,719 - $1,519,612 - $127,037
The result of multiplying tne Total Costs tines the Discount Factor for each year
The result of multiplying the Expected Yearly Benefit times the Discount Factor for each year
Note: A summary sheet should be prepared for each Alternative.
48
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OSWER Directive # 9028.OOb
NPV provides decision makers with a single measure of the
alternative's value over the comparison period. Decision makers
may also find it useful to see the relationship of alternative
cost patterns over the life of the project. This helps them
evaluate the impact of large initial cash outlays or budget
constraints. Exhibit 6-7 and Exhibit 6-8 show two examples'of
graphic presentation of the NPV analysis. Both graphs plot the
cumulative NPV for each alternative at the end of each year (i.e.,
the difference between the present value of benefits and the
present value of costs from project initiation through the end of
the year).
Since most system projects require substantial initial costs,
the NPV in the early years will most likely be negative. In some
cases, it may be important to recover the initial costs as quickly
as possible. Both graphs show where the benefits and costs are
equal (cumulative NPV equals 0). This is typically called the
break-even point. The length of time required to reach this point
is commonly called the payback period. Showing several
alternatives on the same graph allows the decision maker to
compare the time required for each alternative to "break-even." It
also shows the alternative whose NPV is largest at the end of the
comparison. In addition, both graphs allow decision makers to
visually compare alternatives at any point in the life cycle
For a more detailed explanation of NPV refer to Appendix A -
F. ' '
6.2.4. Benefit/Cost Ratio (Source: DOE)
A variation of the net present value approach is the benefit-
cost ratio or benefit-cost index. The benefit-cost ratio (BCR) is
the present value of benefits divided by the present value of the
cost, or: ^
BCR = PV (Benefits)
PV (Costs)
From our example:
BCR = 1.646.719
1,519,682
BCR =1.08
The benefit-cost ratio is a relative measure of an
alternative's value. The BCR provides a measure of the benefits
obtained per dollar spent. In the above example, for each dollar
spent, about $1.08 of estimated benefits are projected. The
higher the BCR, the larger the return. NPV on the other hand is
an absolute measure. In situations where funds are limited, the
BCR provides decision makers with an additional piece of
information. In selecting among alternatives for a particular
49
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OSWER Directive # 9028.OOb
Exhibit 6-7
Graphic Representation of NPV line Chart
2000
> T3
CU 0)
2 *J
-U
Q) -H
4J
(0 W
rH -
3 o
eo
3 o
U ^
-2000 ~
-4000 -
-6000
Current
Shared
Total
Conversion
Exhibit 6-8
Graphic Representation of NPV Bar Chart
Years
50
-------
OSWER Directive f 9028.OOb
project, the BCR shows which alternative provides the largest
return relative to costs.
For a more detailed explanation of BCR refer to Appendix H -
Savings/Investment Ratio.
51
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OSWER Directive # 9028.OOb
7 . How to Refine the Analysis, Sensitivity Analysis
(Source: DOE)
i
Even after measuring all benefits and costs and establishing
a ranking of the alternatives, the benefit-cost analysis is not
complete. Due to the uncertainties in the analysis (assumptions,
estimates, etc.), the decision maker(s) will want to know more
than the results using one set of conditions. Specifically, they
will want to know if a recommendation would change if one or more
of the inputs to the benefit-cost analysis varied. Sensitivity
Analysis is a way of analyzing the effects of- changes in input on
the outcome (NPV, BCR) of the alternative.
Sensitivity analysis is a what-if technique that tests
whether a change in one or more input (e.g., assumptions,
estimates, etc.). will affect the ranking of alternatives. In a
sensitivity analysis, input is varied to test the impact on the
alternatives.
. *
The project team must first determine whether or not a
sensitivity analysis is really necessary. if there is a high
degree of certainty about the input to the benefit-cost analysis
and the ranking of alternatives establishes one alternative as
markedly superior to the rest, the project team should not be
overly concerned about .testing for sen-sitivity. When there is
uncertainty (i.e., where assumptions and key forecasts can be
affected by external changes) and/or no alternative is clearly
superior, the project team should conduct a sensitivity analysis.
When conducting a sensitivity analysis, the project team must
select which input to test. The input selected will vary with the
nature of the benefit-cost analysis. Each benefit-cost analysis
is unique in that it has its own set of assumptions, forecasts,
and estimates. As a rule, sensitivity analysis should examine
input which has a significant impact on NPV. The other factor to
consider in selecting the input to examine is the confidence which
is placed in the assumption or estimate. The input which should
be considered is:
Cost Estimates - Effects of increasing or decreasing
major cost elements; i.e., those which have a
significant impact on the present value cost.
Length of System Life Cycle - Effects of a shorter or
longer system life cycle.
Volume. Mix, or Pattern of Work Load - Effects of
variation in the forecast of volume, mix, or pattern of
work load.
52
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OSWER Directive # 9028.OOb
Requirements - Effects of potential changes in
requirements resulting from either -legislative mandate
or changes in functional or organizational structure.
Configuration of Equipment or Software Effects of
changes in configuration of hardware, software, data
communications, and other facilities.
Conversion Costs - Effects of variation in costs of the
program conversion efforts. The cost of the conversion
process may vary depending on the adjustments necessary
to use the current programs with the new equipment.
One way to conduct a sensitivity analysis is to use
probability matrices. The probability matrix depicts the value of
an input for a series of possible forecasts. Exhibit 7-1 shows a
sample matrix for benefit estimates. The project team would
construct a similar matrix for all input being tested. The
project team can then determine the effect of the changes in any
input on the NPV of the alternatives. However, because input does
not usually change one at a time, the project team can combine the
matrices into several scenarios. The NPV of the alternatives
under different scenarios can then be compared to the original
ranking.
53
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OSWER Directive # 9028.OOb
Exhibit 7-1 Sensitivity Analysis: NPV of Alternatives Under
Varying Assumptions
Original
Benefit- 10% 10% Worst
Cost Benefit Cost Case
Alternative Analysis Reduction Increase Scenario
Shared $1,058 $621 $661 $224 .
Total $773 $338 $346 ($89)
Conversion ($2,740) ($3,120) ($3,399) ($3,779)
54
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OSWER Directive # 9028.OOb
8. Outline for Presenting Benefit-Cost Analysis
*
Once the project team has completed the sensitivity analysis,
having tested the assumptions to a reasonable degree, they may
proceed with presenting the results of the benefit-cost analysis.
The following outline should provide a basis for the format of the
report.
1. Summary of Information Management Problem
2. Methodology and Assumptions
3. Summary of Alternatives
4. Summary of Benefits
4.1. Financial Benefits
4.2. Quantitative Non-Financial Benefits
4.3. Qualitative Benefits
4-1 Benefits Analysis Exhibit (Benefit Categories vs. Time
Matrix. One Matrix per Alternative)
4-2 Benefits Summary Exhibits (Alternatives vs. Time Matrix.
One Line on Exhibit per Alternative)
5. Summary of Costs
5.1. Financial Costs
5.1.1. Non-Recurring Costs
5.1.2. Recurring Costs
5.2. Quantitative Non-Financial Costs
5.3. Qualitative Costs
5-1 Cost Analysis Exhibit (Cost Categories vs. Time Matrix.
One Matrix per Alternative)
5-2 Cost Summary Exhibit (Alternatives vs. Time Matrix. One
Line on Exhibit per Alternative)
6. Summary of Risks
6.1. Description of Risks
6-1 Risks Summary Exhibit (Alternatives vs. Risk Categories
Matrix. One Line on Exhibit per Alternative)
55
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OSWER Directive # 9028.OOb
7. Summary of Discriminating Factors
7.1. Description of Discriminators
7.2. Sensitivity Analysis
7-1 Discriminating Factors Exhibit (Alternatives vs.
Discriminating Factors Matrix)
8. Recommendations
56
-------
OFFICE OF SOLID WASTE
AND EMERGENCY
RESPONSE
(OSWER)
SYSTEM LIFE CYCLE
MANAGEMENT
GUIDANCE
Part 3: Practice Paper
Benefit-Cost Analysis
Appendices
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OSWER Directive # 9028.OOb
Appendices
Table of Contents
A. Economic Life and Project Life (Source: DLA) . 1
B. The Notion of Present Value (Source: DLA) 5
C. Basic Discounting Techniques (Source: DLA) 12
D. Inflation (Source: DLA) 17
E. Terminal Value (Source: DLA) 23
F. Unequal Economic Lives - Uniform Annual Cost
(Source: DLA) , 27
G. Break-Even Analysis (Source: DLA) 34
H. Savings/Investment Ratio (Source: DLA) . . . 41
I. Payback (Source: DLA) , 44
J. Sensitivity Analysis (Source: DLA) 50
K. Benefit-Cost Analysis Review Checklist (Source: DLA) .... 55.
L. -Project Year Discount Factors (Source: DLA) 57
M. Glossary of Terms (Source: DLA) 58
-------
OSWER Directive # 9028.OOb
Note: Materials contained in these Appendices provide
descriptions of analytic methods identified in Chapters 1-8
of this Practice Paper. These materials are taken
. virtually verbatim from the Department of Defense's
"Economic Analysis"1 and the methods they describe may not
match exactly the contents of Chapters 1-8.
iDepartment of Defense, Defense Logistics Agency, "Economic
Analysis", DLAM 7041.1, May 1985.
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OSWER Directive # 9028.OOb
A. Economic Life and Project Life (Source: DLA)
INTRODUCTION
In Chapter 1, benefit-cost analysis was defined as a method of
approaching the problem of choice. A fundamental choice that
faces the decision-maker is whether to spend more money today.and
less tomorrow or less now and more in some future period of time.
Before a choice can be made, one must first determine how far into
the future the period should extend, i.e., the appropriate time
period of the benefit-cost analysis must be established. Once the
economic life is determined, the project team can proceed in
developing cost streams for each alternative.
ECONOMIC LIFE
In general, economic life can be defined as that future period
of time over which the savings or benefits to be gained from a
project may reasonably be expected to accrue.
The economic life will ultimately be limited by three factors:
1. The MISSION LIFE is that period of time over which a need
for the asset or program is anticipated.
2. The PHYSICAL LIFE is the period during which a facility or
piece of equipment will be available before it is exhausted in a
physical sense. The physical life may vary significantly from
project to project depending upon usage.
3. The TECHNOLOGICAL LIFE represents the period before which
obsolescence would dictate replacement of the existing (or
prospective) asset.
As stated above, the economic life of an alternative may be
limited by any of these factors. However, the mission life is in
most cases the driving guideline for determining the economic life
of an alternative. For example, if the need for an asset is
anticipated to be 20 years, and that asset will last physically
only 5 years, the alternative can provide for the replacement of
that asset 3 times within the 20-year economic life of that
alternative. Since the mission life is generally a function of
the objective of the benefit-cost analysis, all alternatives may
be assigned the same economic life, thus simplifying the
comparison of alternatives.
NOTE: Due to planning horizon limitations, it is generally
recommended that economic lives in excess of 25 years not be used
in analyses. Moreover, due to discounting, cost streams beyond 25
years have little effect.
Appendix-1
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OSWER Directive # 9028.OOb
ECONOMIC LIFE GUIDELINES
Even though the equipment or facilities involved may have a
mission, physical, or technological life of a greater number of
years, the maximum economic lives shown in Table A-l will be used
for the categories of investments identified. If the mission,
physical, or technological life is less than the prescribed
maximum, then the actual number of years should be used as the
economic life.
