T"

NATL IMST. OF STAND & TECH

AlllOt l>175b2

NIST

PUBLICATIONS SEMINAR WORKBOOK

Ecbhoifiic Evaluation of

Building Design, Construction,

Operation and Maintenance

U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

NBS Technical

Note 1195
TM he National Bureau of Standards' was established by an act of Congress on March 3, 1901. The

^ Bureau's overall goal is to strengthen and advance the nation's science and technology and facilitate their effective application for public benefit. To this end, the Bureau conducts research and provides: (1) a

basis for the nation's physical measurement system, (2) scientific and technological services for industry and

government, (3) a technical basis for equity in trade, and (4) technical services to promote public safety.

The Bureau's technical work is performed by the National Measurement Laboratory, the National

Engineering Laboratory, the Institute for Computer Sciences and Technology, and the Center for Materials

Science.

The National Measurement Laboratory

Provides the national system of physical and chemical measurement;

coordinates the system with measurement systems of other nations and

furnishes essential services leading to accurate and uniform physical and

chemical measurement throughout the Nation's scientific community, in- dustry, and commerce; provides advisory and research services to other Government agencies; conducts physical and chemical research; develops,

produces, and distributes Standard Reference Materials; and provides

calibration services. The Laboratory consists of the following centers:

• Basic Standards^

• Radiation Research

• Chemical Physics

• Analytical Chemistry

The National Engineering Laboratory

Provides technology and technical services to the public and private sectors to address national needs and to solve national problems; conducts research in engineering and applied science in support of these efforts; builds and maintains competence in the necessary disciplines required to carry out this research and technical service; develops engineering data and measurement

capabilities; provides engineering measurement traceability services; develops

test methods and proposes engineering standards and code changes; develops

and proposes new engineering practices; and develops and improves

mechanisms to transfer results of its research to the ultimate user. The

Laboratory consists of the following centers:

Applied Mathematics

Electronics and Electrical Engineering'^

Manufacturing Engineering

Building Technology

Fire Research

Chemical Engineering^

The Institute for Computer Sciences and Technology

Conducts research and provides scientific and technical services to aid Federal agencies in the selection, acquisition, application, and use of computer technology to improve effectiveness and economy in Government

operations in accordance with Public Law 89-306 (40 U.S.C. 759), relevant Executive Orders, and other directives; carries out this mission by managing

the Federal Information Processing Standards Program, developing Federal ADP standards guidelines, and managing Federal participation in ADP

voluntary standardization activities; provides scientific and technological advisory services and assistance to Federal agencies; and provides the technical foundation for computer-related policies of the Federal Government. The Institute consists of the following centers:

Programming Science and

Technology

Computer Systems

Engineering

The Center for Materials Science

Conducts research and provides measurements, data, standards, reference

materials, quantitative understanding and other technical information fundamental to the processing, structure, properties and performance of materials; addresses the scientific basis for new advanced materials technologies; plans

research around cross-country scientific themes such as nondestructive

evaluation and phase diagram development; oversees Bureau-wide technical programs in nuclear reactor radiation research and nondestructive evaluation; and broadly disseminates generic technical information resulting from

its programs. The Center consists of the following Divisions:

Inorganic Materials Fracture and Deformation^

Polymers

Metallurgy Reactor Radiation

'Headquarters and Laboratories at Gaiihersburg, MD, unless otherwise noted; mailing address

Gailhersburg, MD 20899. "Some divisions within the center are located at Boulder, CO 80303. 'Located ai Boulder, CO, with some elements at Gaithersburg, MD.
NATIONAL BUREAU

OF STAnDAfiDS

NofemT'"'' SEMINAR WORKBOOK

Economic Evaluation of

Building Design, Construction, c c Operation and Maintenance %^

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Applied Mathematics

Operations Researcti Division

Gaithersburg, MD 20899

/

Prepared by:

Rosalie T. Ruegg

Operations Research Division

Center for Applied Mathematics

National Bureau of Standards

U.S. Department of Commerce

Prepared for: Design Programs Branch

Public Building Service

General Services Administration

Washington, DC 20405

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Issued June 1984
National Bureau of Standards Technical Note 1195

Natl. Bur. Stand. (U.S.), Tech. Note 1195, 183 pages (June 1984)

CODEN: NBTNAE

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1984

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402
Preface

This workbook has been prepared for participants in the seminar, "Economic

Evaluation of Building Design, Construction, Operation and Maintenance." It

has two main functions: (1) to provide basic resource materials, references,

and introductions to methods employed in the seminar and (2) to provide

instructional problems for solution by the participants.

Specifically, it contains brief discussions of key elements in performing

economic evaluations: discounting, escalation, establishing a study period,

project selection techniques, and treatment of uncertainty; explanations of

supporting analysis techniques: break-even analysis and replacement theory;

and problems, worksheets, and solutions. Cross references are given to related

sections of a reference manual (NBS Handbook 135) and to case studies which

illustrate the topics.

The objectives of the seminar are to provide participants with a working

knowledge of economic evaluation procedures for making building decisions, and

to improve their decision-making abilities related to cost management and to

the design and selection of buildings and building systems.

The seminar has been developed for building design engineers and architects,

project planning and programming staff, managers of building programs,

procurement officers and contract coordinators, building construction

estimators, and building analysts.

Ill
Acknowledgment

Appreciation is extended to the Public Building Service of the General

Services Administration—particularly to Dave Eakin—for support in developing

and field testing the seminar instructional materials. Appreciation is also

given to the Federal Energy Management Program of the U.S. Department of

Energy (DoE) for its contributions to the initial development of some of the

energy conservation problems presented in this seminar. Earlier versions of

these problems were prepared and presented by the National Bureau of Standards

for DoE Life-Cycle Cost Workshops under the direction of Thomas Benson of the

Federal Energy Management Program,

The author wishes to thank Dr. Harold Marshall, Leader of the Applied

Economics Group of the National Bureau of Standards, for his invaluable

assistance in developing the Workbook; Ms. Barbara Lippiatt, also of the

Applied Economics Group, for her assistance in preparing the manuscript; and

Ms. Laurene Linsenmayer for her patience and skill in typing the manuscript.

IV
Contents

Section Title Page

Preface ill

Acknowledgment iv

Contents v

Sample Seminar Agenda vi

1 References 1-1

2 Discounting 2-1

3 Escalation 3-1

4 Study Period 4-1

5 Project Selection 5-1

6 Sensitivity Analysis 6-1

7 Probability Analysis 7-1

8 Break-Even Analysis 8-1

9 Replacement Decisions 9-1

10 Worksheets 10-1

11 Problem Set A 11-1

12 Problem Set B 12-1

13 Problem Set C 13-1

14 Problem Set D 14-1

15 Problem Set E 15-1

V
Sample

Seminar Agenda

Day 1

8:45 Preliminaries

9:00 Introduction to the Seminar (Section 1)*

9:30 Fundamentals of Benefit-Cost and LCC Analysis (Section 2)

10:15 Break

10:30 Class Problems in Discounting (Section 11)

11:00 LCC, NB, NS , BCR, SIR, IRR, and PB Analysis

12:00 Lunch

1:15 Pipe Insulation Retrofit Problem (Section 5)

2:15 Break

2:30 Programmable Time Clock Problem (Sections 10 and 11)

3:30 Review and Discussion

4:15 Adjournment

* References in parentheses are to sections of the workbook.

VI
Day 2

8:45 Review of 1st Day Material - Questions and Answers

9:15 Determining Project Priority

9:45 Water Conservation Problem (Sections 10 and 12)

10:30 Break

10:45 Project Design, Sizing, and Selection

11:15 Treatment of Cost Escalation

12:00 Lunch

1:00 Team Problem - Planning an Energy Conservation Package (Sections 10

and 12)

2:15 Sensitivity and Probability Analysis (Sections 6 and 7)

2:30 Break

2:45 Problem in Sensitivity Analysis (Section 13)

3:00 Problem in Probability Analysis (Section 13)

3:30 Choosing a Study Period (Section 4)

3:45 Adjournment

vil
Day 3

8:45 Review of 1st and 2nd Day Material - Questions and Answers

9:15 Break-Even Analysis (Section 8)

10:00 Team Problem - Break-Even Analysis in Support of a Labor/Machine

Decision for Procurement (Section 14)

10:30 Break

10:45 Computer Room Waste Heat Recovery Problem (Sections 10 and 12)

12:00 Lunch

1:15 Replacement, Retirement, and Obsolescence (Section 9)

1:45 Team Problem - Determining Optimal Retirement of Equipment

(Section 14)

2:15 Break

2:30 Team Critique of an Economic Evaluation Report (Section 15)

3:20 Group Discussion of Economic Evaluation for Building Decisions

3:45 Adjournment

viii
Section 1

References

This section contains the following selected GSA and 0MB documents

pertaining to the economic evaluation of buildings and building systems:

(1) "Tech Aid on Life Cycle Costing" — Appendix 1-A of the GSA

Design Handbook, which summarizes guidelines for constructionrelated economic decisions,

(2) 0MB Circular No. A-94 revised, which pertains to discount rates to

be used in evaluating time-distributed costs and benefits, and

(3) 0MB Circular No. A-lOA, which pertains to comparative cost analysis

for decisions to lease or purchase general purpose real property.

An additional document which is used extensively in this seminar is

Life-Cycle Cost Manual for the Federal Energy Management Program , NBS Handbook

135 (Rev.). It is provided separately from the Workbook.

Relationship among referenced documents ; Handbook 135 amplifies the

methodology and procedures for life-cycle cost analysis of energy conservation

projects established in Subpart A of Part 436 of Title 10 of the Code of

Federal Regulations, entitled "Federal Energy Management and Planning

Programs." This methodology was developed to be consistent with the

guidelines on discounting in 0MB Circular A-94, revised. However, an

exception to Circular A-94's requirement for a 10 percent discount rate was

provided by Section 405 of the Energy Security Act; the Act established a 7

percent discount rate for energy conservation projects. The GSA Tech Aid on

Life-Cycle Costing, compiled for GSA staff and contractors is in turn

consistent with Handbook 135.

1-1
0MB Circular A-104 presents the method of evaluating lease-buy decisions for

acquisition of general purpose real property valued at $500,000 or more, and

hence, concerns the method of securing the property in question, rather than

the issue of whether or not having the property will be cost effective. This

document is provided for the convenience of the user, because the decisions

concerning project cost effectiveness and cost-effective acquisition of

property generally go hand-in-hand.

1-2
subject LIFE CYCLE COSTING

\^

1. FORMULAE

Unless otherwise directed in contract documents, construction related

economic decisions shall employ a present value life cycle cost analysis

in accord with the Code of Federal Regulations, Title 10, Part 436-A. In

addition, and in summary, the following formulae and considerations shall

apply. Formulae Notation:

PV

FV

TV

e

Present Value

Future Real Value

Today's Value

real growth escalation rate (the differential escalation rate which

exists after removing the influence of general inflation. See 2.4 of

this Appendix)

number of years to occurrence or the analysis period, as appropriate

real discount rate

1.1 Sunk Costs (those already spent or irrevocably committed) shall be

ignored in LCC calculations. Such costs include:

, Study costs

. Construction work already started or completed

. Design costs where the expense is obligated by contract regardless

of design solution.

1.2 Implementation (First) Costs shall be of estimated "today's value"

and as such are by their nature in present value. See paragraph 2.3

of this Appendix. Such costs may include:

. Site acquisition

. Site survey/testing

. Design related fees

. Moving/relocation

. Demolition of existing (less salvage)

. Corrective Repair and Alteration to existing work

. Construction (with contingencies)

. Construction supervision

1.3 Non-recurring future costs will usually involve such needs as:

. Major replacement

. Non-annual maintenance and repair

. Implementation costs for major alterations to existing work

including those cost elements described above for 1.2.

1-3
1.3.1 The present value of such costs can be treated by escalating a known "today's value" to its future value using a real growth

escalation rate, then discounting that future value to a present value.