Table A-l
ECONOMIC LIFE GUIDELINES
1. ADP Equipment 8 Years
2. Other Operating Equipment 10 Years
3. Buildings: -
a. Permanent - 25 Years
b. Semipermanent, nonwood 25 Years
c. Semipermanent, wood . 20 Years
d. Temporary or rehabilitated 15 Years
4. Utility plants and utility distribution systems 25 Years
MULTIPLE ASSETS WITH DIFFERENT ECONOMIC LIVES
Frequently a single project will involve multiple assets with
different economic lives. When this occurs, there are two methods
of handling the problem. The first is to let the economic life of
the dominant asset prevail with subsidiary assets being replaced
as necessary. The second method is to use the shortest economic
life and impute residual value2 to the asset with the longer life.
For example, assume a project with maximum lives for both
buildings and operating equipment. The two options available to
the project team are'to use:
1. A 25-year life for the building with replacement of
equipment every 10 years.
2Residual value is discussed in Appendix E
Appendix-2
-------
OSWER Directive # 9028.OOb
2. A 10-year life for equipment and show residual value of the
Building.
LEADTIME AND PROJECT LIFE
An investment may occur several years prior to the time that the
project starts providing benefits. The period of elapsed time
between initial funding or date of decision and the commencement
of the economic life is referred to as leadtime. For example,
consider an analysis in which the objective is to provide storage
space for material. Viable alternatives might include leasing a
warehouse, utilizing an existing Government warehouse,
constructing a new warehouse, etc. If a warehouse were leased,
the space would be available "immediately" and the leadtime would
be 0. However, if a new warehouse were built, construction might
extend for 2 years before the warehouse would be ready for
storage. The constructioa alternative, then, would have a 2-year
leadtime. The leadtime together with the economic life comprise
what is known as the project life.
CASH FLOW DIAGRAMS
Project life costs can be depicted diagrammatically through the
use of cash flow diagrams. The cash flow diagram is a pictorial
technique for representing the magnitudes and timing of all costs
associated with the alternative. It is customary to draw a cash
flow diagram for each alternative being considered in the
benefit-cost analysis. The first step in preparing a cash flow
diagram is the drawing of a horizontal line to illustrate the
entire time period to be considered. The line is then divided
into equal time periods. Each time period is numbered
chronologically. Illustration of cash flows is accomplished
through the use of vertical lines with arrowheads.
Outflows and inflows are differentiated by direction of the
arrowheads. Downward pointing arrows indicate cash outflows
(expenditures), while upward pointing arrows indicate cash inflows
(receipts).
Figure A-l illustrates a project with an economic life of 7
years. An initial investment expenditure of $10,000 occurs at
"time zero" (right now) and recurring costs of $2,000 are incurred
during each succeeding period. Receipts of $1,000 at the end of
the seventh period represent terminal value (terminal value is
discussed in Appendix E).
Appendix-3
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OSWER Directive # 9028.OOb
GASH FLOW DIAGRAM
$1000
t
. J J J J J J J
,. $2000 $2000 $2000 $2000 $2000 $2000 $2000
$10,000
Figure A-l
When leadtime is considered part of the project life, the cash
flow diagram will be somewhat altered. Figure A-2 shows an
alternative requiring research and development for a 2-year period
before yielding benefits. Investment costs of $20,000 are spread
uniformly over this period. When the alternative becomes
operational in the third year, its economic life .begins. The
economic life is 7 years with annual costs of $3,000. The
leadtime.for this project is shown with dashed lines to indicate
that it is not part of the economic life.
CASH FLOW DIAGRAM-WITH LEADTIME
0 1 2 3 4 5 6 ~" 7 8 9
1
' 1
1
$3000
$10,000 $10,000
J
$3000
J
$3000
J
$3000
1
$3000
1
$3000
1
$3000
Figure A-2
NOTE: Although the cash flows are represented as occurring at
the ends of years, they are presumed to have occurred at some time
during (or throughout) their respective years. This convention
will be adhered to throughout this manual.
Appendix-4
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OSWER Directive # 9028.OOb
B. The Notion of Present Value (Source: DLA)
INTRODUCTION
Money, like other goods and services, is a marketable commodity.
Its use can be bought and sold in the marketplace. The price it
commands is generally referred to as interest. The existence of
interest can be explained by examining both the supply and the
demand situations for money. By supplying money to another, one
deprives himself of immediate satisfaction - that is, he cannot
use his money to buy-consumer goods now (e.g., color T.V., new
car). The greater the fee received by the lender, or the higher
the interest rate, the greater the motive for putting .off
consumption in order to earn a return on invested money. It is
reasonable to believe that, if the return on invested capital were
removed, investment would be nonexistent.
On the demand side, it is sometimes profitable for business
enterprises to borrow money and pay the interest and fees required
by the lender. The reason this may be profitable is that capital
goods such as engineering equipment, machines, and structures are
productive, that is, they return more than they cost.
SIMPLE INTEREST
The interest rate is customarily expressed as a percent or
decimal, representing the fractional amount of a loan the borrower
must pay the lender within a specified interval of time. The
amount of interest I is determined by multiplying the principal P
by the rate of interest i. This may be expressed through the
simple interest formula:
I - P * i
COMPOUND INTEREST - ONE YEAR
Interest and principal are calculated for most accounts on a
compound basis. Compound interest is the result of adding interest
to principal in each period before calculating the interest on the
new principal for the next period.
.Suppose an amount of money P is lent today at an annual interest
rate i. ;":'At the end of the year the borrower will have to return
to the lender not only the original amount P but the additional
amount I. Thus, the total future amount FI due becomes:
FI = P + I
= P + (P * i)
= P (1 + i)
Appendix-5
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OSWER Directive # 9028.OOb
EXAMPLE B-l
Assume that a potential borrower wishes to borrow $1,000. If
the interest rate is 6%, what will be the amount due to the lender
1 year from now?
SOLUTION
P = $1,000, . i = 6%
F! =.P(1 + i)
FI = $1,000(1.06) = $1,060
COMPOUND INTEREST - TWO YEARS
Suppose that a loan is to be repaid at the end of 2 years
instead of 1. The amount Fl that would have been paid at the end
of Year 1 becomes the principal during the second year. Thus, the
formula for determining F2 is:
F2 =.P(1 + i) + i(P(l + i))
=P(1 + i) (1 + i)
=P(1 + i)2 .
.EXAMPLE B-2
Assume that $1,000 is again borrowed at a 6% interest rate.
However, this time the loan is made for a 2-year period. What
amount must be repaid when the loan becomes due?
SOLUTION
P = $1,000, i = 6%
F2 = P (1 + i)2
F2 - 1,000(1.06)2 = $1,000(1.1236) = $1,123.60
COMPOUND INTEREST - n YEARS
The only difference between the expression for 1 year and the
expression for 2 years is the addition of an exponent. It can be
shown through successive repetition of the above reasoning that if
an amount P is lent today at an annual interest i the total amount
repaid to the lender by the borrower at the end of n years is: Fn =
P(l + i)"
Appendix-6
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OSWER Directive * 9028.OOb
THE CONCEPT OF PRESENT VALUE
The inverse of compounding is discounting. Whereas, in
compounding one moves from the present into the future, in
discounting the movement is from the future back to the present.
The relationship of a single current amount of money and its
future equivalent was shown to be Fn = P(l + i)n. Algebraic
manipulation will convert this formula into its in verse
relationship. Thus, the formula used in discounting becomes:
P = Fn * 1/(1 + i)n
P now stands for present value, but it is the same as principal
in the compound interest formula.
EXAMPLE B-3
A grandfather wishes to establish a trust account for his new
grandchild. If the interest rate on the trust fund is 4%, how
much must the initial deposit be in'order to present the child
with $5,000 on his 21st birthday?
SOLUTION .
Fn =. $5,0.00 i - 4% n = 21
P = Fn * 1/(1 + i)n
P = $5,000 *l/(1.04)2i = $5,000(.438834) = $2,194.17
In this example the $5,000 gift 21 years from now could be made
by setting aside $2,194.17 today. It could be stated that,
relative to an interest rate of 4%, the present value of $5,000 21
years from today is $2,194.17.
TIME PHASING OF COSTS AND BENEFITS
It is important that the actual timing of costs and benefits be
accurately portrayed. Failure to do so can result in the
overstatement or understatement of discounted costs or savings.
Those investments involving a single expenditure of funds at the
start of the project can be easily handled, since the investment
costs are already at the present and require no discounting.
Unfortunately, this situation is not the usual case.
Disbursements are generally made throughout the project life.
Therefore, all future costs must be discounted and brought back to
their present values. The present value of the investment can be
determined by taking all funds disbursed in each project year and
applying the discounting formula developed above. The concept of
Appendix-7
-------
OSWER Directive # 9028.OOb
time phasing can be further explained through the following
example:
EXAMPLE B-4
Mr. Spendthrift's subscription to "Pennysaver" magazine is about
to expire. He wishes to continue his subscription for at least 3
years. Assume that there will be no subscription price changes
during this period and that interest rates will remain -at 7%. The
magazine rates are shown at the top of the next page.
Pennysaver magazine subscription rates:
1-year subscription - $10.00
2-year subscription - $19.50
3-year subscription - $28.50
What steps should Spendthrift take in order to minimize the cost
of renewing his subscription?
SOLUTION
Spendthrift has four alternatives from which to choose. By
finding the present value for each/ he will be able to determine
the least expensive alternative. Evaluation of the alternatives
are as follows:
ALTERNATIVE I: Buy a 3-year subscription today. Since this
choice involves a single investment today, no discounting is
required. Thus, the present value is:
PV - $28.50
ALTERNATIVE II: Buy a 1-year subscription today, followed by a
2-year subscription at its expiration. The initial investment
cost of $10 requires no discounting. However, all future costs
must be discounted to reflect the present value. Thus:
PV - $10 + $19.50 * 1/(1.07) - $10 + $18.22 = $28.22 -
ALTERNATIVE III: Buy a 2-year subscription initially, replacing
it with a 1-year subscription. This alternative is similar to
Alternative II. Again discounting is required only for those
costs incurred after the initial funding. The present value
becomes:
PV - $19.50 -I- $10 * 1/(1.07)2= $19.50 + $8.73 = $28.23
ALTERNATIVE IV: Buy a 1-year subscription today and renew each
year thereafter. No discounting is applied to the initial
Appendix-8
-------
OSWER Directive # 9028.OOb
investment. However, each of the succeeding years must be
discounted. Thus, the present value becomes:
PV - $10 + $10 * 1/(1.07)2 = $10 + $9.35 + $8.73 = $28.08
As can be seen in this example the least costly alternative is
Alternative IV. Thus, in order to minimize his costs, Spendthrift
will choose to renew his subscription at the end of each year.
PV COMPARISON OF ALTERNATIVES WITH UNEQUAL LIVES
In comparing alternatives by the present value method, it is
essential that all alternatives be considered over the same length
of time. If the alternatives each have the same expected life,
there is no problem, for that life can be used. When the
alternatives have different expected lives, it is common to use. a
period equal to the least common multiple of the lives, or the
length of time during which the services of the chosen alternative
will be needed, whichever is less. For example, if two
alternatives have expected lives of 3 and 4 years respectively,
then the least common multiple of the lives to use is a period of
12 years. However, if the service for which alternatives are
being compared is expected to be needed for only 9 years, then 9
years should be used. (Also see Appendix F.)
DISCOUNT RATE
The discount rate is generally recognized as a critical datum
for the evaluation of any proposed Government project. Even when
there is little disagreement about the investment's prospective
costs and benefits, the choice of the discount rate figure may
make the difference between acceptance and rejection. For
example, a project which seems to yield substantial net benefits
when evaluated at a 3 percent rate may well appear wasteful if the
rate is 10 percent.
The proper criterion on which to judge the desirability of a
Government project, from the point of view of the general welfare,
is the value of the opportunities which the private sector must
pass by when resources are withdrawn from that sector. A
Government project is desirable if, and only if, the value of the
net benefits it promises exceeds the cost of the lost productive
opportunities which that investment causes. The correct discount
rate for.the evaluation of a Government project is the percentage
rate of return that the resources utilized would otherwise provide
in the private sector.
The current discount factor to be used in evaluating DLA
investment is 10%. This rate is considered to be the most
representative overall rate at the present time. It represents an
estimate of the average rate of return on private investment
before corporate taxes and after adjusting for inflation. Thus,
the 10% rate is the weighted average opportunity cost of private
Appendix-9
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OSWER Directive # 9028.OOb
spending that is reduced as a result of taking money out of the
private sector.
COMMON MISCONCEPTIONS ABOUT .THE 10% RATE
A number of misconceptions have arisen regarding the 10%
discount factor. Some of the more common ones are discussed
below.
1. The 10% factor is often conceived as a measure of the rate
of inflation. Though inflation may have substantial impact upon
any benefit-cost analysis, it is most important that its treatment
not be confused with discounting. The concepts are similar in
that both recognize that future dollars are not worth as much as
today's dollars. However, to differentiate the two concepts the
project team should keep in mind that discounting adjusts a given
future dollar level to reveal how many dollars today, drawing
interest at a given compound-rate, would equate to the same number
of dollars at the given future date (i.e., the present value of
future dollars). On the other hand, inflation merely treats the
future dollar for anticipated erosion of the purchasing power of
today's dollar (a cup of coffee today costs 20 cents, but the same
coffee is expected to cost 30 cents in the future).
2. Some argue that discounting is inappropriate because it
ignores the reality of inflation. This, however, is not true in
the case of the 10% rate prescribed for benefit-cost analysis.
The 10% rate automatically adjusts for a normal rate of inflation.
If, however, inflation is expected to rise above the normal rate,
a further adjustment .could be made. (See Appendix D.)
3. Some argue that present value analysis is inapplicable when
evaluating Government investment proposals because the Government
has no option of "banking" money to earn a return. An overall
budget is set and money not immediately spent"*on one project is
spent on another. Here it must be recognized that the "return"
implied by the 10% discount rate does not refer to the result of
the Government holding money, but rather to the opportunity cost
imputed through the transfer of resources from the private to the
public sector.
4. One school of thought maintains that the discount rate
should be determined by and be equal to the rate paid by the
treasury in borrowing money. This concept is built on the premise
that if particular projects are to be undertaken using borrowed
funds, then the minimum rate of return should be based on the rate
of cost of those borrowed funds alone. However, this argument
proves to be invalid because Government investment is not financed
solely through borrowed funds. The majority of revenue is raised
through taxation. It is this involuntary transfer of resources
from the private sector to the public sector that is used to
finance most Government investments. Because this money could
Appendix-10
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OSWER Directive * 9028.OOb
have been used to finance private investments, it is appropriate
that the private sector rate of return be used.
Inflation is discussed in Appendix D.
Appendix-11
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OSWER Directive # 9028.OOb
C.Basic Discounting Techniques (Source: DLA)
INTRODUCTION
The discount factor 1/(1 + i)n was developed in the previous
appendix (Appendix B). This formula can be applied to simple
examples where cash flows occur in the early years of the project.
However, when evaluating a more complex project involving cash
flows throughout the entire economic life, the computational task
of applying the formula becomes quite tedious. Therefore, it is
convenient to prepare a standard list of discount factors for
reference purposes. Using the prescribed 10% rate, such a list is
developed in Table C-l.
Table C-l
PRESENT VALUE - 10-% DISCOUNT FACTOR
Years from Today Present Value
(n) Factor
0 1/(1.'1)0 = 1.000
1 l/(l.l)i = 0.909
2 " 1/(1.1)2 = 0.826
3 1/(1.1)3 = 0.751
. 4 17(1.1)" = 0.6S3
5 17(1.1)5 = 0.621
DISCOUNT FACTORS
The factors depicted in Table C-l are termed "end-of-year"
factors. This title is appropriate because they are derived under
the assumption that cash flows occur precisely at the ends of
years. In the real world this is generally not the case. Costs
are usually dispersed throughout the year. Thus, a more realistic
discount factor would be one that occurs at some point during the
year. DLA currently employs "continuous" factors which are
derived from the standard present value formula and approximate an
average of the "end-of-year" factors.
Appendix-12
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OSWER Directive # 9028.OOb
Table C-2 illustrates the conversion from end-of-year to
continuous factors. A complete list of continuous present value
factors for years 1-30 is provided in Table A of Appendix L.
The rationale for using continuous factors instead of
end-of-year factors is essentially twofold:
I. After the initial investment cost, most of the annual costs
and benefits associated with a project do not occur at a single
point in time but rather are spread throughout the year. This is
typically true.of operating costs and salaries. Such costs are
best approximated by an annual lump sum payment.
2. The exact time of occurrence of costs and benefits in the
out-years of an economic life may not be known with certainty. In
the absence of more specific information, there is no reason to
assume that these costs and benefits will occur only on the
anniversaries of acquisition; they might occur at any point in the
year. Continuous factors are generally applied to such costs.
Errors on the low side should occur about as often as errors on
the high side. In the long run there will be an offsetting
effect.
Table C-2
END-OF-YEAR vs. CONTINUOUS DISCOUNT FACTOR (10%)
End-of-Year
Year Factor Continuous Factor
0 . 1.000 1.000
1 0.909 - 0.954
2 0.826 0.867
3 0.751 0*788
4 0.683 0.717
5 0.621 0.651
EXAMPLE C-l
DLA is considering the purchase of new ADP equipment to replace
existing equipment. Two alternatives are under consideration.
Both have economic lives of 8 years and yield equivalent benefits.
The following information has been collected:
Appendix-13
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OSWER Directive # 9028.OOb
Alternative A Alternative B
Initial Cost $7,500 $6,000
Yearly Operating
Costs
1 50 200
2 100 275
3 150 350
4 210 : 425
5 270 500
6 340 600
7 410 700
8 500 800
Total Undiscounted
Costs $9,530 $9,850
Which is the more economical equipment to own and operate?
SOLUTION
By applying the appropriate discount factors, the present value
of each alternative can be determined.
ALTERNATIVE A:
PV = $7,500 + $50(.954) + $100(.867) + $150(.788) + $210(.717) +
$270(.651) + $340(.592) + $410(.538) + $500(.489) =
$8,745.30
ALTERNATIVE B: .
PV = $6,000 + $200(.954) + $275(.867) + $350(.788) + $425(.717)
-I- $500(.651) + $600(.592) + $700(.538) + $800(.489) =
$8,458.25
It is clear that Alternative B is more economical even though
Alternative A reflects lower total undiscounted costs.
EXAMPLE C-2
As one alternative in a certain project, DLA is considering
leasing additional warehouse space for a 4-year period. Annual
rental would amount to $10,000. What will be the total discounted
cost if this alternative is chosen?
SOLUTION
Again, discount factors are used to determine the present value
of this alternative:
Appendix-14
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OSWER Directive # 9028.OOb
PV - $10,000(.954) + $10,000(.867) + $10,000(.788) +
$10,000(.717)
= $9,540 + $8,670 + $7,880 + $7,170 = $33.260
The above calculation can be simplified if the recurring $10,000
is factored from each term. Thus:
PV = $10,000 (.954 + .867 + .788 + .717)
In effect, all this operation entails is finding the sum of the
first four factors in Table A and then performing a single
multiplication.
To simplify this task even further, a list of cumulative sums of
Table A factors has been developed. These sums can be found in
Table B of Appendix L. Using Table B, the corresponding
cumulative discount factor for the above problem is 3.326. Thus,
the present value becomes:
PV = $10,000(3.326) = $33,260
This is exactly the same result obtained earlier using Table A
factors.3
EXAMPLE C-3
DLA is planning to automate one of its management information
systems. One of the alternatives being considered has an 8-year
life and projected costs as follows:
*.
Initial Costs $35,000
Operating Costs
Year 1 2,000
Year 2 2,500
Years 3-8 3,000
What will be the discounted cost of the project for this
alternative?
SOLUTION ...
The solution to this problem involves the use of both Tables A
and B of Appendix L. To discount the single amount factors in
years 1 and 2, Table A factors must be used. Years 3-8, however,
Discrepancies occasionally occur between answers obtained by
the Table A method and the Table B method; these are attributable
to rounding off error. Table A factors have been computed from
mathematical formulae rather than simple addition of Table A
factors.
Appendix-15
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OSWER Directive f 9028.OOb
involve a uniform series of costs. For these years, Table B
factors are applied by considering the difference between the 2nd
year factor and the 8th year factor. Thus, for this example the
cumulative discount factor for years 3-8 is 3.776 (i.e., 5.597 r
1.821).
Therefore, the total present value is:
PV = $35,000-+ $2,000(.954) + $2,500(.867) + $3,000(3.776)
= $35,000 + $1,908 + $2,168 + $11,328 - $50,404
CUMULATIVE DISCOUNT FACTOR RULES
Two general rules for the application of cumulative discount
factors may be stated as follows:
Rule 1 - To find the present value of a series of uniform
recurring cash flows beginning in Year 1 and continuing through
Year n, multiply the amount of the annual payment by the nth_year
factor from Table B, Appendix L.
Rule 2 - To find the present value of a series of uniform
recurring cash flows beginning in Year m and continuing through
Year n, multiply the amount of the annual payment by the
difference between the factors for Year n and Year m-1 in Table B,
Appendix L.
Appendix-16
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OSWER Directive # 9028.OOb
D . Inflation (Source: DLA)
INTRODUCTION
For a benefit-cost analysis to be a useful decision-making tool,
estimates of future costs and benefits must be as realistic as
possible. The forecasting of such costs becomes more complicated
when there is a persistent and appreciable rise in the general
level of prices over time. This condition is commonly referred to
as inflation. The problem caused by inflation is not simply that
future acquisitions are likely to cost more than today's
estimates, but that there is an uncertainty as to how much more
they will cost. It is this uncertainty which so complicates
financial planning and the benefit-cost analysis as well.
Therefore, some method of determining the rate of inflation must
be established.
MEASURING INFLATION
To determine current and past rates of inflation, measurements
of price changes can be made by means of index numbers. A "price
index" is a percentage comparison of the total cost of a selection
of commodities and services between two periods of time. Index
numbers of the aggregate type may be simple or weighted. A simple
aggregate index is calculated by adding the total prices actually
paid for a group of commodities for a given period, perhaps a
year. This total can then be compared, on a percentage basis, with
the total prices for the same items for the base period.
Weighing is accomplished by simply multiplying the prices paid
for each unit of a commodity by the number of units sold during
the given period. A weighted aggregate index avoids the bias of
the simple arithmetic average.
The use of price indexes is limited by the fact that only a
limited number of commodities can be considered, so only the "most
important" are used as a sample. Other problems encountered in
constructing price indexes are: getting an accurate sample of
prices; allowing for quality improvements; and deciding which
average to use (arithmetic or geometric mean, median).
AVAILABLE PRICE INDEXES
The Consumer Price Index (CPI) and the Wholesale Price Index
(WPI) are the most commonly known indexes. The problem with using
these indexes in DoD benefit-cost analysis is that they do not
apply very well to defense expenditures. These and most other
available indexes are unsuitable because they do not include a
sufficient cross section of military items.
However, other special indexes and techniques exist which can be
used or developed for use in predicting inflation for benefit-cost
analysis. The Office of the Secretary of Defense (Comptroller)
Appendix-17
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OSWER Directive # 9028.OOb
regularly disseminates cost escalation projections for military
construction and family housing; research,' development, test, and
evaluation (RDT&E); and other major areas of procurement. The DoD
Comptroller also compiles a personal pay index which .includes both
military and civil service compensation. Other indexes can be
derived for component subgroups of available indexes compiled by
the Bureau of Labor Statistics. Whatever their source, officially
disseminated cost projections should not be construed as anything
more than a general guideline. Where available, specific local
data may be used to establish a more realistic cost model. All
sources should, of course, be explicitly documented.