Escalate the known today's value to the future value in

constant dollars... FV = TV (1+e)", then discount that

future value back to the present value. PV = FV/(1+d)".

The term (1/1+d)" is known as the Single Present Worth

(SPW) factor and is tabulated on page 114 of the referenced

LCC Manual.

1.3.2 Or the combined procedure is represented by the equation

PV = TV (l+e/1+d)n. Note: If e = o, then PV = TV(1/1+d)n

1.4 Uniform Annually Recurring Constant Dollar Costs may involve such

costs as:

. Service contracts with an inflation adjustment clause

. Preventive maintenance

. Scheduled minor replacements

. Annually recurring costs which increase in price at the same rate

as general inflation.

1.4.1 These can be converted to present value by the Uniform Present

Worth (UPW) formula:

PV = TV (UPW), Where UPW = (Ud)"- 1

,

d (1+d)"

The Uniform Present Worth (UPW) factor is tabulated on page

115 of the referenced LCC Manual.

1.4.2 This assumes that the cost of an activity will escalate with

inflation and hence has a zero real growth rate.

,5 Annually recurring costs which escalate in real value are usually

associated with such costing elements as:

. Service/maintenance which involves increasing amounts of work

and/or an escalation in cost different from general inflation.

. Fuel (utility) costs (see paragraph 1.6).

. Certain types of frequent replacement which escalate at a different

rate than general inflation.

1-4
.5.1 The Present Value relationship of such costs can be calculated

by using the following modified version of the UPW formula

(UPW*) which allows for cost escalation:

PV = TV (UPW»),

Where if e = d, UPW* = n if e ^ d, and e is constant over n, then

UPW» =

or

((Ue)/(Ud))" - 1

1 - (1+d)/(1+e)

[B-][ ^<m)]

NOTE: The 1980 ASHRAE Systems Handbook representation of this

equation is incorrect (p. 45.4) and so noted in its errata.

1.6 Recurring fuel cost can be represented in present value by employing

a modified Uniform Present Worth (UPW*) factor that takes into

account multiple escalation rates. The UPW* factors are found in the

CFR, Title 10, Part U36-A, shown tabularly in Tables B-1 thru 11 by

Region, Billing Sector (e.g., commercial). Fuel Type, and analysis

period. The formula to be applied is as follows:

PV = TV (UPW*)

1.6.1 Generally, the Today's Value (TV) of fuel costs should be

calculated as the annual quantity of fuel times the actual

local fuel pricing charged by the impacted utility at the

beginning of the study period.

1.6.2 Electric demand charges should be assumed to escalate at the

same rate as shown in Tables B-1 thru 1 1 for electricity consumption unless actual escalation rates for demand are provided by the local utility.

2. PROCEDURES AND APPROACH

2.1 When defining alternates for life cycle costing, an acceptable level

of overall building service must be maintained for the analysis

period. Costs which are common to all options may be ignored.

2.2 All design alternates shall be compared against a baseline reference

option.

1-5
2.2.1 The baseline must represent all costs and actions necessary to

support the impacted service functions over the entire analysis period for the lowest total installation cost of the

considered options.

2.2.2 Where the existing conditions will form part of the baseline,

there shall be those additional costs necessary to offer code

compliance to impacted services, and all associated work identified in GSA Repair and Alteration Planning documents, and

all costs necessary to ensure reliable operation.

2.2.3 The baseline must represent a logical evolution of building

costs employing state-of-the-art design options.

2.2.4 Generally, the building system designs and guidance contained

in this Design Management Handbook shall serve as input to the

baseline for performance and policy requirements.

2.3 Unless directed otherwise in contract documents, all first costs of

implementation shall be assumed to occur instantly, at the beginning

of the analysis period. See paragraph 2.8 of this appendix.

The Code of Federal Regulations (CFR) Title 10, Part 436-A, presently

speaks to a 10% adjustment to the initial investment for all energy

conservation projects. Hence, only 9055 of the initial investment

costs are included in calculating the net benefit and the cost

indices mentioned in Section 3.1 of this Appendix. This reduction

allowance was provided in the LCC Rulemaking to compensate for external beneficial side effects associated with conservation measures;

socio-economic, national security, etc. This factor shall be applied

to all concepts which have been developed specifically to conserve

energy (such as in energy studies).

However, the adjustment factor looses meaning when applied to new and

retrofit projects where the compared design alternates involve energy

usage but are not being pursued expressly to conserve energy. Here

the 10% adjustment serves only to benefit the concept which has the

highest dollar return, which may be more associated with non-energy

cost avoidance such as repairs, maintenance, etc. Consequently, for

all new construction projects and for projects not specifically

developed to conserve energy, the 10% adjustment should be ignored,

allowing the total investment cost to be applied in the analysis.

2.4 All future cost projections shall be established by escalating a known "today's value" with a real escalation rate: this will

represent that cost in "constant dollars." That constant dollar

future cost shall be discounted with a real discount rate to present

value: In this process of discounting, future costs are expressed in

"constant dollars."

1-6
When converting escalation projections which are actual cash flow

rates (also referred to as budgetary or nominal rates) to an escalation rate in real terms (without inflation) , the following formula

applies:

E = e + I + eI, or e= ^-:j r-j - 1 Where: E = budgetary escalation

e = real growth escalation

I = inflation rate

Hence, to convert a given budgetary projection of 15/5 to real terms,

allowing for say 10% inflation, the real growth escalation would be:

e = ((1 + .15)/(1 + .10)) - 1, for e = 0.0454 or 4.54%.

2.5 An exact accounting shall be made for those alternate and baseline

investment and replacement costs directly associated with implementation and continued building service. However, to simplify the

analysis, all recurring cost avoidance may be considered to be in

relationship to the initial differences that exist between the alternate and the baseline: Hence, for simplicity, an expected future

change in, say, a baseline's annual energy consumption may be

ignored, allowing the consumption usage of the initial baseline

condition to be assumed over the entire analysis period. An exact

accounting of fluctuating recurring costs will be required only if so stated in contract documents.

2.6 The analysis period shall be as required to fully represent all major

costs to the Government and as stated within the CFR, Title 10, Part

436-A.

2.6.1 All mutually exclusive options shall be considered over the same analysis period.

2.6.2 Where possible, the analysis period should be the smallest

whole multiple of the service lives for the major systems

involved in the analysis. (Example: With Option A the

service life of 2 years is expected before replacement; with

Option B the life of 3 years is anticipated; the smallest

whole multiple of 6 would then be an appropriate analysis

period.) Life expectancies of major equipment can best be

obtained from manufacturers. Also, the ASHRAE Systems

Handbook, page 45.2, has equipment life listings which may be

appropriate.

2.6.3 Unless otherwise directed in design programming documents, the

analysis period shall in no case exceed 25 years.

1-7
2.7 For those instances where either the baseline or alternate have

service life beyond the analysis period, an allowance shall be provided for that associated residual service worth. This shall

involve: (1) identifying the residual constant dollar value at the

end of the analysis period, defined by the intercept of a straight

line depreciation from the installed constant dollar cost to its end

of service salvage value, and (2) discounting that residual constant

dollar value to its present value.

2.8 Because of the design and construction process, the period between

the identification of a retrofit option and its implementation may

involve a lead time of several years. When comparing a retrofit

option which has a multi-year lead time to a baseline case, the

following applies to the treatment of costs impacted by the lead time,

2.8.1 All costs that must be incurred during the lead time,

regardless of whether the retrofit option is adopoted , should

be deemed sunk and excluded from the analysis of both the

baseline case and the retrofit option.

2.8.2 All deferable lead time costs that are avoidable if the

retrofit option is adopted, should be included as a cost for

the baseline case but not for the retrofit option. To simplify this analysis, the lead time can be compressed and the

avoidable costs for the baseline can be assumed to occur at

the start of the analysis period as with the investment cost

of the retrofit option: When doing so, however, all future

planned year projections of investment and replacement cost

occurrence must be adjusted to occur earlier in the analysis

by the length of the lead time period.

2.8.3 For mutually exclusive options where lead time results in

significant differences in cost advoidance, a more rigorous

analysis shall be provided which reflects the lead time. This

nay require the discounting of investment and other costs to

take into account their lead time.

3. ANALYSIS PRESENTATION

3.1 Indices: Unless otherwise noted, the following relationships shall

be calculated for life cycle cost alternates.

3.1.1 For all life cycle cost analyses, calculate:

- Savings to Investment Ratio (SIR) : The ratio of the

present value savings of an alternate to its increase in

present value implementation costs.

- Net Savings (NS): The difference in total life cycle cost

between the baseline and a concept alternate.

1-i
3.1.2 For energy conservation retrofit projects, also calculate:

- Energy Savings to Investment Ratio (ESIR): The ratio of

the annual source energy savings in 1,000 Btu's (MBTU) to

the initial investment costs in dollars.

Energy Cost Savings Ratio (ECSR): The ratio of the present

value energy savings to the initial investment cost.

3.2 For each design option, the life cycle costing elements shall be

summarized in the format as shown on the attached data sheet.

3.3 Detailed calculation cost back-up sheets may consist of the forms

shown in the referenced LCC Manual or any other orderly format as agreed-to by GSA Reviewing Officials.

3.4 Computer representation of costs shall be acceptable only if provided

with a manual example showing equivalency of calculation with one of

the computerized solutions.

4. INTERPRETATION

4.1 Due to possible margins of error, where comparative economic analysis

shows a difference less than 10 percent, the economic analysis may be

considered indeterminate at the discretion of GSA Reviewing Officials,

4.2 Life Cycle Cost analysis may be subject to overriding qualitative

considerations: e.g., occupancy impact, safety concerns, or problems

of reliability.

references

originator office of design and construction

DESIGN MANAGEMENT DIVISION

DESIGN PROGRAMS BRANCH

1-9
Bui Iding Name:

ject Name:

cept Title:

Build

Proje

ing Number:

Pro 'ct Number:

Con

Ana lysis Data: Period = Ye ars, Real Discount Rate _ %, Date: / /

Ene rgy Data: Saved Fuel Type _

Unit Fuel Cost

»

» Source Amount

DOE Region

= z = MBTU/YR.

, Sector

COST ELEMENTS BASELINE ALTERNATE DIFFERENCE

a. Construction Cost $ $ $

b. Contingencies (0.05 x a) $ $ c. Design Fee + Award Costs $ $

d. Construction Supervision $ $ e. Moving Costs $ $

f. Relocation Costs $ $

g. Initial Training Costs $ $

h. Other First Costs $ $

(1) SUBTOTAL (add above) $ »$ w. $

i. TV Energy Cost/Year $ $

J. PV All Energy Costs $ $ y. $

k. TV Maintenance Cost/Year $ $

1. PV All Maintenance Costs $ $ m. TV Service Cost/Year $ $ n. PV Service Costs

SUBTOTAL (j + 1 + n)

$ $

(2) $

* V. $

o. TV Future Replacements $ $

p. PV All Future Replacements $ $

q. TV Salvage $ $

r

.

PV Salvage $ $

- s. Depreciated Residual Worth $ $

t. PV Residual Worth $ $

(3) SUBTOTAL (p - r or t)

TOTAL LIFE CYCLE COST

(1)+(2)+(3)

X. $

u. $

Net Savings (NS) = u„

Savings to Investment Ratio (SIR) = v/(w + x) =

* For Energy Conservation Projects, this value should be adjusted tc be 10%

less than estimated actual investment cost.

For Energy Conservation Projects:

Energy Savings to Investment Ratio = z/w = Energy Cost Savings Ratio = y/w =

1-10
EXECUTIVE OFFICE OF THE PRESIDENT

OFFICE OF MANAGEMENT AND BUDGET

WASHINGTON. DC 20503

March 27, 1972 CIRCULAR NO. A-9 4 Revised

TO TKZ HEADS OF EXECUTIVE DEPARTMENTS A.N'D ESTA3LISKKENTS

SUBJECT: Discount rates to be used in evaluating tinedistributed costs and benefits

1. Purpose . This Circular prescribes a standard discount

rate to be used in evaluating the measurable costs and/or

benefits of programs or projects when they are distributed

over time.