ESTIMATION OF INFLATION
Once a method of measuring inflation has been established, a
major problem is posed in determining what rate to use since
benefit-cost analyses are comparisons of future costs and
benefits. Forecasting future inflation rates can be accomplished
in several ways. One method is to forecast that the current rate
will continue in the future. This method will yiej-d credible
estimates if the current rate and the rate which has been
experienced in the recent past are relatively constant. If the
trend in recent inflation rates has been significantly increasing
or decreasing, a forecast that the current rate will continue is
suspect.
Another method of estimating the future rates, which will
alleviate some of the problems of forecasting a continuance .of the
current rate, is to project the future on the basis of a i
regression analysis of past rates. This is accomplished through
the method of Least Squares. Estimation of future inflation rates
by linear regression assumes that the future will be the same as
the past. The more historical data points used, the more the
trend will average out deviations, i.e., the ..double digit
inflation rate experienced in 1973 and 1974 will be offset by
lower rates in other years.
A third method of estimating future rates, which does not assume
a linear correlation with time alone, is the use of econometric
models. These models attempt to find those factors which cause
inflation and to establish their mathematical relationship with
inflation. Factors generally incorporated in econometric models
include: unit labor cost; material input costs; and excess demand
variables (such as unfilled orders, capital utilization rate, or
inventory/sales ratio). Building such a model requires the
expertise of a trained econometrician.
What method should be used? A practical solution is to use a
combination of methods, i.e., introduce a range of inflated costs
in the analysis using two or more of the foregoing methods.
Appendix-18
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OSWER Directive # 9028.OOb
TREATMENT OF INFLATION IN COMPUTATION
Department of Defense policy regarding the treatment of
inflation in benefit-cost analyses, as promulgated by DoDI 7041.3,
benefit-cost analysis and Program Evaluation for Resource
Management, requires a two-phased approach:
1. The analysis should be performed first in terms of constant
dollars; i.e., all estimates of costs and monetary benefits during
the project life should-be made in terms of base-year prices.
2. If inflation is deemed important to the conclusion of the
study (i.e., the ranking of alternatives), a second computation
should be made in terms of current dollars. Costs and monetary-
benefits stated in current dollars reflect the actual amount which
will be paid including any amount due to future price changes.
The requirement to perform a baseline analysis in constant
dollars promotes consistency among comparative economic studies.
Since the standard 10% discount factors implicitly escalate dollar
cost estimates at a normal rate, the baseline comparison should
suffice in many cases. Moreover, it will be found frequently that
introduction of inflation factors into the analysis will have
little or no effect in the final ranking of the alternatives.
However, for those instances when an inflated dollar comparison
is nonetheless considered appropriate, only a differential
inflation rate (i.e., the expected difference between the average
long-term rate for the particular cost or cost element) should be
applied in the escalation of the base-year annual, cost estimate.
Recall that a normal escalation component is automatically
introduced when discount factors are applied.
INFLATION/DISCOUNT FACTORS
-M
Once the differential rate has been selected, the project team
may proceed with the inflating and discounting of project costs.
This is accomplished by developing and applying combined
differential inflation/discount factors that reflect both the
differential and discount rates. The following formulae yield
these factors:
Singles year factor:
Cn - (e - i) / ((i-D) * e»
-------
OSWER Directive f 9028.OOb
where:
n = the number of year(s),
e = 2.718281828459..., the base of the natural logarithms,
I = In (1+i) In (1.1) 0.09531018 ,
i = 0.10, the effective annual discount rate,
D = In (1+d), and
d = the effective annual differential inflation rate.
The following example illustrates the procedure to be used when
inflation is to be included in a benefit-cost analysis.
EXAMPLE D-l
A particular project being evaluated 6y DLA has an initial
investment cost of $2,000 and a future investment cost of $500 in
Year 3. The project also has a uniform recurring cost of $300
occurring in Years 1 through 5. Determine the present value for
this particular project if the recurring costs are expected to
escalate at 3% per year above the normal rate and the single year
investment in Year 3 is expected to escalate at 2% below the
normal rate.
SOLUTION
The first step in accordance with DoD policy is to perform the
analysis in constant dollars. in Table D-l the present value is
calculated, assuming no inflation.
Table D-l
PV WITHOUT INFLATION
Year
Costs
0 $2,000
1-5 300
3 500
Discount
Factor
1.000
3.977
.788
Discounted
Costs
$2,000
1,193
394
Cumulative
Discounted
Costs
$2,000
3,193
3,587
PV = $3,587
Appendix-20
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OSWER Directive # 9028.OOb
The next step is to perform the analysis in terms of current
dollars. The differential inflation rate is -2% for the single
year cost and 3% for the uniform recurring costs. Using the joint
inflation/discount factors calculated by the formulae, the present
value is calculated in Table D-2.
Table D-2
PV WITH INFLATION
Combined Cumulative
Inflation Inflated/ Discounted/
Discount Discounted 'Inflated
Year Costs Factor Costs Costs
0 $2,000 1.000 $2,000$2,000
1-5 300 4.261 1,278 3,278
3 500 .750 375 3,653
PV = $3,653
INFLATION AND THE BUDGET
. While the method described above is appropriate for the
economic analyst, it should not be used by the budgeter-for
funding purposes. The budgeter is interested in the actual cash
flows that will occur. Budgetary adjustments will be made as
directed by the Comptroller.
EXAMPLE D-2
Assume fiscal year 1985 to be the present. Given-the
following.construction cost escalation projections:
8% FY 85 to FY 86
7% FY 86 to FY 87
6% FY 87 to FY 88
6% . FY 88 to FY 89
Escalate a construction cost estimate of $1.20 M (FY 85
dollars) to the budgetary amount expected to be funded in FY 89.
SOLUTION
The FY 85 estimate must be escalated 8% to produce a FY 86
estimate, which in turn must be escalated 7% to yield a FY 87
estimate, and so on. The final estimate is:
Appendix-21
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OSWER Directive # 9028.OOb
FY 89 estimate = ($1.20 M) (1.08) (1.07) (1.06) (1.06)
= $1.56 M
0
The above calculation yields the escalated amount which is
actually expected to. occur. The simplistic approach of adding
each year's percentage escalation to produce an aggregate 4-year
percentage escalation, viz., 27% = 8% + 7% + 6% + 6%, understates
the final result as the following calculation shows:
($1.20 M)11.27) = $1.52 M
In general, the higher the yearly escalation figures or the
longer the overall escalation period, the greater will be the
distortion introduced by simply adding each year's percentage
escalation to produce an aggregate figure.
CONSTANT INFLATION CALCULATION
Year-to-year price index^projections are generally not
available for future periods as long as 15, 20 or .25 years. If
such an inflated analysis is to be performed, choice of an
inflation rate is at best a process of educated guesswork. In the
interest of computational expediency, it is usually best to apply
a constant "i" percent throughout the project life. The zero year
cost estimate C0 is escalated to an nth year estimate as follows:
Cn = C0 (1 + i) (1 + i) . . . (1 + i) = C0 (1 + i)"
This has exactly the same form as the general n year interest
formula discussed in Appendix B.
Appendix-22
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OSWER Directive # 9028..OOb
E. Terminal Value (Source: DLA)
INTRODUCTION
In many instances value can be imputed to assets no longer
being utilized.. This value can be either terminal or residual.
Terminal value is defined as the expected value of land, buildings
or equipment at the' end of its useful life and is treated as a
reduction in the cost of the particular alternative for which the
use of the asset is intended. Residual value is the computed
value of assets no longer being utilized at any point in time.
Residual value may or may not coincide with terminal value.
Probably the most important criterion for determining the
terminal/residual value is what will be done with the asset. Will
it be sold? Reutilized? Or will it continue in operation for
another cycle? Each of the above situations would probably call
for a different value. If the asset is sold or reutilized the
value will depend upon the actual market value for the item less
costs of sale or redistribution. If the asset is to be scrapped,
then the only value is the scrap value less costs of dismantling
and selling. If the asset is to continue in use, then a pro-rata
amount would be correct.
SALE OF AN ASSET/REUTILIZATION
In many investments, the proposed purchase of a new'piece of
equipment or facility eliminates the need for an existing piece of
equipment or facility. The cost associated with that investment
depends not only upon the purchase price of the asset but also
upon its expected market value at the end of its economic life and
the value of any assets released. If property is sold, the
proceeds benefit the Government. The value of the asset would be
the actual sale price less costs of sale.
If property is redistributed to some other Federal Agency,
that Agency is benefited even though there is no reimbursement or
cash flow to the Agency which controlled the property initially.
In this case the asset's value is determined by its current worth
in the market less costs attributed to redistribution. The
following example demonstrates how to treat the sale of an asset
at the expiration of its economic life as well as reutilization of
assets replaced.
EXAMPLE E-l
Replacement of certain operating equipment at a Government
facility will result in an annual savings of $500,000. The new
equipment will cost $2,000,000 and will have an expected sale
value at the end of its 10-year life of $200,000. The existing
operating equipment at the facility will be redistributed to
another Federal Agency; the fair market value is assessed to be
Appendix-23
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OSWER Directive # 9028.OOb
$600,000. Determine the net present value savings to. result from
this investment.
SOLUTION
The combined cash flow diagram is shown in Figure E-l.
$600K ' $70QK
$500K $500K $500K $500K $500K $500K $500K $500K $5QOK
V
10
Figure E-l
The investment cost is the cost of the new equipment less the
market value of the old equipment to be reutilized and the present
value of the new equipment to be sold 10 years later. The
investment cost (C) is:
C = $2,000,000 - $600,000 - $200,000 (.405) = $1,319,000
Present Value Saving is:
PVS = $500,000(6.447) = $3,223,500
Thus, Net Present Value Saving is:
NPVS = PV5 - C
= $3,223,500 - $1,319,000 = $1,904,500
TERMINAL VALUE AND DISCOUNTING
Terminal value will often have a limited impact upon an
investment decision. For example, an asset with a terminal value
of $10,000 in Project Year 26 (after 25 years of usage) Is reduced
to only $970 after discounting. This would hardly become a major
factor in deciding whether or not to invest $1 or $2 million.
Hence, such terminal value will not ordinarily be included in the
analysis. If however, the terminal value is expected to be
significant, this value should be included in the analysis.
Accompanying this value should be explicit assumptions used in
deriving the estimate.
CONTINUED USE OF AN ASSET
Appendix-24
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OSWER. Directive # 9028. OOb
Often the need for a service will extend far into the future.
When this occurs, the automatic replacement of assets and
repeating cash flows will result in a repetitive cycle of
expenditures. A single project involving multiple assets with
different lives can be handled two ways. The first is to let the
economic life of the dominant asset prevail with subsiding assets
being replaced as necessary. The second method is to use the
shortest economic life and impute residual value to the asset with
the longer life. Residual value in this case is determined by a
pro-rata amount. This is true because the project is of an
ongoing nature and there is no actual termination taking place.
Note, however, if an asset were actually to be'sold before the end
of its economic life, straight-line depreciation would not be
used.
EXAMPLE E-2
In order to expand an existing facility, both additional
warehouse space and increased operating equipment is needed.
Determine the net present value, given the following information:
Costs Economic Life
Equipment $ 5 M .10 yrs
Buildings $20 M 25 yrs
Annual O&M $ 4 M .
This situation can be handled either by using a 25-year life,
replacing equipment every 10 years or by using a 10-year life,
showing residual value for the building. This solution considers
the second method.
SOLUTION
The pro-rata value of the buildings after a 10-year period is
15/25 of the original cost, or $12 million. The cash flow diagram
is.shown below.
$12M
I
9 10
J J 1 J J J J 1 1
$4M $4M $4M $4M $4M $4M $4M $4M $4M
25M
1
$4M
Figure E-2
Appendix-25
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OSWER Directive # 9028.OOb
The net present value is:
NP,V - $25M + $4M (6.447) - $12M (405)
= $25M + $25.8M - $4. 9M = $45.9M
Appendix-26
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OSWER Directive # 9028.OOb
F. Unequal Economic Lives - Uniform Annual Cost (Source:
DLA)
INTRODUCTION
So far, comparisons of investment proposals have been limited
to the use of the present value technique. This involves putting
all costs and receipts for each alternative in terms of their
worth as of the date a comparison is made. The present value
technique is designed for alternatives having equal economic
lives. It is not unusual, however, for service lives to differ
from alternative to alternative. When this occurs, it is
necessary to put all the alternatives on a common basis of time in
order, to make a valid comparison. A technique used to accomplish
this is the Uniform Annual Cost method.
UNIFORM ANNUAL COST
The Uniform Annual Cost (UAC) technique is a cost-oriented
approach to evaluating alternatives with unequal economic lives.
The technique involves putting all life cycle costs and receipts .
for each alternative in terms of an average annual expenditure.
Assuming that the alternatives are equally effective, the
alternative with the lowest UAC is the most economical choice.
To understand the rationale behind the technique, consider
the cash flow diagrams shown in Figure F-l.
CASH FLOW DIAGRAMS - UNEQUAL ECONOMIC LIVES
0 1 2 3 4 5 6 7 8 9 10 11 -12
ALT A i i i i i i i i i i i i
I J I I I J J I J I J I
ALTB
JJIIJMJ
Figure F-l
The following assumptions apply:
Appendix-27
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OSWER Directive # 9028.OOb
1. The cash flow diagrams represent alternatives
addressed to the same requirement.
2. No end is foreseen to the requirement, nor do
technological considerations play any significant role. It is,
therefore, the limitation of physical life which constrains the
economic lives of Alternatives A and B to 12 and 8 years,
respectively.
3. The only costs_associated with each alternative are
the uniform recurring costs shown in Figure F-l.
4. The two alternatives provide an equivalent level of
benefits per year. Thus, even if these benefits are difficult to
quantify, it is clear in view of the unequal economic lives that
the total benefits afforded by Alternatives A and B are not the
same.
5. The annual cost of Alternative A exceeds that of
Alternative B (as suggested by the cash flow diagrams).
Which alternative is preferable? Alternative B costs less
per year, but Alternative A provides benefits over a longer period
of time, and the requirement is open-ended.
Actually, the choice can be simplified if one additional
assumption is made:
6. Each alternative may be repeated indefinitely, with
the same cash flow pattern,
If assumption 6 is valid, Alternative A may be reinstated
once and Alternative B twice to arrive at the situation depicted
in Figure F-2.
CASH FLOW DIAGRAMS - UAC
ALT A ° 1 f . . " " " 24
' ii -n i
ALTB ° * f . « 8 » *6 " 2,4
' '!
Figure F-2
Appendix-28
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OSWER Directive # 9028.OOb
This strategy extends both alternatives to a common point in
time. Because of the general assumption that the alternatives
yield comparable benefits per year, the extended Alternatives (A:
and B! ) provide equivalent levels of total benefits over the
common 24-year period. From Figure F-2 it is obvious that
Alternative BI costs less it requires a smaller expenditure in
each of the 24 years. On this basis, Alternative B is preferred.
In real life one could scarcely expect cash flow patterns to
be so simplistic. More likely, there would be substantial
investment cost, and perhaps other one-time costs as well. There
is no guarantee that the annual recurring costs would be uniform.
A general unequal-economic-life situation might resemble that
of Figure F-3. Here the better economic choice is not obvious even
if the costs and economic lives are explicitly known.
CASH FLOW DIAGRAMS - TYPICAL UNEQUAL ECONOMIC LIFE SITUATION
ALT A
01234
n-1 n
rn
ALT B'
m-1 m
Figure F-3
The technique of uniform annual cost consists of converting each
alternative into an equivalent hypothetical alternative having
uniform recurring costs such as those in Figure F-l. The
conversion is such that the total net present value costs of the
actual alternative and its hypothetical equivalent are the same.
The hypothetical alternatives may then be compared. Once the
preferred hypothetical alternative is determined, the
corresponding actual alternative becomes the economic choice for
the project.
Appendix-29
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OSWER Directive # 9028.OOb
CALCULATION OF UAC
The analytical mechanism for calculating the UAC for an
actual alternative is as follows:
First, determine the present value (PV) cost of the
alternative. That is, find the sum of each year's discounted
costs using the discount rate of 10%.
Second, divide the PV by the sum of the discount factors for
the economic life of the alternative. Cumulative discount factors
are found in Table B of Appendix L. The formula for determining
the Uniform Annual Cost therefore becomes :
UAC = PV/bn
where bn represents the nth year Table B factor.
The UAC represents the amount of money which, if budgeted in
equal yearly installments, would pay for the project. Note that
this is not the same as taking a simple average. For example, a
theoretical building with a 25-year life and an acquisition cost
of $100 million would have an average annual acquisition cost of
$4 million. Using the technique of UAC, the annual cost would be
approximately $10 million for the same building.
Simple Avg. U.A.C.
$100M/25 = $4M PV/bn = $100M/9.524 = $10M
The use of a simple average for determining average annual
cost for benefit-cost analysis purposes is inappropriate because
it fails to acknowledge the time value of money. The UAC on the
other hand does incorporate this concept in its formula. In the
above example, the significance of the $10M uniform annual cost is
this: If $10M were to be spent each year for 25 years, the total
net present value of the payments would be $100M, the same as the
actual net PV cost of the alternative.
The financing of a new car provides a typical example of the
use of the UAC concept. When purchasing a new car on time, the
finance company will use the UAC concept to arrive at the amount
and number of payments necessary to reduce the balance to zero.
(Since car payments are usually monthly, the payments are based on
an equivalent monthly cost instead of equivalent annual cost . ) The
payments will be higher than the simple arithmetic average due to
interest charges. Thus, UAC is a type of average cost that
includes interest costs.
Appendix-30
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OSWER Directive '# 9028. OOb.
EXAMPLE F-l
New operating equipment will be purchased for one of the
DCASRs. Two equally effective alternatives are under
consideration. The following information has been provided:
Alternative A Alternative B
Initial Cost $350 $300
Yearly Operating Costs
1 45 25
2 45 25
3 45 25
4 50 45
5 90 30
6 50
7 50 -
Service life 7 yrs 5 yrs
Which is the more economical equipment to own and operate?
SOLUTION
First, it is necessary to compute the PV cost for both
alternatives. The calculations are displayed below:
PVA = $350 + $45(2.609) + $50(.717) + $90(.651) + $50(5.108 -
3.977) =$618
- PVB = $300 + $25(2.609) + $45(.717) + $30(.651) = $417
Each PV is then divided by the cumulative present value factor
corresponding to that alternative's economic life. The uniform
annual cost computations for the two alternatives are as follows:
Alternative A: PVA/b7 = $ 618/5.108 = $121
Alternative B: PVB/bs =$417/3.977 = $105
Since Alternative B has the lower uniform annual cost, it is the
one to be recommended.
UAC AND LEADTIME
Note that the technique of uniform annual cost spread cash
flows over the actual economic life only, and not over any period
Appendix-31
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OSWER Directive # 9028.OOb
of leadtime, even if costs are actually incurred during such a
period. Consider the following example:
EXAMPLE F-2
. Perform a uniform annual cost comparison on the two
alternatives represented by the cash flow diagrams shown in Figure
F-4.
o-
10
ALT A
J
100 100 10(
J
100 100
250
180
ECONOMIC LIFE
160
ALT B 0
180
180
2 3 4
100 100
12
100
13
100
14 .
100
II
15
10
Figure F-4
Alternative A, which starts offering benefits immediately,
has an investment cost of $250 and an annual-cost of $100. The
extra one-time cost of $80 in the tenth year might be, .say, for
demolition, dismantling and removal of an asset.
Alternative B has a total investment cost of $360 spread
uniformly over a 2-year leadtime. The alternative does not become
operational until the beginning of year 3, at which point its
economic life starts. (The leadtime period is dashed in the cash
flow diagram to indicate that it is not part of the economic life.
The total 15-year period shown is referred to as the project life
of the alternative.) This alternative, too, requires an annual
expenditure of $100. Terminal value of the asset is $160.
SOLUTION .
Alternative A:
PV = $250 -I- $100(6.042) + $180(0.405) = $927
Appendix-32
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OSWER Directive f 9028.OOb
UAC = $927/6.447 = $144
Alternative B:
PV $180(1.821) + $100(7.980 - 1.821) - $160(0.251) = $904
UAC = $ 904/6.519 - $147
Note that the economic life of Alternative B extends over a
13-year period (from the beginning of Year 3 through the end of
Year 15). The equivalent uniform annual cost, $147, is that
amount which, if paid annually from Year 3 through Year 15, would
total $904 in today's dollars, the same as the PV of the actual
alternative.
A generalization of the approach used in this example would
be the following: If an alternative has a project life of n
years, of which the first m years is l.eadtime (and therefore not
part of the economic life), its uniform annual cost is given by:
UAC = PV / (bn - bm)
In the example shown, Alternative A is economically
preferable because it has .the lower uniform annual cost;.plus, it
has the added benefit of being available 2 years earlier.
However, had the mistake been made of dividing $904 by 7.980 (the
15-year cumulative present value factor) in the UAC computation
for Alternative B, $113 would have been obtained. Since this is
less than the UAC obtained for Alternative A, Alternative B would-
have been concluded erroneously to be preferable. Since the major
use of the UAC is to compensate for differing economic lives among
alternatives, leadtimes are not considered in-the computation.
The point of the UAC is to evaluate the alternative only over the
time in which the project provides benefits.
SUMMARY
In summarizing the key ideas presented in this Chapter, it
should be reemphasized that Uniform Annual Cost is a benefit-cost
analysis-technique used to compare two or more alternatives having
different lives. The technique converts a stream of expenditures
over a number of years to a constant amount for each year in the
time frame. Calculation of the UAC involves dividing the present
value of the alternative by the cumulative discount factor
associated with its economic life, thereby taking into account the
time value of money. Thus, the analysis does not reflect actual
cash outlays, but is only used for comparison.purposes as part of
the decision-making process.
Appendix-33
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OSWER Directive # 9028.OOb
G. Break-Even Analysis (Source: DLA)
INTRODUCTION
Break-even analysis is an important analytical technique used
to study the relationship between alternative cost patterns.
Here, the analysis focuses on finding the value of the variable
(the "break-even point") at which the manager is indifferent
regarding two possible courses of action. At the break-even
point, the economic desirability of the two alternatives is equal.
To either side of the point one alternative or the other has the
economic advantage.
BREAK-EVEN CHART
Break-even analysis is usually carried out with the use of
so-called break-even charts. Figure G-l is an example. Such a
chart serves as a convenient and effective means for communicating
with the decision-maker, and is readily,acceptable and easily
understood.
In Figure G-l, the horizontal axis is scaled to measure time
in yearly intervals. However, any other convenient and meaningful
measurement could be used, such as the number of units produced or
hours of machine operation. The vertical axis is scaled off in
dollars. Accordingly, the chart depicts the cost patterns
(cumulative total cost over time) for each alternative. The
intersection of the two cost curves determines the break-even
point. In this case it occurs during Year 4.
BREAK-EVEN CHART
Costs
($)
400
300
200
100
0
3 4
Figure G-l
Alt 1
Alt 2
Break-even
point
End of
Years
Appendix-34
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OSWER Directive # 9028.OOb
To the left of the point for the example presented in Figure
G-l, the cumulative cost for Alternative 1 is less than the cost
for Alternative 2. At the break-even point the two alternatives
are equal. To the right of the point, the cumulative cost for
Alternative 1 is greater than for Alternative 2. Thus, as
demonstrated in Figure G-l, graphical break-even analysis provides
a quick, visible means of comparing alternative cost patterns.