2. Rescission . This Circular replaces and rescinds Office

of Management and Budget (0MB) Circular N'o. A-9 4 dated

June 26, 19 69.

3. Scooe.

a. This Circular applies to all agencies of the executive branch of the Federal Government except the U.S. Postal

Service. The discount rate prescribed in this Circular

applies to the evaluation of Government decisions concerning

the initiation, renewal or expansion of all programs or

projects, other than those specifically exempted below, for

which the adoption is expected to commit the Government to a series of m^easurable costs extending over three or more

years or which result in a series of benefits that exte.nd

three or more years beyond the inception date.

b. Specifically exempted from the scope of this Circular

are decisio.ns concerning water resource projects (guidance

for which is the approved Water Resources Principles and

Standards ) , the Government of the Dismct: of ColumiJia, and

non-Federal recipients of Federal loans or grants

c. The rem^aining exemptions derive from the secondary

nature of the decisions involved; that is, how to acquire

assets or proceed with a program after an affirmative decision

to initiate, renew, or expand such a program using this

Circular. Thus:

(1) This Circular would not apply to the evaluation

of decisions concerning how to obtain the use of real propsuch as by lease or ourchase.

1-11
(2) This Circular would net apply to the evaluation

cf decisions concerning the acquisition of coinmercial-type

ser'/ices by Govern.Tient or contractor operation, guidance

for which is CM2 Circular Nc . A-75

(3) This Circular would not apply to the evaluation

of decisions concerning hew to seiec* automatic data processing equipment, guidance for which is 0MB Circular No. A- 5

and QMS Bulletin No. 60-6.

d. The discount rates prescribed in this Circular are:

(1) Suggested for use in the internal planning

documents cf the agencies in the executive branch;

(2) Required for use in program analyses submitted

to the Office of Management and Budget in support of legislative and budget prcgram.s . This Circular does not supersede agency practices which are

prescribed by or pursuant to law, Executive order, or other

relevant Circulars . Agencies should evaluate their program.s

and projects in accordance with existing requirements and,

in addition, sum£7.arize the present value costs and/or benefits using the discount rate prescribed in this Circular.

4. Definitions. Analvtic docum.ents submitted to the Office

of Managemenw and Budget should be based on the following

concepts where relevant:

a. Exoectec annual cost m.eans the expected annual dollar

value (in constant dollars) of resources, goods, and services

required to establish and carry out a program^ or project.

Es tim.ates of expected yearly costs will be based on established definitions and practices fcr program, and ^rc^ecevaluation. However, all econcm.ic coses, including acquisition, possession, and operation costs, must be included

wheiher or not actually paid by tine Federal Government.

Such costs not cenerallv invclvmc a direct: Federal payment

include im.pu-ed m.arket values of public property and Sta"ce

ani _cca_ orcoe*"*"''' ^^x'^^ *-Qr'^<^/^^o

b . Exoectec annual benetit m.eans the dollar value {in

cons tan- col_arsj cf goccs and services expected to result

from a prccrami cr orciect for each of the vears it is in

ocerat.ion. Estim.ates cf exoected v2£.^l',' benefits will oe

oasec en esi ac lis had d'^f"''"itions and or^ctices d'^'/'^"'coec b'.*

1-12
c. Expecred annual effects means an objective, nonmonetary measure of progra." effects expected for each of

the years a program or project is in operation. When

dollar value cannot be placed on the effects of comparable

programs or projects, an objective measure of effects may be

available and useful to enable the comparison of alternative

means of achieving specified objectives on the basis of

their relative present value costs. These effects should

be estimated for each year of the planning period and are

not to be discounted.

d. Discount rate means the interest rate used in calculating the present value of expected yearly costs and benefits.

e. Discount factor means the factor for any specific

discount rate which translates expected cost or benefit in

any specific future year into its present value. The discount

factor is equal -to l/(l+r)t, where r is the discount rate

and t is the number of years since the date of initiation,

renewal or expansion of a program or project.

f. Present value cost means each year's expected

yearly cost m.ultiplied by its discount factor and then

summed over all years of the planning period.

g. Present value benefit means each year's expected

yearly benefit multiplied by its discount factor and then

sumjr.ed over all years of the planning period.

h. Present value net benefit means the difference

between present value benefit (item c) and present value

cost ( item f )

.

i. Benefit-cost ratio means present value benefit

(ite.m a) divided by present value cost (item f ) .

Attachm.ent A contains an exam.ple that illustrates calculation of the present value information,

5. Treatment of inflation . All estimates of the costs and

benefits for each year of the planning period should be .made

in constant dollars; i.e., in term.s of the general purchasing

power of the dollar at the time of decision. Estimiates may

reflect chances in the relative prices of cost and/or benefit

components , where there is a reasonable basis for estimating

such changes, but should not include any forecasted change

in the general price level during the planning period.

1-13
6. Treair.enr cr ur.cer -air.ry . Act:ua_ ccsis anc cer.erits ir.

future years are iikely -c differ fror. these expected at

the ti~e of decision. For these cases for which there is a

reasonable basis to esti.'aare the variability of future cosrs

and benefits, the sensitivity of proposed procrajns and

projects to this variability should be evaluated.

The expected annual costs and benefits (or effects) should

be supplemented with estirr.ates of mini.-nurn and maxir.um values.

Present value cost and benefits should be calculated for

each of these estimates. The probability that each of the

possible cost and benefit esti-ates r.ay be realized should

also be discussed, even when there is no basis for a precise

quantitative estimate . Uncertainty of the cost and benefit

(or effects) estimates should be treated explicitly, as

described above. The prescribed discount rate should be

used to evaluate all alternatives. Specifically, the evaluations should not use different discount rates to reflect the

relative uncertainty of the alternatives.

7. Discount rate oolicv. The discount rates •;lc be used for

evaluations of programs and projects subject t:o the guidance

of this Circular are as follows:

a. A rate of 10 percent; and, where relevant,

b. Any other rate prescribed by or pursuant to law,

Executive order, or other relevant Circulars.

The prescribed discount ra-e of 10 percent represents an

es-im^ate of the average raie of return on private investm.ent,

before taxes and af~er inflation.

To assist in calculation, Aotachm.ent 3 con-ams discount

factors for the discount rate of 10.0 percent for each cz

the '-'ears from, one to fiftv.

3. Znteroreiation. Guest.ions concerninc interore~a*^ion of

~ni5 Circu_ar snculd be addressed to the Assis'can'C Director

n> y^ V

f^ '^'^.'^

1-14
ATTACHMENT A

Circular No. A-94

Revised

SAMPLE FORMAT FOR DISCOUNTING DEFERPJ:D COSTS M^D BENEFITS

Assume a ten-year program which will commit the Government to

the stream of expenditures appearing in column (2) of the

table below and which will result in a series of benefits

appearing in column (3). The discount factor for a 10 percent

discount rate is presented in column (4) . Present value cost

for each of the ten years is calculated by multiplying column (2)

by column (4) ; presen-^ value benefit for each of the ten years

is calculated by multiplying colmnn (3) by column (4). Present

value costs and benefits are presented in columns (5) and (6),

respectively

Present Present

Year since value value

initiation

Expected Expected Discount cost benefit

renewal or yearly yearly factor for [Col. (2) X [Col. (3) X

ex::ansion cost benefit 10 Dercent Col. (4)] Ccl. K)]

(1) (2) (3) (4) (5) (6)

1 $10 $0 0.909 $9.1 $0.0

2 20 0.826 16.5 0.0

3 30 5 0.751 22.5 3.8

4 30 10 0.683 20.5 6.8

5 20 30 0.621 12.4 18.6

6 10 40 0.564 5.6 22.6

7 5 40 0.513 2.6 20.5

8 5 40 0.467 2.3 18.7

9 5 40 0.424 2.1 17.0

10 5 25 0.386 1.9 9.7

$95.5 $117.7

The sum of column (5) is present value cost: $95.5

The sum of column (6) is present value benefit: $117.7

Present value net benefit is the difference between present

value total benefit and oresent value total cost:

$117.7 - $95.5 = $22.2.

The benefit-cost ratio is 117.7/95.5 = 1.23.

NOTE: For more difficult discounting problems, a recomumended

reference is Princioles of Encineerinc Economy, bv ' Eucene L. Grant and W. G. Ireson, Ronald Press Com^oanv,

1960.

1-15
Circular No. A- 9

4

Revised

DISCOUNT FACTORS

Year since Year since

initiation, initiation

,

renewal or Discount renewal or Disccunt

exrjansion factors* exDa.nsicn factors*

1 0,909091 26 0.083905

2 0.826446 27 0.076278

3 0.751315 28 0.069343

4 0.683013 29 0.063039

5 0.620921 30 0.057309

6 0.564474 31 0.052099

7 0.513158 32 0.047362

8 0.466507 33 0.043C57

9 0.424098 34 0.039143

10 0.385543 35 0.035534

11 0.350494 36 0.032349

12 0.318631 37 0.029405

13 0.289664 38 0.026735

14 0.263331 39 0.024 304

15 0.239392 40 0.022095

16 0.217629 41 0.020036

17 0.197845 /

•* 0.018260

13 0.179859 43 0.0166:0

19 0.163508 44 0.0150 91

20 0.148644 45 0.013719

21 0.135131 46 0.012472

22 0.122846 47 . 011333

4^ ^ 0.11167S 48 0.010307

24 0.101526 49 . 9 3 7 C 25 0.092296 5 0.00 3 519

*The disccunt factors prese.nted in the table above irp.plici.ly

assuzie end-cf-year lunrp-sum costs and returns. When costs

and returns occur in a steady strear. , applying mid-year disccun- factors Tiay be more apprcpria-e . Present: value zz.sa.'^d benefit computed from this table ca.n be converted to a .mid-vear disccuntinc basis bv multiolvinc them bv the factor

1.043309.

Fcr example, if the present value cost: of a series of annual

expenditures ccm.puted from, the above table is $1,200.00. the

present: value cost c.n a m.id-ysar discou.ntiinc basis is

SI, 2 COO X 1.0 48309 or $1,2 5 3.5:".

1-16
EXECUTIVE OFFICE OF THE PRESIDENT

OFFICE OF MANAGEMENT AND BUDGET

WASHINGTON. a.C. 20503

June 14, 1972 CIRCULAR NO. A-104

TO THE HEADS OF EXECUTIVE DEPAHT!^NTS AND ESTABLISHMENTS

SUBJECT: Comparative cost analysis for decisions to lease

or purchase general purpose real property

^' Purpose . This Circular prescribes the economic basis

for determining whether general purpose real property to

be acquired for Government programs should be leased or

purchased.

2. ScoDe.

a. The economic analysis prescribed in this Circular

applies to the acquisition of general purpose real property

such as office buildings, warehouses, and associated land

for which estimated land and construction costs or market

value is $500,000 or more.

b. The Circular does not preclude non-economic considerations, such as historic values, special conditions

applying to overseas property, restricted access, and

statutory requirements

c. Analyses and decisions made under the guidance of

this Circular should be based upon maximum agency use of

long-term lease authority that may be requested of the

General Services Administration as provided by the Federal

Property and Administrative Services Act (40 USC 486(d),

490(h)(1) and Federal Property Management Regulations

(101-18. 107b)

3 - Applicability .

a. This Circular applies to all agencies of the

executive branch of the Federal Government except the

United States Postal Service. It does not apply to the

Government of the District of Columbia, or to non-Federal

recipients of Federal loans or grants.

b. This Circular does not supersede agency practices

concerning the acquisition or use of general purpose real

property which are prescribed by or pursuant to law, Executive order, or other Circulars except for those portions

1-17
of paragraph 6, Circular Mo. A-16, Revised, dated August 30,

1967, that apply to the deter:nination of mini.-uum cost leaseor-purchase alternatives.

c. This Circular dees not preclude consideration of

undisccunted cash flows for budgetary or other purposes.

rlowever, undisccunted cash flow analysis will not be the

basis for identifying the most economic of lease-cr-purchase

alternatives

.

d. The guidelines in this Circular are suggested for

use in the internal planning docuinents of the agencies in

the executive branch and required for use in all prospectuses

,

proposed legislation, budget justifications or other proposals submitted to the Office of Management and Budget and the

Congress

.