THE CLASSICAL CASE
When comparing two alternatives, the project team generally
performs a break-even analysis of their life cycle cost patterns.
Cumulative discounted costs for each alternative are compared over
time, and the point at which the alternatives are equal is
determined. When a proposed investment is compared against its
status quo, the break-even point -determines the exact point when
annual net savings will begin to accrue. Example G-l demonstrates
this use of break-even analysis. .
EXAMPLE G-l
Use break-even analysis to graphically compare a proposed
investment with the status quo. Cumulative discounted costs are:
Year Status Quo Proposal .
0 $0 $200
1 76 219
2 146 236
3 209 252
4 266 266
5 318 280
6 366 291 ~
7 409 302
8 448 312
SOLUTION
Cumulative costs for each alternative were computed from the
following cost data and are graphed in Figure G-2. The status quo
has an annual cost of $80, while the proposal had an initial
investment of $200 and an annual cost of $20.
Appendix-35
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OSWER Directive # 9028.OOb
BREAK-EVEN CHART CLASSICAL CASE
Cumulative
Discount Costs
($)
500
400
300
200
100
0
Status
Quo
Proposal
Break-even
point
0
End of
Years
Figure G-2
The reader should note that all numerals on the horizontal graph
represent the end of years. Thus, the chart shows a break-even
point at the end of Year 4, i.e., when cumulative costs for both
alternatives are $266.
BREAK-EVEN ANALYSIS AND VARIABLE OPERATING COSTS
Break-even analysis is also a useful tool for analyzing the
financial characteristics of alternative operating systems whose
relative desirability is dependent upon some future variable (such
as the number of units produced, the number of hours of machine
operation, or the quantity of packages handled). Here, the
analysis focuses on how total cost's vary with output as operations
become more mechanized or automated, thus substituting fixed costs
for variable costs.
The following example is a simple illustration of- a
break-even analysis involving two production systems where the
time value of money is not involved.
EXAMPLE G-2
This problem involves selecting between two types of lathes,
the engine lathe and the turret lathe. For each machine, there is
a certain cost of setting up the equipment for production, In
addition, there is a cost charged for each unit produced on the
equipment. Given the following cost data, determine the job size
that represents the break-even point between the two alternatives:
Appendix-36
-------
Engine Lathe
Set up costs
Unit cost
$2.00
$1.50
. OSWER Directive # 9028.OOb
Turret Lathe
$3.50
$1.00
SOLUTION
Figure G-3 depicts the break-even analysis. The vertical
axis represents dollars per job while the horizontal axis measures
number of units per job. Cost lines for each machine are plotted.
BREAK-EVEN CHART ~ OPERATING ENGINE
$ Per Job
10
8
6
4
2
Engine Lathe"
I
Break-even
point
3 4
Figure G-3
Units
Per Job
The cost line for the engine lathe is below that for the
turret lathe when there are fewer than three units per job. When
more than three units are required, the turret machine is cheaper.
Of course, if the job requires exactly three units, then there is
no difference between the two machines on the basis of costs.
ALGEBRAIC BREAK-EVEN ANALYSIS
Although break-even charts provide a useful means of
illustrating cost relationships, algebraic techniques are
typically a more efficient means for analyzing decision problems.
The algebraic technique for solving a break-even problem consists
of setting the cost equations for each alternative equal and
solving for the unknown. The general cost equation is: TC = FC +
VC(x), where:
TC = total cost
FC = fixed cost
Appendix-37
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OSWER Directive # 9028.OOb
VC = variable cost x = unknown break-even point
The two equations for Example G-2 become:
TC engine = $2 + $1.50x
TC turret = $3.50 + $1.00x
Setting them equal and solving for "x" gives:
$2.00 + $1.50 x = $3.5Q + $1.00x
$.50 x =$1.50
x = 3
Thus, the break-even point is three units.
The following example incorporates the time value of money
and algebraically solves for the break-even point in a problem
involving variable operating costs.
EXAMPLE G-3
Two motors are being considered for installation in an
elevator system. Both have a 5-year life. Given the following
cost data, determine the number of hours of operation per year
that will represent the break-even point.
Motor A Motor B
Investment Cost . ' $450 $350
Operation Cost per hour $0.1714 $0.1819
Salvage Value $50 $40
SOLUTION
In this case, the future cost is dependent upon the number of
hours that the elevator is in operation. Hours of annual usage is
symbolized by "x." Cash flow diagrams are shown below.
Appendix-38
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OSWER Directive # 9028.OOb
$50
1
Motor A
$0.
1714x
$0
.1714x
$0.
1714x
$0
.1714x $0.171.
X
$450
$50
Motor B-
J
J [
$350
$0.1819x $0.1819x $0.1819x $0.1819x $0.1819x
Figure G-4
Here, the cost equation is represented by the present value of the
two alternatives:
PVA = $450 + ($0.1714x) (3.977) - $50(.651)
$450 + $0.68x - $32.55
$417.45 + $0.68x
PVB = $350 + ($0.1819x) (3.977) - $40(.651)
$350 + $0.72x - 26.04
$323.96 + $0.72x
To determine the break-even point, set the two present values
equal and solve for "x":
PVA = PVB
$417.45 + $0.68x = $323.96 + $0.72x
$93.49 = $0.04x
Appendix-39
-------
OSWER Directive # 9028.OOb
x = 2337 hours
Thus, operation of 2337 hours per year will result in identical
costs with either motor. As operational hours become greater than
2337, the motor with the lower operating cost (Motor A) will be
more economical. If the operation decreases to less than 2337
hours, the motor with the higher operating cost (Motor B) would
yield the greater cost reduction that accompanies less usage - and
would be more desirable.
With this information, the project team need not have a fixed
estimate of future use. They are concerned only with whether the
usage will be greater than or less than 2337 hours per year. Of
course, if anticipated usage is a range around 2337, the
break-even technique has not really solved the analyst's original
problem. Quite often, however, the break-even point falls outside
the anticipated range and selecting an investment for
recommendation has been simplified.
Appendix-40
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OSWER Directive # 9028.OOb
H. Savings/Investment Ratio (Source: DLA)
INTRODUCTION
Typical of many benefit-cost analyses is the situation where
a given requirement is already being met at the present time, but
a better solution (i.e., one whose PV cost is lower than that of
the existing alternative) is perceived. To measure the degree of
financial benefit attained from that investment, one may compute a
savings/investment ratio (SIR).
The SIR can be defined as the relationship between future
cost savings (or avoidances) and the investment cost necessary to
effect those savings. An SIR of 1 indicates that the PV of
savings is equal to the PV of the investment. Thus, for an
investment to be economically sound, the SIR must be equal to or
greater than 1.
Notice that nowhere in the discussion have benefits been
mentioned. The SIR is a characteristic of costs only and can be
used to analyze individual investments, for comparison of
alternatives, or to rank individual projects.
COMPUTATION OF SIR
In order to understand the concept of SIR, consider the
general situation depicted in Figure H-l below. Cash flow Diagram
A represents the status quo and Diagram B shows the proposed
alternative. Both extend over an economic life of n years.
CASH. FLOW DIAGRAMS - SIR EXAMPLE
A.
Status
Quo
TTT
ii-1 n
n
A -A
n-1 n
0123
B.
Proposal
i
1
1
B2 1
... j l
Bn-lB
' Bl B3
Figure H-l
Appendix-41
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OSWER Directive # 9028. OOb
When computing an SIR, the project team is not interested in
total operations costs - only the difference between life cycle
operating costs for the two alternatives, that is, the effect the
investment has on the operation. Thus, the crucial question in
Figure H-l is the following: Are the recurring savings of B
relative to A sufficient to warrant the investment cost I that
would be necessary to implement Alternative B? By "savings" is
meant the reduced amount of annual expenditure resulting from
replacement of the status quo by the proposed alternative. In
Figure H-l, the total present value savings (of Alternative B
relative to A) are:
PV(S) = PV(A! - BI) + PV(A2 - B2) + ... + PV(An - Bn)
where S denotes savings and the notation PV means "present value
of." The savings/investment ratio is therefore:
SIR = PV(S) / I .
Clearly, Alternative B should not be undertaken unless the
SIR exceeds unity (i.e., unless future discounted savings more
than offset the initial investment cost) .
REFINEMENT OF SIR
The above equation captures the essence of the
savings/investment ratio idea. A refinement to the SIR can be
made by closely examining the nature and timing of the cost
elements involved. For example, if the investment I associated
with the proposed alternative B extends over more than 1 year, the
total present value of I should be inserted into the SIR,
yielding:
SIR = PV(S) / PV(I)
If the Alternative B also includes a terminal value T, the present
value of T should be netted against the investment I as follows:
SIR = PV(S) /(PV(I) - PV(T))
The presence of other similar cost elements, such as the value of
assets replaced or a refurbishment cost to sustain the status quo,
would necessitate still further refinements.
EXAMPLE H-l
Production management has proposed purchase of a numerically
controlled cutting machine. The initial investment will be
$35,000. It is anticipated that this machine will reduce
operating costs by $6,000 per year during its 10 years of
operation. Salvage value after 10 years is $5,000. Is this
investment economical?
Appendix-42
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OSWER Directive # 9028.OOb
SOLUTION :
"A single cash flow diagram depicting the differential costs
between the proposed alternative and the status quo is shown at
the top of the next page.
$11,000
$6000 $6000 $6000 $6000 $6000 $6000 $6000 $6000 $6000
-------
OSWER Directive # 9028. OOb
I. Payback (Source: DLA)
Probably the most widely understood method for comparing
alternative investments (or for evaluating a single investment) is
"payback" analysis. Most simply defined, payback is the period of
time required for a project's total accumulated savings or
benefits to offset investment costs. Thus, if one were to
consider a project costing $100, yielding savings of $25 annually,
its undiscounted payback period would be 4 years.
Note that the economic connotation of payback is not affected
by the duration of the project's life. (For example, a 4.5-year
payback means the same thing whether the economic life is 10 years
or 25 years.) Thus, the payback method can be used to establish
priorities for competing projects. Projects having quick payoffs
are generally preferred.
LIMITATIONS TO UNDISCOUNTED PAYBACK
The example described above is not a true representation of ,
payback as used in DLA. There are two major shortcomings.
First, the 4-year payback represents an undiscounted payback.
By failing to distinguish the timing of cash flows within a
project payoff period, undiscounted payback ignores an important
element, the "time value of money." For example, a project costing
$350,000 that will return $50,000 per year for 10 years appears to
be a good investment. The return will be $500,000. Thus, it
appears that the project will amortize itself in 7 years.
However, application of the 10% discount factor over the full 10
years yields present value savings of only $322,350. Thus, such a
return would not adequately cover investment costs.
A second weakness of the example lies in its failure to
address cash flows beyond a period necessary to recover initial
investment costs. If significant one-time costs (e.g., major
repair or overhaul costs, or terminal site restoration costs) are
to occur after the estimated point of payback, the economic
attractiveness of the proposed project will be overstated.
DISCOUNTED PAYBACK METHOD
By incorporating a "time value" element and including all
future cash flows, the concept can be modified to determine the
"discounted payback" period. Thus, payback would be achieved when
total accumulated present value savings are sufficient to offset
(i.e., amortize) the total present-value costs of a proposed
alternative. The payback period is simply the total elapsed time
between the point of initial investment and the point at which
payback will occur. This is the method that will be used in DLA
benefit-cost analyses.