4. General requirements for analysis . The analysis of

lease-or-purchase alternanives should be based on the

following guidelines:

a. All economic costs incurred as a result of Federal

acquisition of property must be included whether or not

actually paid by the Federal Government- Such costs not:

generally involving a direct Federal payment include imputed

marke-c values of public property, Sta-ce and local proper-ty

taxes , and imputed insurance premiums

.

b. The ccsts that will occur in each year of the period

of analysis must be estimated in constant dollars (i.e.,

effects of inflation excluded) in terms of the general price

level at the time of acquisition.

c. A.cquisition alternatives will be compared on the

basis of the expected uimte period of stable program use of

the property. if such period is greater than the contract

cerm permitted under authority for Icng-term leasing, the

analysis should assume renewal of the lease at the last,

constant dollar payment.

d. Cost projections may be changed over the period of

analysis to reflect only real changes in costs due to

Cxhanges in amounts of services or their prices relative to

the general price level—for example, an increase in amount

of repair and improvements at prices in effect at the

beginning of the period of analysis or an increase in the

relative arice of these services.

1-18
e. The present values of alternative cost projections

over the relevant time period will be the basis for determining the most economic choice.

f

.

The discount rate applied to cost projections to

determine present value will be seven percent. This rate

represents an estimate of the internal rate of return on

general purpose real property leased from the private

sector, exclusive of property taxes and expected inflation.

This rate is influenced by IRS tax treatment of real

property and by separate handling of property taxes in this

Circular"; this rate is specific to lease-or-purchase

decisions and is not comparable to before tax rates of

return that the Office of Management and Budget specified

in Circular No. A-9 4, Revised. The Office of Management

and Budget will periodically review this estimate based

upon the above criteria and will revise the rate as necessary

5. Costs to be included . Constant dollar cost projections

will include the follcwing, adjusted as necessary to insure

valid comparisons:

a. Federal purchase alternative .

(1) Purchase costs (include all construction,

installation, site, design, management, and other costs

associated with the acquisition of the asset and its preparation for use)

;

(2) Repair and improvement;

(3) Operation and maintenance;

(4) Imputed property taxes (exclude consideration

of foreign taxes on overseas acquisitions unless actually

paid) ;

( 5) Impated insurance premiums ; and

(6) Cost offset: residual value at end of period.

b

.

Lease alternative .

(1) Lease payments;

(2) Repair and improvement (if not included in

lease payments) ; and

(3) Operation and maintenance (if not included in

lease payments)

.

1-19
4

c. Lease-curchase (or purchase-contract) alternative .

(1) Lease payments;

(2) Repair and improvement (after purchase or if

not included in lease payments prior to purchase)

;

(3) Operation and maintenance (after purchase or

if not included in payments prior to purchase)

;

(4) Purchase costs (when acquired) less applicable

credit for previous payments

;

(5) Imputed property taxes (after purchase or if

not included in payments prior to purchase)

;

(6) Imputed insurance premiums (after purchase)

;

and

(7) Cost offset (after purchase) : residual value

at end of period.

6. Costs that may be excluded . Some costs may be excluded

from each of the alternative cost projections if they are

estimated to be the same for all alternatives or too small

to affect the economic choice among the alternatives under

consideration;, for example, such conditions may exist for:

a. Repair and improvement costs;

b. Operation and maintenance ccs~s;

c. Property taxes; and

d. Insurance premiums.

7. Estimating certain costs . Potential problems of

estimating certain cosrs should be resolved as follows:

a. Purchase costs . Determine marke-c value for property

that is already owned , donated, or acquired by condemnation.

b. Imnuted crocertv :> taxes. i. M

(1) Determi.ne the property tax rate for comparable

property in the intended locality. If there is no basis by

which to estimate future changes in tax rates and assessed

(taxable) value, the first-year rate and assessed value can

be aoDlied to all vears

.

1-20
(2) Multiply the assessed value by the tax rate

to determine the annual charge.

(3) As an alternative to the procedure of section

7.b(l)-(2) above, obtain an estimate of the local effective

property taxes from the Building Owners and Managers Association's Regional Exchange Reports . If there is no basis for

estimating future property taxes, the first-year rate can

be applied to all years.

c. Imputed insurance premiums . Determine local estimates

of standard, commercial coverage for like property from the

Building Owners and Managers Association's Regional Exchange

Reports .

d. Annual lease payments.

(1) Determine annual lease payments for comparable

property and terms of lease in the intended locality at the

time of proposed acquisition.

(2) When estimates of lease payments are based on

actual lease contracts on comparable property, they should

be adjusted to exclude the expected inflation for the period

to first renewal, as described in Attachment A.

e. Cost offset: residual value at end of period .

(1) The objective is to predict the market value of

the property at the end of the time period under consideration, excluding inflacicn.

(2) Residual values of property are determined by

applying a method that best approximates the historically

observed changes in market values experienced by the Government. The residual value of the property is obtained by

adding the results of a decrease in the constant dollar market

value of the building and an increase in the constant dollar

market value of the site. To approximate the residual value

of the building, a decay and obsolescence rate of 1.7 percent

should be applied to each year's remaining constant dollar

market value. To approximate the residual value of the site,

the constant dollar market value should be increased by

1.5 percent each year. To assist in calculation, Attachment 3

contains building decay and obsolescence factors of 1.7 percent and site appreciation factors of 1.5 percent compounded

for each of the years 1 to 30.

(3) Whenever possible, the residual value of the

property should be adjusted to incorporate the current

1-21
market value for comparable prcperuv in similar locales

for simjLlar commercial property whose age is acproximarely

equal to the period of analysis.

8. Present value calculations and format for comparisons .

a. Calculation of present values of the alternative

cost projections will be performed in accordance with

established discounting procedures, using either continuous

or end-of-year discount factors.

b. Attachment C illustrates the method to be used in

developing the present value comparisons

.

c. Attachment D illustrates the required format for

the com.parative analysis of lease-or-purchase alternatives

presented in prospectuses, proposed legislation, budget

justifications, or other proposals for submission to CMB

.

All assumptions and basic cost data must be explicitly

provided in the materials presented.

d. As required for particular activities, the Office

of Management and Budget m^ay request additional, special

analyses and information and may change the requirements

for reoorts to the 0MB and to Ccnaress.

CASPAR W. WEINBERGER

DIRECTOR

Attachments

1-22
ILLUSTRATION

ATTACHMENT A

Circular No. A-104

PRESENT VALUE CONSTANT DOLLAR ANNUAL PAYMENT CALCULATIONS

To determine the present value constant dollar annual payments, where,

for example,

the date of initial acquisition is January 1972;

the initial period of level payments = n = 20 years;

- the annual payment is $1,123,000 for 250,000 net square feet; and

the payments are made at the end of the year,

calculate the average annual rate of inflation during the past n years . The average inflation rate is found by (1) dividing the consumer price

index at the beginning of the contract period (See the Economic Report of

the President , February 1972, Table B-45, p. 247 for consumer price

indexes.) by the consumer price index n years ago, and (2) comparing

this result to the compound interest factors for n years. In this

example, the consumer price index for 1971, 121.3 is divided by the

consumer price index for 1951, 77.8 yielding 1.56. According to compound interest tables, the rate which would yield 1.56 in 20 years is

approximately 2.2 percent.

Then, apply the determined constant dollar price deflator to each

annual payment .

In this example, each annual current dollar payment of $1,128,000 must

be multiplied by the appropriate constant dollar price deflator at

2 . 2% per year

.

Finally, multiply each constant dollar annual payment by the appropriate

7 pe rcent present value discount factor

.

Constant 7% present

Current dollar price Constant value

dollar deflator dollar discount Present

Year payment

1,128,000

@ 2.2% payment

1,103,184

factor value

1 .978 .935 1,031,477

2 ,957 1,079,496 .873 942,400

• 3 .937 1,056,936 .816 862,460

4 .917 1,034,376 .763 789,229

5 .897 1,011,816 .713 721,425

6 .878 990,384 .666 659,596

7 .859 968,952 .623 603,657

8 .840 947,520 .582 551,457

9 .822 927,216 .544 504,406

10 .804 906,912 .508 460,711

11 .787 887,736 .475 421,675

12 .770 868,560 .444 385,641

13 .754 850,512 .415 352,962

14 .737 831,336 .388 322,558

15 .722 814,416 .362 294,819

16 .706 796,368 .339 269,969

17 .691 779,448 .317 247,085

13 .676 762,528 .296 225,708

19 .661 745,608 .277 206,533

20 1,128,000 .647 729,816 .258 188,293

1-23

10,042 061
ATTACHMENT 3

Circular No. A-104

BUILDING DECAY-OBSOLESCENCE AND SITS APPRECIATION

Period Building Site

of Decay-Obsolescence Appreciation

Analvsis Factors* Factors*

1 0.98300 1.01500

2 0.96629 1.03023

3 0.94986 1.04568

4 0.93371 1.06136

5 0.91784 1.07728

6 0.90224 1.09344

7 0.88690 1.10984

8 0.87182 1.12649

9 0.85700 1.14339

10 0.84243 1.16054

11 0.82811 1.17795

12 0.81403 1.19562

13 0.80019 1.21355

14 0.78659 1.23176

15 0.77322 1.25023

16 0.76007 1.26399

17 0.74715 1.28802

13 0.73445 1.30734

19 0.72197 1.32695

20 0.7 9-6 9 1.34686

21 0.69763 1.36706

22 0.68577 1.38756

23 0.67411 1.40338

24 0.66265 1.42950

25 0.65139 1.45095

26 0.64031 1.47271

27 0.62943 1.49480

28 0.61873 1-51722

29 0.60821 1.53993

30 0.59787 1.56308

*Tlie factors presented in the table above i:mplicitly

ass'oiue end-of-year building decay-obsolescence and

site appreciation changes.

1-24
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ATTACHMENT D

Circular IJc . A-104

ILLUSTRATION

PRESENT VALUE COST SUM:4ARI£5 FOR

ALTEP>NATIVE METHODS OF ACQUISITION

[Federal Office Building, City, State]

(In thousands of dollars)

Item 2 vears ; 7'

8 ,845

3 , 556

515

714

PURCHASE :

Improvements 10 , 50

Site = . 1,350

Repair and improvement 947

Property taxes 2 , 120

Subtotal 14,917

Less residual value 2,392

Total 12,525

LEASE :

Total annual payments** 10 , 042

LEASE- PURCHASE (or PURCHASE-CONTRACT)*

Annual payments until purchase***

Purchase cost less credit

Repair and improvement (after purchase) .

Property taxes (after purchase),

Subtotal ' 13,63

Less residual value 2^392

Total

*Operation and maintenance costs are borne by the Government

and are assumed to be identical for all three acquisition

methods. Therefore, they are omitted in this comparison.

Imputed insurance premiums are estimated to be negligible

relative to other costs and therefore omitted.

Annual lease payments in constant dollars are calculated.

Than, each constant dollar lease payment is discounted at

7 percent (See Attachment A)

''*Arinual lease-purchase (or purchase-contract) payments of

$1,400 + purchase of $21,000 (15 years annual payments)

less credit of $14,000. The annual payments in constant

dollars are calculated- Then each constant dollar payment

is discounted at 7 percent (technique is shown in

Attachment A)

1-26
Section 2

Discounting

To perform a valid economic evaluation of a project, it is necessary that

all cash flows be stated in time-equivalent amounts. "Discounting" is the

term often given to the technique for adjusting cash flows to time equivalency

by taking into account the time value of money. This section is provided as a

brief introduction to discounting because it is a fundamental tool used in

solving all of the capital investment problems addressed by this seminar.