Appendix-44
-------
OSWER Directive # 9028.OOb
EXAMPLE 1-1
Preliminary studies indicate that by purchasing a $5,000
copying machine DLA can save $1,500 annually. During its fifth
year, major overhaul costing $3,000 will be needed. In 8 years
the machine will be worthless. Determine the discounted payback
for purchasing this machine.
SOLUTION
The present value of the total investment is:
PV(I) - $5,000 + $3,000(.651) = $5,000 + $1,953 = $6,953
The present value of the savings can be computed as follows:
Year
1
2
3
4
5
6
7
8
Savings
$1,500
$1,500
$1,500
$1,500
$1,500
$1,500
$1,500
$1,500
10%
Discount
Factor
.954
.867
.788
.717
.651
.592
.538
.489
PV(S)
$1,431
$1,301
$1,182
$1,076
$ 977
$ 888
$ 807
$ 734
Cumulative
PV(S)
$1,431
$2,732
$3,914
$4,990
$5,967
$6,855
$7,662
$8,396
The total present value savings over the life cycle is
$8,396. However, it is not until Year 7 that the cumulative PV(S)
= PV(I). At that point all discounted investment costs are
recouped. The exact point of payback can be found through
interpolation. First, subtract Year 6 Cumulative PV(S) from the
PV(I). This will give the discounted dollar value of sayings
occurring in Year 7 which attribute to payback ($6,953 - $6,855 =
$98). Next divide this amount by the total PV(S) for Year 7 to
find the proportion of that year during which the investment is
being paid back ($98/$807 = .121). Thus, the "discounted payback"
is 6.1 years.
Note: When annual savings remain constant throughout the entire
economic life, payback can be computed using the cumulative
discount factors in Table B. Discounted payback for the above
example would be computed as follows:
Appendix-45
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OSWER Directive # 9028.OOb
First, divide the PV(I) by the annual savings:
PV(I)/Annual Savings = $6,953/$l,500 = 4.635
Nekt, compare this value to the cumulative discount factors
in Table B. The corresponding project year will be the "point of
payback. The value 4.635 falls between the discount factors for
years 6 and 7. Again, by interpolating, the exact point of
payback is computed to be 6.1 years.
DISCOUNTED PAYBACK AND THE ESTABLISHMENT OF PRIORITIES
The discounted payback technique is often used to establish
priorities for competing projects. This method of analyzing and
comparing potential projects is particularly useful when capital
investments must be rationed. The technique provides a basis for
the selection of those programs which will provide the quickest
return for the resources invested. Alternatives can be ranked in
order of discounted payback and a budget prepared for optimal
economic utilization of funds.
EXAMPLE 1-2
A maintenance facility at DDMT has developed a group of
projects as current possibilities for adoption. The total PV
investment costs and the estimated annual savings for each project
is given below. Terminal value for all projects is considered
negligible.
Estimated Annual
Project Savings PV of Investment
A $1,230 . $10-000
B 1,470 " 13,000
C 912 6,000
D 1,080 8,000
E 1,420 10,000
F 3,000 15,000
G 1,400 9,000
1. Rank the proposed projects in terms of their discounted
payback.
2. Determine which projects should be funded if available
funds amount to $30,000 and $50,000.
SOLUTION
1. Using the cumulative discount factors in Table B, the
payback for Project A is computed as follows:
Appendix-46
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OSWER Directive # 9028.OOb
PV(I)/Annual Savings = $10,000/$1,230 = 8.130
By comparing the 8.130 value to the Table B factors, the reader
can see that discounted payback will occur during -Year 16. For
purposes of this example, it is not .necessary to interpolate to
determine the exact point of payback.
Discounted payback can be found in a similar manner for each
of the proposed projects. In the following table the proposed
projects are ranked according to their discounted paybacks.
Rank Project Discounted Payback PV(I)
IF' 7 years $1.5,000
2 G 10 years 9,000
3 C 11 years 6,000
4 E 12 years 10,000
5 D 13 years 8,000
6 A 16 years 10,000
7 B 20 years 13,000
2. If the budget is $30,000, the choice of projects is
simple. The three projects with the shortest paybacks have a
combined investment cost equal to the $30,000 budget. Therefore,
projects F, G and C should be chosen.
However, if the budget is equal to $50,000, the selection may
not be so clean-cut. One choice is to select the five top-ranked
projects for.a total investment cost of $48,000. A second choice
involves the selection of projects that will use the entire
$50,000 budget. In this case, logical choice is to select
projects F, G, C, E and A.
Note: Although the project team may wish to include
recommendations in the analysis, the ultimate choice will be left
to the decision-maker.
DISCOUNTED PAYBACK VS. BREAK-EVEN ANALYSIS
It is important that discounted payback not be confused with
break-even analysis.
Break-even analysis focuses on finding the value of the
variable at which the manager is indifferent regarding two
alternative means of meeting a specific objective. A break-even
point occurs when the cumulative discounted costs of the
alternatives are equal.
Payback refers to the period of time over which a proposed
alternative's accumulated present value savings are sufficient to
offset its total present value investment costs. While a
break-even analysis may be performed on any two alternatives,
Appendix-47
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OSWER Directive # 9028.OOb
payback can be computed only when there is a status quo with which
to compare the proposed alternative (i.e., Type I analysis).
When comparing a proposed investment against its status quo
both the break-even point and discounted payback can be computed.
The break-even point and payback may or may not occur at the same
point in time. The following example illustrates the use of both
techniques.
EXAMPLE 1-3
Certain office equipment is currently being leased for $800
per.year. A proposal has been made to purchase similar equipment
for $2,000. Projected annual maintenance costs for the purchased
equipment are $200. An additional one-time cost of $600 for a
major overhaul will be made in year 6.
1. Determine the break-even point for the two alternatives.
2. Determine the discounted payback for the proposed
investment.
SOLUTION
1. Cumulative discounted costs for the two alternatives are:
Year Status Quo Proposal
0 $ 0 $2,000
1 763 2,191
2 1,457 2,364
3 2,087 2,522
4 '2,661 2,665
5 3,182 2,795
6 3,656 ~ 3,268
7 4,087 3,376
8 4,477 3,474
The break-even point occurs during Year 5. At this point in time,
cumulative discounted costs for the two alternatives are equal.
2. The present value of the total investment cost is:
: PV(I) = $2,000 + $600(.592) = $2,355
Cumulative discounted savings associated with the proposed
alternative are:
Appendix-48
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OSWER Directive # 9028.OOb
Year Cumulative Savings
1 $ 572
2 1,092
3 1,565
4 1,995
5 2,386
6 2,742
7 3,065
8 3,358
The above table shows that the discounted investment cost of
$2,355 will be fully recouped during Year 5. This is when payback-
will occur.
Appendix-49
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OSWER Directive # 9028.OOb
J. Sensitivity Analysis (Source: DLA)
INTRODUCTION
Once all costs and benefits have been measured and a
preference ranking of alternatives has been established, the
project team may find his task yet incomplete. For the
decision-maker may need to know not only the economic choice
implied by the "best estimate" of the input variable, but also'
whether or not that decision would change if one or more of the
inputs should vary within a reasonable range of uncertainty. It
is the role of sensitivity analysis, the last of the six basic
steps of benefit-cost analysis, to provide this dimension of
information.
SENSITIVITY ANALYSIS-
Sensitivity refers to the relative magnitude of change in one
or more elements of a benefit-cost analysis that will cause a
change in the ranking of alternatives. Thus, in a sensitivity
analysis if one particular factor or cost element can be varied
over a wide range without affecting the alternatives, the
alternatives are said to be insensitive to uncertainties regarding
that particular element.
UNCERTAINTY AND SENSITIVITY
One of the primary reasons for undertaking a sensitivity
analysis of the factors, costs, or elements of a benefit-cost
analysis deals with the uncertainty associated with their
derivation. Regardless of the estimating technique employed, an
estimate has some inherent error and can be viewed as only one
value from a possible range of values which are distributed in a
probabilistic fashion. Thus, whenever anyone attempts to estimate
costs or predict future occurrences over a long period of time,
there are bound to be variations between the estimates and the
actual occurrence. How these variations affect the results of a
benefit-cost analysis is the heart of the sensitivity analysis
technique.
AN APPROACH TO SENSITIVITY ANALYSIS
There is no single aspect or criterion which can be presented
that will provide a sure-kill approach to selecting the most
important parameter or factor in all sensitivity analyses. Each
analysis is unique in that it possesses its own set of costs and
assumptions. However, as overall guidance, some of the elements
which should be scrutinized are the basic assumptions, requirement
changes, program schedule, and cost estimating methodology.
A general rule when considering cost data is to examine the
input variables, i.e., those which have a significant impact on
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the total present value cost and/or benefits of a given action.
An easy method for identifying these variables consists of
developing the percentage values of each element of cost against
total cost. Here it is suggested that discounted dollars be used.
Identification of the major cost contributors does not
necessarily mean that the truly sensitive items have been
isolated. The choice of input variables for sensitivity may
depend not only upon relative dominance but also upon the degree
of confidence which can be placed in these estimates. Thus
sensitivity analysis should be directed toward the task of
determining those factors having the greatest uncertainty.
EXAMPLE J-l '
I. Given the following cost data, determine the less costly
alternative:
Alternative A Alternative B
(Proposal) (Status Quo)
Initial Investment Cost $ 100
Annual Recurring Cost $ 5 $ 17
Economic Life 20 years 20 years
2. Perform a sensitivity analysis to determine the impact on
the decision if the actual initial investment cost is expected to
be within ± 5% of the $100 estimate.
3. Test the sensitivity of the proposed alternative if the
range of uncertainty in the recurring $5 estimate is ± 50%.
-*
SOLUTION
1. The net present values over a 20-year life for
Alternatives A and B:
PV (Alt A) = $100 + $5(8.933) = $145
PV (Alt B) = $17(8.933) - $152
Thus, the less costly alternative is Alternative A, the proposed
alternative.
2. Subject to the constraint that the initial investment
cost be within ± 5% of the $100 estimate, the potential impact is:
PV = $105 + $5(8.933) = $150
Since $150 is less than $152, Alternative A remains the preferred
alternative.
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3. If the range of uncertainty in the $5 recurring cost is ±
50%, the potential impact is:
PV = $100 -I- $7.50(8.933) = $167
In this case, the present value of the proposed alternative
becomes greater than that of the status quo, making the status quo
the desirable alternative. Thus, the original decision to choose
the proposed alternative is sensitive to the uncertainties
regarding the recurring cost element.
EVALUATING AND PRESENTING THE RESULTS
The last step of a sensitivity analysis is the presentation
of the results. This is commonly done through the use of graphs.
The trend of the factor or cost under analysis can be clearly
shown by using percent change or accumulated dollars in the graph.
Another feature of graphs is the ability to superimpose several
sensitivity results for comparative purposes. For example, the PV
life cycle cost for Alternative A in Example J-l can be depicted
for simultaneous variations in annual recurring costs and initial
investment cost. If the initial investment cost is denoted by I
and the recurring annual cost by. R, total PV life cycle cost is
given by:
PV = I + (8.933)R
Figure J-l shows plots of total PV life cycle cost for various i
combinations of one-time and recurring costs. The annual cost is
plotted on the horizontal axis and the one-time cost I is treated
as an exogenous variable. The lattice of PV life cycle cost points
readily indicates which combinations of one-time cost and annual
cost are economically preferable to the status quo. Th» circled
point represents the "best guesses" (I = $100, R = $5) used in the
original analysis.
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SENSITIVITY ANALYSIS
PV (Status
Quo) = 152
Recurring
Costs
Figure
J-l
Inspection of the graph reveals whether or not the proposed
alternative is economically justified - it is if, and only if, the
PV point for the proposed alternative lies below the status quo
threshold. Moreover, visual interpolation between designated
one-time and recurring costs is possible. For example, if the
actual one-time cost were $102 and the annual recurring cost were
$4 then the PV would be approximately $137 (see point Y in Figure
J-l) .