The following topics are treated in brief below:

(1) Definition

(2) Purpose

(3) Approach

(4) Selecting a Discount Rate

(5) Formulas (Table 2-1)

(6) Application

(7) Discount Factors Based on a 7% Discount Rate (Table 2-2)

(8) Discount Factors Based on a 10% Discount Rate (Table 2-3)

(9) Where to Find UPW* Factors for Discounting Energy Costs or Savings

(10) Problem Illustrations

Definition

Discounting is a technique for converting cash flows that occur at different

times to equivalent amounts at a common time.

Purpose

The costs and benefits associated with building projects are typically spread

over time. The dollar estimates of costs and benefits must be adjusted to

a common time basis before they can be combined to determine a measure of

2-1
economic performance. Because of the earning potential of money over time, as

indicated by interest, a dollar now is worth more than a dollar at some later

t ime

.

Approach

Discounting is performed by applying interest (discount) formulas, or

corresponding discount factors calculated from the formulas, to the estimated

costs and savings that result from a given investment. The application of the

appropriate formula or factor to a cash amount will convert that cost or

saving to its equivalent value at the selected base time.

Selecting a Discount Rate

A key element in the discount formulas is the discount rate, the rate of

interest reflecting the invester's time value of money. If future cash flows

are stated in constant dollars, the discount rate should be selected to

reflect only the real earning power of money over time; i.e. , the time value

of money remaining after inflation is removed. This is the approach

recommended for Federal project evaluation. If future cash flows are

estimated to include inflation, the discount rate can be selected to also

include inflation, and the discounting technique can be used to adjust both

for the effects of price inflation and for the real earning power of

capital. This approach is often used for commercial project evaluation

because it facilitates the treatment of tax effects. The relationship between

a nominal discount rate, D, and a real discount rate, d, is as follows:

D = (l+d) • (l+I) -1 = d + I + dl

1+D

and d = • -1, where I is the rate of general price inflation.

l+I

(See section on Escalation)

2-2
Application

The appropriate discount formula to use for adjusting a cash amount to an

equivalent value at another time depends on the time distribution of the cash

amount and the time basis selected by the analyst for the economic evaluation.

For example, to find the equivalent value in the future of a single cash

amount received today, the single compound amount formula (SCA) is used. To

find the equivalent value in the future of a stream of uniform cash amounts

over a period of years, the uniform compound amount formula (UCA) is used. To

find the present value equivalent of a single amount to be received in the

future, the single present worth formula (SPW) is used. To find the present

value equivalent of a uniform series of future cash amounts, the uniform

present worth formula (UPW) is used. And, to find the present

value equivalent of a series of future amounts escalating in amount each year,

the modified uniform present worth formula (UPW*) can be used. To express a

present value as an equivalent uniformly recurring annual value, the uniform

capital recovery formula (UCR) is used. The dollar amounts will, of course,

differ depending on the time base chosen, but present values, annual values,

and future values, if time-equivalents, will lead to the same investment

decision. It is most customary in economic evaluations, however, to convert

all cash flows to either present values or annual values, and, in the Federal

Energy Management Program, the use of present values is requested to

facilitate comparisons among agencies and projects.

2-3
Table 2.1 Discounting Equations

Name Schematic Illustration Application Algebraic Forma*b

Single Compound-Amount

(SCA) Equation

Single Present-Worth (SPW) Equation

Uniform Sinklng-Fund

(USF) Equation

Uniform Capital-Recovery

(UCR) Equation

A? + A? &-

—'\n} —

E

— [f]

A? + A?

Uniform Compound-Amount

(UCA) Equation [a] + [a] + [a] F?

Uniform Present-Worth (UPW) Equation P? ^H + H a

To find F when

P is Icnown

To find P when

F is known

To find A when

F is known

To find A when

P is known

To find F when

A is known

To find P when

A is known

F = P- [d+d)"^]

P = F

L (1+d)N

'' = '[(1+d)N-1

A= P

F = A

P = A

[

• d(1 + d)"

|_(1 + d)N - 1

r(i + d) -

1

t

(1 + d)N - 1 d(1 + d)N

Modified Uniform

Present-Worth (UPW*) Equation^

where:

P? A2 . . .

An

To find P when

known Ao is _ ^ , fA±^ f

. _ fA±l\ N]

escalating *^ ^\d-eJl \^ + dj J

at rate e

P = present sum of money,

F = future sum of money equivalent to P at the end of N periods of time at d interest or discount rate, A = end-of-period payment (or receipt) in a uniform series of payments (or receipts) over N periods at d interest or discount rate, Aq = initial value of a periodic payment (receipt) evaluated at the beginning of the study period, A, = Ao • (1 + e)', where t = 1, . .

.

, N, N = number of interest or discount periods, d = interest or discount rate, and

e = price escalation rate per period.

'Note that the USF, UCR, UCA, and UPW equations yield undefined answers when d = 0. The correct algebraic forms for this special case would be as follows: USF formula, A=F/N; UCR formula, A=P/N; UCA formula, F=A N; and UPW

formula, P=A N. The UPW* equation also yields an undefined answer when e=d. In this case, P=Ao N. 'The terms by which the known values are multiplied in these equations are the formulas for the factors found in discount

factor tables. Using acronyms to represent the factor formulas, the discounting equations can also be written as F = P SCA, P = F • SPW, A = F USF, A = P • UCR, F=A UCA, P=A UPW, and P=Ao UPW.*

'To find P when Aq escalates at a different rate over each of K escalation periods,

1 +e5\ J

" j=1 \ 1+d / V 1+d / j=i ^ 1+d ^

(Mil')' /11^\"^ . / ^^«K-1\ "K-1 "^K /1 + e^

y \1+d/ \1+d/ \ 1+d/ j=i \1+d /

where nj = the number of interest or discounting periods over which a given escalation rate, e„ is assumed to hold

(-:%-)-,"', (^)'=(-^)[-(-^)"']

Source: NBS Handbook 135.

2-4
Table 2-2 Discount Factors Based on 7% Discount Rate

1 " ~ Single Single Uniform Uniiorrn

Compound Present Capital Present

Amount Value Recovery Value

Factor Factor Factor Factor

SCA SPW UCR UPW

Civen P F F A

To Find F P A P Period

N

1

2

34

5

6

78

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

1.070 .9346 1.070

1.145 .8734 .5530

1.225 .8163 .3811

1.311 .7629 .2952

1.403 .7130 .2439

1.500 .6663 .2098

1.606 .6227 .1855

1.718 .5820 .1675

1.838 .5439 .1535

1.967 .5083 .1424

2.105 .4751 .1334

2.252 .4440 .1259

2.410 .4150 .1196

2.578 .3878 .1143

2.759 .3624 .1098

2.952 .3387 .1058

3-159 .3166 .1024

3.380 .2959 .0994

3.616 .2765 .0967

3.870 .2584 .0944

4.141 .2415 .0923

4.430 .2257 .0904

4.740 .2109 .0887

5.072 .1971 .0872

5.427 .1842 .0858

5.807 .1722 .0846

6.214 .1603 .0834

6.649 .1504 .0823

7.114 .14056 .0814

7.612 .1314 .0805

8.145 .1227 .0798

8.715 .1147 .0791

9.325 .1072 .0784

9.978 .1002 .0778

10.68 .0937 .0772

11.4 2 .0875 .0767

12.22 .0818 .0762

13.03 .0764 .0758

13.99 .0715 .0754

14.97 .0668 .0950

.9346

1.808

2.624

3.387

4.100

4.766

5.389

5.971

6.515

7.023

7.499

7.943

8.358

8.745

9.108

9.447

9.763

10.06

10.33

10.59

10.83

11.06

11.27

11.47

11.65

11.83

11.99

12.14

12.28

12.41

12.53

12.65

12.75

12.85

12.95

13.03

13.12

13.19

13.26

13.33

Uni f orn

Si nkin:'^ Fund

Factor

US I-

"pA

1.0000

.4831

.3110

.2252

.1739

.1398

.1155

.0975

.0835

.0724

.0634

.0559

.0496

.0443

.0398

.0358

.0324

.0294

.0267

.0244

.0223

.0204

.0187

.0172

.0158

.0146

.0134

.0124

.0114

.0106

.0098

.0091

.0084

.0078

.0072

.0067

.0062

.0058

.0054

.0050

UnJ u,r:,t ; Cor~l)C)!)n.! i AmoiioL ! Factor ' UCA

^_ i

1.000

2.070

3.215

4.440

5.751

7.153

8.654

10.26

11.98

13.82

15.78

17.89

20.14

22.55

25.13

27.89

30.84

33.99

37.38

40.99

44.86

49.00

53.44

58.18

63.25

68.68

74.48

80.70

87.35

94.46

102 '.0 110.2

118.9

128,

138,

148

160,

172,

185,

199,

A] 1 formulae assume end-of-pe r iod payments.

= a present sum of money; F ~ a future sum of money, equivalent to P at the end of H periods of tiir.e at discount rate of d ; A --= an cad of period

payment (or recei])ts) in a uniform series of payments (or receipts) over

N periods at d interest rates.

2-5
Table 2-3 Discount Factors Based on 10% Discount Rate

Single Single Uniform Uniform Uniform Uniffir.i j Compound Present Capi tal Present Sinking Compo.md | Amount. Value Recovery Value Fund Amount ! Factor Factor Factor Factor Factor F.'ctor

SCA SPW UCR UPW USF UCA

f Given 1' F }' A F ^'

i T(j Find F P A P A y .1 Period

N

1

i

1

1 1.100 .9091 1.100 .9091 1.000 1.000

2 1.210 .8264 .5762 1.736 .4762 2.100

3 1.331 .7513 .4021 2.487 .3021 3.310

4 1.464 .6820 .3155 3.170 .2155 4.641

5 1.611 .6209 .2638 3.791 .1638 6.105

6 1.772 .5645 .2296 4.355 .1296 7.716

7 1.949 .5132 .2054 4.868 .1054 9.487

8 2.144 .4665 .1874 5.335 .0874 11.44

9 2.358 .4241 .1736 5.759 .0736 13.58

10 2.594 .3855 .1627 6.145 .0627 15.94

11 2.853 .3505 .1540 6.495 .0540 18.53

12 3.138 .3186 .1468 6 . 814 .0468 21.38

13 3.452 .2897 .1408 7.103 .0408 24.52

14 3.798 .2633 .1357 7.367 .0357 27.98

15 4.177 .2394 .1315 7.606 .0315 31.77

16 4.595 .2176 .1278 7.824 .0278 35.95

17 5.054 .1978 .1247 8.022 .0247 40.54

18 5.560 .1799 .1219 8.201 .0219 45.60

19 6.116 .1635 .1195 8.365 .0195 51.16

20 6.728 .1486 .1175 8.514 .0175 57.28

21 7.400 .1351 .1156 8.650 .0156 64.00

22 8.140 .1228 .1140 8.772 .0140 71.40

23 8.954 .1117 .1126 8.883 .0126 79.54

24 9.850 .1015 .1113 8.984 .0113 88.50

25 10.83 .0923 .1102 9.077 .0102 98.35

26 11.92 .0839 .1092 9.161 .0092 109.2

27 13.11 .0763 .1083 9.237 .0083 121.1

28 14.42 .0693 .1075 9.307 .0074 134.2

29 15.86 .0630 .1067 9.370 .0067 148.6

30 17.45 .0573 .1016 8.427 .0061 164.5

31 19.19 .0521 .1055 9.479 .0055 181.9

32 21.11 .0474 .1050 9.526 .0050 201.1

33 23.23 .0431 .1045 9.569 .0044 222.3

34 25.55 .0391 .1041 9.609 .0001 245.5

35 28.10 .0356 .1037 9.644 .0037 271.0

36 30.91 .0323 .1033 9.676 .0033 299.1

37 34.00 .0294 .1030 9.706 .0030 330.0

38 37.40 .0267 .1027 9.733 .0027 364.0

39 41.14 .0243 .1025 9.757 .0025 401.4

40 45.26 .0221 .1023 9.779 .0023 442.6

Al] f ormulao assume end-of-p eriod payments.

I' ^ a present sum of money; F --= a future sum of money, equivalent Lo P at the end of H periods of Lime at discount rate of d; A ^ an end of period

payment (or receipts) in a uniform series of payments (or receipts) over

N periods at d interest rates.

2-6
Where to Find UPW* Factors for Discounting Energy Costs or Savings

Modified Uniform Present Worth Factors (UPW*), based on a 7 percent discount

rate for evaluating Federal energy projects, can be found in Appendix B of NBS

Handbook 135, pp 118-128. These factors are given for each of 10 Department

of Energy (DoE) regions, for different types of energy, and for residential,

commercial, and industrial use. (As explained in the Handbook on pp. 116-117,

these factors are subject to periodic revision. To obtain the most recent

factors, contact the Federal Programs Office of the U.S. Department of

Energy.)

2-7
Problem Illustrations

1. Find the present value (P) of a future amount of $5,000 in 10 years (N),

assuming the discount rate (d) to be 10%.

(a) Using the Single Present Worth (SPW) Discount Formula (from Workbook

Table 2-1):

1 P = F (l+d)N

1 = $5,000 > (1 + .10)10

= ($5,000) • (0.3855)

= $1,928

(b) Using the SPW Discount Factor for d = 10% and N = 10 (from Workbook

Table 2-3):

P = F . SPWiOyr, 10%

= ($5,000) • (0.3855)

= $1,928

2. Find the present value (P) of a uniform series of annually recurring

future amounts (A) of $2,000 per year over the next 10 years (N) , assuming

the discount rate (d) to be 7%.

(a) Using the Uniform Present Worth (UPW) Discount Formula (from Workbook

Table 2-1):

(l+d)N -1

P = A

d(l+d)N

(1 + .07)10 -1

= $2,000 '

= $2,000

.07(1 + .07)10

0.9672

0.1377

2-8
= ($2,000) • (7.024)

= $14,048

(b) Using the UPW Discount Factor for d =7% and N=10 (from Workbook Table

2-2):

P = A ^ UPWiOyr, 7%

= ($2,000) • (7.023)

= $14,046 (Note small difference due to rounding)

3. Find the future value (F) in 15 years (N) of a present amount (P) of

$1,000, assuming a discount rate (d) of 10%.

(a) Using the Single Compound Amount (SCA) Formula (from Workbook Table

2-1):

F = P . (l+d)N

= $1,000 • (1 + .10)15

= ($1,000) • (4.177)

= $4,177

(b) Using the SCA Factor for d = 10% and N = 15 (from Workbook

Table 2-3):

F = P . SCAi5y^^ 10%

= ($1,000) • (4.177)

= $4,177

4. Find the Future Value (F) in 15 years (N) of a uniform series of

annually recurring amounts (A) of $1,000, assuming a discount

rate (d) of 10%.

2-9
(a) Using the Uniform Compound Amount (UCA) Formula (from Workbook Table

2-1):

(l+d)N -1

F = A

d

(1 + .10)15 _i

= $1,000

.10

= ($1,000) ' (31.77)

= $31,770

(b) Using the UCA Factor for d = 10% and N = 15 (from Workbook

Table 2-3):

F = A . UCAi5y^^ 10%

= ($1,000) (31.77)

= $31,770

5. Amortize in uniform annual payments (A) over 20 years (N) a present

amount (P) of $100,000, assuming a discount rate (d) of 10%.

(a) Using the Uniform Capital Recovery (UCR) Discount Formula (from

Workbook Table 2-1)

d(l+d)N

A = P (l+d)N -1

.10 (1 + .10)20

= $100,000 • (1 + .10)20 -1

= ($100,000) - (0.1175)

= $11,750

2-10
(b) Using the UCR Discount Factor for d = 10% and N = 20 (from Workbook

Table 2-3):

A = P UCR20yr, 10%

= ($100,000) •' (0.1175)

= $11,750

6. Find the uniform amount that mist be cumulated annually (A) in order to

have a future amount (F) of $30,000 in 8 years (N), assuming a discount

rate (d) of 7%.

(a) Using the Uniform Sinking Fund (USF) Discount Formula (from Workbook

Table 2-1):

d

A = F ' (H-d)N -1

.07

= $30,000

(1 + .07)0 _i

= ($30,000) • (0.0975)

= $2,925

(b) Using the USF Discount Factor for d = 7% and N = 8 (from Workbook

Table 2-2):

A = F . USFgyr, 7%

= ($30,000) • (0.0975)

= $2,925

7. Find the present value (P) of a non-uniform annually recurring amount (A)

that is valued at $5,000 at the beginning of the study period (Aq), and

escalates thereafter at 5% per annum (e) over 12 years (N) , assuming a

discount rate (d) of 12%.

(a) Using the Uniform Present Worth Modified (UPW*) Discount Formula

(from Workbook Table 2-1):

2-11
(1+e) 1+e N

P = Ao 1-

(d-e) 1+d

(1 + .05) = $5,000 • 1-

(.12 - .05)

= $5,000 • [(15) • (0.5390)]

= ($5,000) • (8.085)

= $40,425

1 + .05\ 12

1 + .12

(b) Using the UPW* Discount Factor for d = 12%, e = 5%, and N = 12

(from Handbook 135, Table B-14, p. 131):

P = Aq . UPW*i2yr, 12%, 5%

= ($5,000)' (8.086)

= $40,430 (Note small discrepancy due to rounding)

Find the present value (P) of the estimated cost of natural gas to heat

a Federal office building in Minnesota over 10 years (N) , assuming that

the annual cost is initially valued at $10,000 (Aq) , and using the Federal

discount rate of 7% for energy projects and the appropriate projected

energy escalation rates,

(a) Using the Uniform Present Worth Modified (UPW*) Discount Formula

for multiple escalation rates (from Workbook Table 2-1, footnote a);

and the escalation rates for DoE Region 5, for the Commercial Sector,

and for natural gas, of 8.87% for the period 1981-1985, 1.76%

for 1985-1990, and 3.10% for 1990 and beyond (from Handbook 135,

Table C-5 , p. 138):

2-12
P = A. "1 J ^1 n2 J

I [(l+ei)/(l+d)] + [(l+ei)/(l+d)] • I [(l+e2)/(l+d)] + [(1+ei)/

j=l j=l

n^ n2 n3 j

(1+d)] . [(l+e2)/(l+d)] . I [(l+e3)/(l=d)]

=$10,000

2 j 2

I [(l+.0887)/(l+.07)] + [(l+.0887)/(l+.07)]

j = l j 2 (1+.07)] + [(1+. 0887)7(1+. 07)]

• I [(1+.0176)/

j = l 5 [(l+.0176)/(l+.07)]

3 j I [(l+.0310)/(l+.07)]

=$10,000 (l+.0887)/(.07-.0887) • fl- [ (l+.0887)/( 1+.07) ] J+ [ ( l+.0887)/( 1+.07)

]

[(l+.0176)/(.07-.0176)] •

I 1- [(l+.0176)/(l+.07)] + (l+.0887)/( 1+.07)

(l+.0176)/(l+.07) (1+. 0310)/ (.07-. 0310) 1- [(l+.0310)/(l+.07)]

=$10,000 [(-58.22) • (-0.0353) + (1.035) • (19.42) • (0.222) + (1.035) •

(0.7780) • (26.44) • (0.1054)]

=$10,000 [2.055 + 4.462 + 2.244]

=($10,000) • (8.761)

= $87,610*

(b) Using the Federal UPW* Discount Factor for DoE Region 5, for the

Commercial Sector, for natural gas, for 10 years (from Handbook 135,

Table B-5 , p. 122):

P = Ao . UPW*iOyr, 7%, DoE 5

= ($10,000) • (9.60)

= $96,000*

* Note discrepancy in (a) and (b) answers. The difference reflects the fact

that the (a) calculations use the escalation rates directly, based on mid1983 as the beginning of the study period, while the (b) calculations use UPW* factor tables based on niid-1981 as the beginning of the study period.

2-13

Section 3

Escalation

This section has the following objectives: to review the procedure for

escalating costs, to distinguish budgetary needs for escalation from the

requirements of economic analysis, and to compare economic evaluations made

(a) in constant dollars using real escalation and discount rates and (b) in

current dollars using nominal escalation and discount rates.

It contains the following topics:

(1) Escalation Procedure

(2) Budgetary Versus Economic Analysis Requirements for Cost

Estimates

(3) Concept of Differential Price Escalation

(4) Constant Dollar Versus Current Dollar Analyses

Escalation Procedure

An initial amount, Cg, can be escalated at rate e over N periods of time to a

future amount, Cfj, by applying the single compound amount formula based on

rate e and period N, to the initial amount; i.e., Cjyj = Cq (1+e)'^.

An initial amount, Cq , can be escalated over N periods of time at changing

escalation rates, e^ , 62, ... e^, each of which holds for a designated

interval of time, p^ , P2 ... Pn ''which together sum to a total of N

compounding periods) as follows:

P, P^ P

Cn = Co(l+ei) 1 (1+62) 2...(i+e^) n.

3-1
Budgetary Versus Economic Analysis Requirements for Cost Estimates

Budget estimates project the actual number of dollars expected to be

required to purchase a building system or component at the planned time of

acquisition. That is, budget estimates are generally stated in "current", or

"nominal," dollars including projected price inflation.

In contrast, it is imperative in an economic analysis that all dollars have

the same unit of purchasing power. Hence, purely inflationary or deflationary

effects must be eliminated from projected cash flows in an economic analysis.

Concept of Differential Price Escalation

0MB Circular A-94 instructs Federal Agencies to make all estimates of future

costs and benefits in constant dollars, reflecting in the estimates only

changes in relative prices "where there is a reasonable basis for estimating

such changes". Estimates should not include any forecasted change in the

general price level.

We can define the relative price change in terras of a "differential

escalation rate", i.e., the expected percentage difference between the rate of

increase assumed for a given item of cost (such as energy), and the general

rate of inflation. Let us denote the total escalation rate, "E"; the

differential escalation rate, "e"; and the general rate of price inflation,

"I".

3-2
Cash flows that are projected to increase in amount at about the same rate as

general price inflation (i.e., E = I) have no real or differential escalation

(i.e., e = 0) , and, therefore, will remain unchanged in constant dollars from

the initial amount. Routine maintenance costs, for example, are often assumed

to remain the same in constant dollars.

Cash flows that change at a rate different from the rate of general price

inflation (i.e., E ^ I and e ^ 0) , change in constant dollars. In a

Federal analysis, the projected real or differential escalation rate, e, can

be used with the single compound amount formula to calculate future amounts in

constant dollars.

The three figures below illustrate three cases of differential escalation. In

each figure, time is measured on the x-axis and dollar costs on the

y-axis. The solid line in each figure, projected from the y-axis, traces the

actual rise in price over N years of an item which initially costs Cq. That

is, the solid line, defined by the equation Cg = Cg (1 + E)'^, depicts current

dollar costs for a given E over N years. The dashed line in each figure

traces the rise in cost over N years that would occur if the item increased

in price at the rate of general price inflation, I. It is defined by the

equation Cj = Cq (1 + I)^. The dashed-dot line traces the change in constant

dollar cost over N years. It is defined by the equation Cg = Cq (1 + e)^.

Figure 1, where the dashed line and solid line are coincident, shows the case

for which the rate of total change in the price of the item, E, is just equal

to the rate of change in the general price level, I (i.e., the differential

escalation rate, e, is zero). In this case, the future current dollar cost

3-3
$

C4

C3

C2

Ci

Co

#Ce=c,

:.=.-^^^^L

N 1 N

Fig. 3-1 Change in Dollar Values Over

Time as a Function of Price

Escalation: E = I and e = 0.

Fi 3-2 Change in Dollar Values Over

Time as a Function of Price

Escalation: E > I and e > 0,

Fig 3-3 Change in Dollar Values Over

Time as a Function of Price

Escalation: E < I and e < 0. 3-4
in Nj^ years is C2 , i.e., Cq ( 1 + E)^! = C2 . But in constant dollars, the

future cost, Cg , is still Cq , because e = and the constant dollar cost, Cg

,

is equal to Cq (1 + e)^.