SUMMARY
The objective of a sensitivity analysis is to provide
additional information to a decision-maker. It serves as the
means of answering "what if" questions about the major
uncertainties in a benefit-cost analysis. A cost or factor is
considered truly sensitive if reasonable changes in that item
cause a change in the ranking of the alternative. The use of
sensitivity analysis does not require any sophisticated
techniques. What is required is a logical'systematic approach and
the ability to make reasonable judgment as to the uncertainty
involved in the particular benefit-cost analysis under study. The
number of key elements to be included and the complexity of the
sensitivity analysis, are basically a function of time and the
criticality of the decision. But remember, any analysis, even a
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very basic attempt, is bound to be better than guessing.
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OSWER Directive f 9028.OOb
K. Benefit-Cost Analysis Review Checklist (Source: DLA)
A. THE OBJECTIVE, ASSUMPTIONS AND ALTERNATIVES
1. Is the objective clearly stated? Does it define the
'purpose of the program/project or activity under study?
2. Are all reasonable assumptions identified and explained?
3. Are assumptions too restrictive? Too broad?
4. Are intuitive judgments identified as such? Are
uncertainties treated as facts? Can the facts be
verified?
5. Are any feasible alternatives omitted?
6. .Are the alternatives well defined and discrete? Do they
overlap?
B. THE COST ESTIMATE
1. What costing method was used? Is it appropriate?
2. Are all relevant costs included? Are the directly
related support and training costs included?
3. Are cost factors current and supportable?
4. Does the study indicate why certain costs are considered
relevant and others not?
5. Are sunk costs excluded?
6. Have opportunity costs been considered?
7. Is terminal value associated with any of the
alternatives?
8. Are the sources of cost estimates included? Are they
accurate?
9.' Are cost estimates properly classified and of proper
quality for the status of the program?
C. THE BENEFIT DETERMINATION
1. Have all Relevant benefits been determined? Does the
analysis ignore some portion of total output?
2. Were.the criteria used to measure benefits justified by
the context of the study?
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OSWER Directive # 9028.OOb
3. Was the benefit, in fact, immeasurable? Has there been a
rational assessment of nonquantified factors?
4. Was an expert opinion used? Were these experts properly
qualified?
5. Have cost reductions been excluded from the benefit list
to avoid double counting?
6. Have cost avoidances been considered?
COMPARISON OF ALTERNATIVES
1. Has the time value of money been considered? Have all
costs and benefits been properly time-phased? Has the
present value been determined for each alternative?
2. Do benefits exceed costs for alternatives considered?
3. Have other techniques, such as Break-Even Analysis or
the SIR, been applied to compare alternatives?
4. Is a sensitivity analysis needed? Were the methods and
sources of the study adequately documented?
CONCLUSIONS AND RECOMMENDATIONS
1. Are the results of the analysis conclusive? Can a
concrete ranking of alternatives be established?
2. Are the conclusions and recommendations logically
derived from the material?
3. Are the recommendations feasible in the real world of
political, cultural, or policy considerations? Have all
other relevant factors been considered?
4. Are the recommendations based upon significant
differences between the alternatives?
5. Are recommendations intuitively satisfying and
supportable?
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L. Project Year Discount Factors (Source: DLA)
Table A Table B
PRESENT VALUE OF $1 '(Single PRESENT VALUE OF $1
'(Cumulative Amountused when cash flows Uniform
Seriesused
accrue in varying amounts each when cash flows accrue in the
year) same amount each year)
Project
Year 10% 10%
1 0.954 0.954
2 0.867 1.821
3 0.788 2.609
4 0.717 3.326
5 0.651 3.977
6 0.592 . 4.5.70
7 0.538 5.108
8 0.489 5.597
9 0.445 6.042
10 0.405 . 6.447
11 0.368 . 6.815
12 0.334 7.149
13 0.304 7.453
14 0.276 7.729
15 0.251 7.980
16 0.228 8.209
17 0.208 8.416
18 0.189 a.605
19 0.172 8.777
20 0.156 8.932
21 0.142 9.074
22 0.129 9.203
23 0.117 9.320
24 ., 0.107 9.427
25 -;'; 0.097 9.524
26 ,, 0.088 9.612
27 0.080 9,692
28 0.073 9.765
29 0.066 9.831
30 '0.060 . 9.891
NOTE: Table B factors represent the cumulative sum of Table A
factors through any given project year.
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M. Glossary of Terms (Source: DLA)
Alternatives - The different courses of action, means, or methods,
by which objectives may be obtained.
Assumptions - Explicit statements used to describe the present
and future environment upon which the benefit-cost analysis is
based. Assumptions are made to support and reasonably limit the
scope of the study.
Baseline Date - The starting point for .the benefit-cost analysis,
beyond which decisions deal with future courses of action. It is
the "today" in the analysis. It may be referred to as the
baseline year (or analysis year 0).
Benefits - Outputs or effectiveness expected to be received or
achieved over time as a result of undertaking a proposed
investment.
Benefit/Cost Ratio - An economic indicator of efficiency,
computed by dividing benefits by costs. When benefits are
quantified in dollar terms, it is customary to,, discount both the
benefit stream andvthe cost stream to reflect theypresent value of
future costs and benefits.
Break-Even Analysis - A procedure for evaluating alternatives in
terms of a common unknown variable. It involves solving for the
value of the variable which will make the cumulative discounted
costs for the alternatives equivalent; this value is the
break-even point.
i~1 ',
Cash-Flow Diagrams - A pictorial representation showing the
magnitudes and timing of costs associated with an alternative.
Compound Interest - Interest; which is computed on both the
original principal~and its accrued interest.
Constant Dollars - An estimate is said to be in constant dollars
''if costs for all work are adjusted so that they reflect the level
of prices of a base year.
Cost - A resource input to a project, program or activity
expressed in dollar terms.
Cost Avoidance - Saving realized by obviating a planned
nonrecurring expenditure of resources. A cost avoidance can only
occur when adopting a non status quo alternative.
Cost Benefit Analysis - A technique for assessing the range of
costs and benefits associated with a given option, usually to
determine feasibility. Costs are generally in monetary terms, but
benefits need not be in monetary terms.
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Current Dollars - When prior costs are stated in current
dollars, the figures given are the actual amounts paid out. When
future costs are stated in current dollars, the figures given are
the actual amounts expected to be paid including any amount due to
future price changes .
v
Discount Rate - A rate used to relate present and future dollars.
This rate is expressed as a percentage and is used to reduce the
value of future dollars in relation to present dollars to account
for the time value of money.
Discounted Payback - A technique for determining the time period
over which accumulated present value savings are sufficient to
offset the total present value investment costs of a proposed
alternative to the status quo.
Economic Analysis - A systematic approach to quantifying,
portraying, and evaluating the relative worth of proposed
projects. Basically, it consists of six steps:- stating the
objective; listing assumptions; defining the alternatives;
determining co'sts and benefits; comparing and ranking
alternatives;" and performing a sensitivity analysis.
Economic Life - The period of time over which the benefits, to be
gained from a proposal may be reasonably expected to accrue..1 The-.
economic life of a project begins the year the investment starts
producing benefits and may be- -limited by Its mission life,
physical life, or technological life. :7
Effectiveness - A quantitative measure used to evaluate
performance level in relation "to end objectives.
Fixed Cost - The component of production cost which ^.
change in the short run if production volume "rrs within a ^ Specified
range. - "" l :: - ' . r "
Historical Cost - The cost of- any objective, based uport actual
asset outlay, determined aftef-'the fact. Any method of cost
determination may be used.
Incremental Cost - The change in cost associated with a change
in the level of output. :
Inflation - A persistent rise in the general level of prices over
time.
Intangible Benefits - Those improvements in system performance
which cannot be quantified in terms of dollars or other measures.
Interest - A price (or rent) charged for the use of money.
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Investment Cost - One-time costs associated with acquisition of
real property, nonrecurring services, nonrecurring operations, and
maintenance (startup) costs and "other one-time costs. Despite
their one-time nature, investment costs may extend over periods of
more than 1 year.
Leadtime - The period of elapsed time5 between initial funding or
decision and the commencement of the economic life.
Life Cycle - The time from the beginning date of the project to
the end of the; program/project li~fe.
Mission Life - The period of time over which a need for an asset
is anticipated.
Net Discounted Costs - Discounted dollar costs minus discounted
dollar benefits. (This can be a negative value.)
Nonrecurring Cost - Cost which occurs on a one-time basis; to be
distinguished from annually recurring costs.
Objectives - Goals or results that the decision-maker wants to
attain. It is the desired end product, or output, of a program.
"The-;obj"ectives ju'stilfy the existence of the organization and its
consumption of resourc'es.
Opportunity Cost - The cost of foregone opportunities; the
sacrificed amount of money, equipment, or units of production that
could have been- rea-1-ized by a "separate course of action
(alternative) with the same--time1 -and effort expended.
Output - The products, functions, tasks, services, or capabilities
which an- organization exi'stls to produce, accomplish, attain or
maintain.
Output Measures - Useful descriptors of functions, tasks or
missions performed by an organization-, expressed in relation to
those assigned.
Physical Life - The estimated number of years that a machine,
piece of equipment or building can physically be used in
accomplishing the function for which it was procured or
constructed.
Present Value - The estimated current worth of future benefits or
costs derived by discounting the future values, using an
appropriate discount rate.
Program/Project - A major mission-oriented, agency endeavor,
which fulfills statutory or executive requirements, and which is
defined in terms of the principal actions required to achieve a
significant end objective.
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Program Evaluation - Analysis of ongoing activities to determine
how best to improve an approved program/project based on actual
performance. Program evaluation studies entail a comparison of
actual performance with the approved program/project goals and
objectives, and provide a basis for deciding whether objectives
are being accomplished in the most cost-effective manner.
Project Life - The leadtime together with the economic life.
Recurring Costs - Expenses- for personnel, material consumed in
use, operating, overhead, support services, and other items which
recur annually in execution of a given program or work effort .
Residual Value - The computed value of assets no longer being
utilized at any point in time.
Savings /Investment Ratio (SIR) - The ratio of discounted
future cost savings (or avoidances) to the discounted investment
cost necessary to effect those savings. An SIR of 1 indicates
that the present value of savings is equal to the present value of
the investment .
Sensitivity .-.Analysis - A technique for; assessing the exte~nt to
which reasonable changes in assumptions .or input variables will
affect the preference ranking of alternatives.
Sunk Cost - A past cost which is incurred befor.e the
date. Because sunk costs .have .been irrevocably; -expended or
committed, they play no role in a choice between alternatives
Tangible Benefits - Those improvements i-n system performance
which can , be quantified. They, dp .not include savings , in . recurring
operating expenses; these savings are reflected as reductions in
costs .
.Technological Life r The estimated number o-f years before
technology will make the existing or proposed equipment or
facilities obsolete.
Terminal Value - The expected value of land, buildings or
equipment at the end of its economic life.
Time Value o£ Money - A name to the notion that the use of money
costs money. A dollar today is worth more than a dollar tomorrow
because of the interest costs related to expenditures and benefits
which occur over time. Annual savings or cash in flows projected
for tomorrow have present values less than their undiscounted
.dollar values.
Type, I - An analysis employed to help determine whether an
existing situation or procedure (status quo) should be changed in
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some way to take advantage of dollar savings available through
some other situation or set of procedures (proposed alternative).
Type II - An analysis used once a deficiency or changed
requirement has been identified to determine which of several
planning alternatives would most economically satisfy the
deficiency.
Uniform Annual Cost - A constant amount which, if paid annually
throughout the economic life of a proposed alternative, would
yield a total discounted cost equal .to the actual present value.
life cycle cost of the alternative.
Variable Cost - That component of production cost which is
directly proportional to the volume of production.
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