Figure 2 describes costs for the case where the rate, E, of total change in

the price of the item exceeds the rate, I, of change in the general price

level, such that the differential rate, e, is positive. In this case, the

future current dollar cost in year Nj is greater than C2—it is C3 in the

example—and in constant dollars the future cost, Cg, is higher than Cq ,

because E > I and e > 0.

Figure 3 shows dollar costs for the case where the rate, E, of total change in

the price of the item is less than the rate, I, of change in the general price

level, such that the differential rate, e, is negative. In this case, the

future current dollar cost, Cg , in year Nj is less than C2—it is C^ in the

example—and in constant dollars the future cost, C^, is below Cq because E <

I and e < 0.

Constant Dollar Versus Current Dollar Analyses

When future costs and benefits are stated in constant dollars, incorporating

only the relative price change and excluding inflation, it is appropriate to

discount the future values to a common time basis using a real discount rate,

denoted "d", which does not include inflation. The 7 percent discount rate

specified for evaluating Federal energy conservation projects and the 10

percent discount rate specified for evaluating other kinds of Federal projects

(not specifically exempted) are both real discount rates.

3-5
ifnen future cash flows are estimated to include inflation, the discount rate

should also include inflation; that is, a nominal discount rate, which can be

denoted "D," should be used for discounting current dollar cash flows. Market

interest rates are nominal rates. The weighted cost of capital (expressed as

a percent), which is often used by corporations as a discount rate, is a

nominal rate.

If correctly formulated, an analysis in constant dollars worked with a real

discount rate will yield the same result as an analysis in current dollars

worked with a nominal discount rate. While the constant dollar approach is

recommended for Federal analyses, the current dollar approach is often

preferred for the analysis of taxable investments because it can facilitate

the analysis of tax effects.

To see the relationships between the two approaches, the following

relationships should be noted:

a) E = (1 + e) (1 + I) -1

= e + I + el,

1 + E b) e = 1,

1 + I

c) D = (1 + d) (1 + I) -1

= d + I + dl, and

1 + D

d) d = 1 .

1 + I

3-6
where

E = the rate of total change in the price of a given item,

e = the differential rate of change in the price of the item,

I = the rate of general price inflation,

D = a nominal discount rate, and

d = a real discount rate.

By pairing E and D for escalation and discounting, purely inflationary effects

cancel out of the analysis. By pairing e and d for escalation and

discounting, purely inflationary effects are simply omitted from the

analysis.

References ;

Discussion of the Causes of Changing Monetary Values Over Time—See Handbook 135, pp. 7-8.

Federal Energy Price Escalation Rates—See Tables C-1 through C-11, Handbook 135, pp. 134-144.

UPW* Factors for Combined Escalation and Discounting—See Tables B-1 through

B-11, Handbook 135, pp. 118-128.

UPW* Factors for Combined Escalation and Discounting Based on Various Discount

Rates and Escalation Rates (Non-Specif ic to Federal Energy Costs) —See

Tables B-12 through B-14, Handbook 135, pp. 129-131.

Year-By-Year Method of Calculating the Value of Energy Savings (when it is

necessary to adjust for changes in the annual quantity or source of

energy) —See Appendix G, Table G-2 , and accompanying text. Handbook 135,

pp. 219-223.

3-7

Section 4

Study Period

The purpose of this section is to provide guidelines for setting the length of

the study period, the time over which project costs and benefits will be

assessed. The discussion is organized into the following parts:

(1) Maximum Study Period

(2) Selecting a Study Period for Present Value Comparisons of Projects

(3) Selecting a Study Period for Savings -to-Investment Ratio (SIR)

Comparisons of Projects

(4) Reconciling Project Life and Study Period

(5) Delays Between the Time of Project Evaluation and Project

Initiation

Maximum Study Period

For evaluating Federal energy conservation projects, an upper limit of 25

years is set for the study period, reflecting uncertainty in projecting energy

prices for longer periods of time.

Selecting a Study Period for Present Value Comparisons of Projects

For selecting among mutually exclusive project alternatives based on present

value LCC or NS, the same study period should be used to evaluate the

alternatives. The use of different study periods would result in different

present values even if the alternatives were equal in cost effectiveness.

Reference : See Section 3.10, Handbook 135, pp. 33-34.

4-1
Selecting a Study Period for SIR Comparisons of Projects

The rankings of projects according to their SIR's will not be affected by

having different study periods for different projects _if there is no

differential price escalation included in project cash flows. If differential

price escalation _i£ included, the comparative rankings of projects may be

affected somewhat by the use of unequal study periods. In this case, the use

of equal study periods will avoid any biasing of results. The life-cycle cost

guidelines of the Federal Energy Management Program, however, do not require

that all projects be evaluated for the same study period when ranking them

according to their SIR's. This decision reflects the desire to simplify the

evaluation procedure where possible. The simplification in this case is the

avoidance of many repetitions of the calculations for short-lived projects.

Reconciling Project Life and Study Period

Replacement and salvage values are used to reconcile differences between

study periods and project or component lives when these are unequal.

Delays Between the Time of Project Evaluation and Project Initiation

Economic analyses performed for the purpose of determining the cost

effectiveness of a project generally do not give the same level of attention

to the details of cash flows during the planning and construction phase as

would a cost analysis aimed at controlling construction costs. Often the

following two simplifying assumptions are made: (a) all construction costs

occur at the outset of the study period, which is coincident with the time the

analysis is performed, and (b) operational costs accrue at the end of each

year thereafter. In most cases, the inaccuracies introduced by these

assumptions will be small and will not affect the decision.

4-2
In choosing among projects with substantially different time delays, however,

it may be important to take into account those delays, since the relative cost

effectiveness of the projects may be affected. For example, suppose the

choice were between two mutually exclusive energy retrofit projects, each with

a 10 year life, for a facility expected to be in service another 10 years. If

one alternative could be implemented immediately, but the other would require

a delay of 5 years, the timing of the projects would be relevant to the

choice, since the effective life of one of the alternatives is reduced to 5

years and benefits during the delay interim are lost to that alternative.

In comparing the life-cycle costs of a project with a delay in implementation

against the life-cycle costs of a base case condition (i.e., not having the

project) , a distinction should be made between those costs which can be

avoided during the delay period if the project will eventually be undertaken,

and those which cannot be avoided. Consider, for example, a proposed project

which could be implemented three years from the present. If knowledge that

the proposed project were forthcoming would allow the avoidance of certain

costs during the interim three years that would otherwise be incurred under

the base case, the cost avoidances should be attributed to the proposed

project. This can be done by including these costs in the Base Case but not

in the Proposed Project costs. Costs that cannot be avoided during the

interim (i.e., those that are sunk) can either be included in both the

evaluation of the Base Case and the Proposed Project or omitted from both,

since they will in any case cancel out of the analyses.

4-3

Section 5

Project Selection

The term "project selection" is used here to cover the following types of

project investment decisions, each of which is discussed below:

(1) Accepting or Rejecting a Given Project

(2) Designing and Sizing Individual Projects

(3) Ranking Projects for Funding Priority

(4) Determining Combinations of Interdependent Projects

(5) Jointly Designing/Sizing and Ranking Projects

Following the discussion of each of these decisions, a problem example Is

given with step-by-step solution. The problem solution illustrates how the

following techniques of economic evaluation are used in project selection:

o Life-Cycle Costing (LCC)

o Net Benefits (NB) or Net Savings (NS)

o Benefit-to-Cost Ratio (BCR) or Savings-to-Investment Ratio (SIR)

o Payback — Simple (SPB) or Discounted (DPB)

References :

Definitions, Formulas, and Applications of Evaluation Techniques — see

Section 2.3, Handbook 135, pp. 14-22.

Accepting or Rejecting a Given Project

A project is usually deemed cost effective if (a) its life-cycle costs are

lower than other alternatives for achieving the same objective, one of which

must be adopted; (b) it results in benefits or savings in excess of its costs;

(c) it yields an internal rate of return higher than the minimum acceptable

rate of return; (d) the ratio of overall net cash flow is positive after

payback is achieved,

5-1
Cost-effective projects are "worth doing," other things being equal, but

further analysis may be needed to determine if a given project

should be selected over other project choices.

References ;

Discussion—See Section 2.4.1, Handbook 135, p. 22.

Accept-Reject Problem Example: See Workbook Section 11, Problem Set A,

"Programmable Time Clock Problem"

Designing and Sizing Individual Projects

Often the decision maker has choices of design, size, material, or other

attributes of a given project. These are "mutually exclusive" alternatives in

that choosing one means not choosing another. The economic objective is to

choose the alternative which results in the greatest net benefits or net

savings. If the alternatives are considered apart from possible budget

constraints, the economically efficient choice will satisfy at least one of

the following conditions: (a) project life-cycle costs are minimum; (b)

project net benefits or net savings are maximum; or (c) the ratio of benefits

or savings to costs for the last increment of investment is one; or (d) the

yield on the last increment of investment approaches the minimum acceptable

rate of return.

References

:

Discussion—See Sections 2.4.2 and 2.4.3, Handbook 135, pp. 24-25.

Sizing Example: See at the end of this Section, "Pipe Insulation Retrofit

Problem—A Case Example of Project Selection"

5-2
Ranking Projects for Funding Priority

When funds are limited and there are more cost-effective projects than can be

funded, choices must be made among non-mutually exclusive projects, i.e.,

projects for which acceptance of one would not preclude the acceptance of

others, aside from the funding constraint.

The economic objective is to select the combination of projects that will

maximize net benefits or net savings for the available budget. This can often

be done by ranking and selecting projects in descending order of their

benefit-to-cost or savings-to-investment ratios, until the budget is

exhausted. If the project ratios fall below one before the available budget

is exhausted, then project acceptance should terminate with the last project

whose ratio exceeds one. If, due to "lumpiness" in project size, higher

ranked projects cost more than the available budget, while lower ranked

projects are affordable within the budget, lower ranked projects (but with

ratios greater than one) should be selected in descending order until the

budget is exhausted.

References ;

Discussion—See Section 2.4.4, Handbook 135, pp. 25-26.

Ranking Projects Example: See at the end of this Section, "Pipe Insulation

Retrofit Problem—A Case Example of Project

Selection," and Workbook Section 12, Problem Set B,

"Water Conservation Problem"

Determining Combinations of Interdependent Projects

In evaluating candidate projects for a particular building or facility, the

problem of interdependency among projects may arise; that is, undertaking one

project may affect the relative life-cycle costs and savings of remaining

projects. For example, the value of adding an automatic environmental control

5-3
system will differ depending on the level of insulation in the building

envelope and vice versa. Undertaking one will tend to diminish the value of

the other. An approach to this problem is to evaluate each of the candidate

projects independently of one another, select first the one with the highest

BCR or SIR value, and then adjust the BCR or SIR value of any remaining

projects that are expected to be substantially altered by the first, higher

priority, selection. The selection process would then be continued, with

necessary adjustments to remaining projects being made as each project is

chosen.

References : See Workbook Section 12, Problem Set B, "Team Problem—Planning

an Energy Conservation Package"

Jointly Designing/Sizing and Ranking Projects

Where there are several, non-mutually exclusive projects with positive net

benefits and there is an insufficient budget to fund all of them, the

theoretically correct approach would be to size each project such that the

incremental BCR or SIR would be equal for all projects and equal to the ratio

available on the last increment of the next best investment (i.e., equal to

the opportunity cost). Then projects would be selected on the basis of

descending BCR's or SIR's computed on the total project costs and benefits

(savings) until the budget is exhausted.

Due to the difficulty of simultaneously equating the incremental ratios on all

projects, second-best approaches are often used. One is to size each project

so that the incremental ratio is equal to one, and then select projects as

before in descending order of BCR's or SIR's until the budget is exhausted.

This may lead to inefficient, oversized projects when there are budget

constraints. A second approach, and one that is generally preferred to the

5-4
first one, is to set up the sizing decisions when possible in the same context

as the ranking decisions under a budget constraint, thereby constructing the

problem in such a manner that the sizing of given projects and ranking of a

set of projects will occur simultaneously.

References:

Problem Example: See at the end of this Section, "Pipe Insulation Retrofit

Problem—A Case Example of Project Selection"

5-5
Pipe Insulation Retrofit Problem — A Case Example of Project Selection

[Note: This is a hypothetical example for use only to illustrate the

evaluation technique.]

This case demonstrates (a) the discounting of costs and savings; (b) the use

of the evaluation techniques of life-cycle cost (LCC) , savings-to-investment

ratio (SIR), and discounted payback (DPB) to determine if a project is cost

effective; (c) the use of net savings (NS) and incremental SIR (ASIR) to

determine efficient project size if there is no budget constraint; and (d) the

use of the SIR and ASIR to rank the project and its size increments relative

to other projects competing for limited funds.

Problem Statement

Approximately 100 ft of hot water pipes running through the basements of each

of 10 buildings of a Federal laboratory facility in Massachusetts have been

found to be uninsulated. Data and assumptions are as follows:^

Quantity of Uninsulated Pipe: 100 ft/Bldg x 10 Bldgs = 1,000 ft

Required Water Temperature: 180°

Pipe Size: 1 1/2" Diameter

Operation: 4 hr/day x 260 days/yr = 1,040 hrs/yr

Type of Energy: Distillate Oil

Agency Base-Year Price of Distillate: $9.00/10^ Btu

Plant Efficiency: .55

Remaining Building Life: Indefinite

Insulation Life: Indefinite

Available Insulation Choices: 1" or 2" of Fibrous Material

^For the purpose of demonstrating the basic procedures, this sample problem

is kept simple. In actual practice, there would likely be other considerations for energy conservation than those included here, such as the

possibility of reducing the water temperature.

5-6
Step 1. Calculate the quantity of annual energy savings (AES) for the

alternative sizes of insulation

o Formulate Estimating Relationship:

AHLR/hr/ft • hrs/yr • ft

AES (lO^Btu) = eff • 106

where AES = annual quantity of energy savings,

AHLR = decrease in Btu heating load requirements, and

eff = plant efficiency.

(Note: The numerator is divided by 10" in order to state AES in terms of

millions of Btu.)

o Refer to Figure 5-1 (or use other appropriate approaches) to estimate

the value of AHLR/hr/ft with and without the insulation.

o Refer to Problem Assumptions for the number of hours, linear feet of pipe,

and plant efficiency.

o Calculate AES:

(150 - 20)Btu/hr/ft • 1,040 hrs/yr • 1,000 ft

AESi" = 0.55 • 106

= 245.8 X lO^Btu

(150 - 12.5)Rtu/hr/ft • 1,040 hrs • 1,000 ft

AES2" = 0.55 • 106

= 260.0 X lO^Btu

Step 2. Calculate the present value of energy cost savings (PVgg) over the

life cycle (study period) for the alternative sizes

o Formulate the estimating relationships:

PVgs = AES • P/lO^Btu • UPW*

where PVgg = present value dollar energy savings over the study period,

AES = annual quantity of energy savings.

5-7
Figure 5-1

LCC PROBLEM SOLUTION — ESTIMATION

OF ENERGY SAVINGS

Determine Heat Loss Rates With & Without Insulation:

I "

Uninsulated Pipe: 150 BTU/hr/ft

• 1 " Insulated Pipe: 20 BTU/hr/ft

• 2" Insulated Pipe: 12.5 BTU/hr/ft

C«BMr>Hiwt U e*l»il*« talUt^a. tor. I*7«

5-t
P/lO^Btu = initial price per 10°Btu of energy, and

UPW* = modified uniform present worth discount factor.

o Designate the length of the study period.

o Refer to Problem Assumptions for initial price of energy.

o Refer to Problem Assumptions for the DoE Region in which the laboratory

facility is located, the nature of the building (residential, commercial,

industrial), and the type of energy, and find the corresponding UPW* for

the appropriate study period from Appendix B of Handbook 135. In this

case the UPW* = 17.77 (from Table B-1 , Handbook 135, p. 118).

o Calculate PVgg:

For 1" of Insulation:

PVes .. = 245.8 X lO^Btu • $9.00/106Btu • 17.77

= $39,311.

For 2" of Insulation:

PVes .. = 260.0 X lO^Btu • $9.00/l06Btu • 17.77

= $41,582.

Step 3. Calculate project investment costs for the alternative sizes of

insulation

o Formulate the Estimating Relationship:

I = P/ft X ft X (1 - FEMP Adj. Factor),

where I = project investment cost (in present value $),

P/ft = price per linear foot of insulation,

ft = linear feet required, and

5-9
FEMP Adj . Factor = 10% reduction in investment costs as a rough measure of the

social benefits of energy conservation not reflected in

market prices. (Note: this was established as a temporary

procedure which may be eliminated.)

o Refer to Table 5-1 (or use other appropriate approach) to estimate Project

Investment Costs.

o Calculate Investment Costs:

II" = $2.50/ft • 1,000 ft • 0.9

= $2,250.

I2" = $4.55/ft • 1,000 ft • 0.9

= $4,095.

Step 4. Calculate present value net savings for the alternative sizes of

insulation

o Formulate the estimating relationship:

NS = PVes - I

where NS = net savings in present value dollars,

PVgg = present value energy savings,

I = project investment cost,

o Calculate NS

NSy = $39,311 - $2,250

= $37,061.

NS2" = $41,582 - $4,095

= $37,487.

5-10
Table 5-1 Costs for Insulating Various Pipe Sizes

Installed Cost/Linear Foot of Pipe Insulation*

Pipe Size 1 Inch Thickness 2 Inch Thickness

(Inches) (Fibrous Material) (Fibrous Material)

($) i$)

1/2 2.00 3.70

3/4 2.10 3.95

1 2.20 4.15

1 1/4 2.40 4.45

1 1/2 2.50 4.55

2 2.70 4.74

2 1/2 2.85 5.15

3 3.10 5.45

3 1/2 3.40 5.80

4 3.90 6.40

5 4.30 7.20

6 4.80 7.75

8 6.45 9.55

10 7.20 11.15

12 8.30 12.25

Source: Mechanical and Electrical Cost Data 1979 , R. S. Means Co., Inc.

* These are average installed costs, including labor and materials, for pipe

located in accessible areas. Inaccessibility would cause increases in

costs.

Note: There is a small discrepancy in this example between the year's

dollars in which energy savings and investment costs are expressed.

That is, the UPW* factors used to find the present value of energy

savings are based on a mid-1981 starting point, whereas the above

investment costs are in 1979 dollars. To provide a greater degree of

accuracy, investment cost data for 1981 could be used, or, if they were not available, the 1979 prices could be adjusted to a 1981 basis

by applying to them a ratio comprised of a 1981 price index divided by

a 1979 price index for the appropriate category of building materials.

5-11
Step 5. Answer the question, "Is it cost effective to insulate the laboratory

hot water pipes?"

Answer: Positive net savings indicate that the investment is cost effective.

Step 6. Verification of Project Cost Effectiveness by Other Evaluation

Techniques. [Note: This step is unnecessary in so much as the NS

technique is reliable for determining cost effectiveness; it is

included only to illustrate the use of other techniques.]

Life-Cycle Costing (LCC) Evaluation

Approach: Calculate the total present value of energy costs plus other costs

over the study period for the base case (i.e., without the retrofit project)

and for the proposed retrofit project in its alternative sizes, and see if the

total is lower with the project.

o Calculate present value life-cycle costs for the base case (LCCg^):

LCCbc = (150 Btu/hr/ft 1,040 hrs • 1,000 ft) • Sg.OO/lO^Btu • 17.77

0.55 ' 10^

= $45,362.

o Calculate present value life-cycle costs with the retrofit project for

each size alternative (LCCj^) :

(20 Btu/hr/ft ' 1,040 hr • 1,000 ft)

LCCr = . Sg.OO/lO^Btu • 17.77 + $2,250

i" 0.55 • 106

= $8,298.

(12.5 Btu/hr/ft ' 1,040 hr • 1,000 ft)

LCCr = $9.00/106Btu • 17.77 + $4,095

2" 0.55 • 106

= $7,875.

Conclusion: Ldfe-cycle building costs are lower with the project in either

size alternative than without it, indicating that the project in either size

is cost effective.

5-12
Savings-to-Investment Ratio (SIR) Evaluation

Approach: Calculate the SIR for each project size alternative and see if it

exceeds 1.

(150-20)Btu/hr/ft • 1,040 hr • 1,000 ft

SIRi"

0.55 • 10^

= 17.47

(150-12. 5)Btu/hr/ft • 1,040 hr • 1,000 ft

$9.00/106Btu • 17.77 X $2,250

SIR2"= $9.00/l06Btu • 17.77 T $4,095

0.55 • 106

= 10.15

Conclusion: The SIR is greater than 1 for both size alternatives, indicating

that either is cost effective.

Discounted Payback (DPB) Evaluation

Approach: Calculate the cumulative present value energy savings for each

project size and determine in what year (Y) the cumulative discounted

savings exceed the investment cost for that size alternative, i.e., for what Y

is PVes(Y) - I > 0.

The cumulative net savings numbers shown in table 5-2 are calculated as

follows

:

UPW*

for

(150-20)Btu/hr/ft • 1,040 • 1,000 ft N=l

pves^..(y=i)-i= • $9.00/106Btu • 0.96

0.55 • 106

-$2,250 = -$126.

5-13
PVes „(Y=2)-I=

UPW*

fon

(150-20)Btu/hr/ft • 1,040 • 1,000 ft N=2

• $9.00/106Btu • 1.88

0.55 • 106

$2,250 = $1,909.

PVes „(y=i)-i=

'(150-12. 5)Btu/hr/ft • 1,040 br • 1,000 ft

' • $9.00/106Btu • 0.96

0.55 • 106

-$4,095 = -$1,849.

PVeS2..(Y=2)-I=

(150-12. 5)Btu/hr/ft • 1,040 hr • 1,000 ft

• $9.00/106Btu • ].!

0.55 • 106

-$4,095 = $304.

Table 5-2. Discounted Payback Solution

Cumulative Present Value

Energy Savings

Cumulative Net Savings

1" Insulation 2" Insulation 1" Insulation 2" Insulation

1 2,124

2 4,159

2,246

4,399

$2,250

-126

1,909

-$4,095

-1,849

304

5-14
Conclusion: For both size alternatives, payback occurs in the second year—long

before project life and energy savings are expected to end. Since there are no

anticipated project costs after initial installation, the project in either size

is cost effective.

Step 7. Answer the question, "Which Project Size is Most Cost Effective?"

Answer: 2" insulation results in greater net savings than 1" and, therefore,

2" is more cost effective if there is no budget limitation.

Step 8. Verification of Most Cost-Ef fective Project Size by Other

Evalution Techniques. [Again note that this step is unnecessary and

is included merely to illustrate the use of other techniques.]

Life-Cycle Costing (LCC) Evaluation

Approach: Compare LCC's of size alternatives to see which is less:

LCC

Size Alternative ($)

1" 8,298

2" 7,875

Conclusion: LCC is lower with 2" of insulation than with 1", indicating that

2" is more cost effective if there is no budget limitation.

Incremental SIR (ASIR) Evaluation

Approach: Determine if the ASIR is greater than 1. Note that the ASIR is the

ratio of savings to investment for the last increment of investment, in this case

the extra investment required to increase insulation thickness from 1" to 2";

i.e,, $4,095 - $2,250 = $1,845, The incremental dollar savings is based on the

reduction in the hourly heat loss rate from 20 Btu/hr/ft with 1" of insulation to

12.5 Btu/hr/ft with 2" of insulation.

5-15
(20-12. 5)Btu/hr/ft • 1,040 • 1,000 ft

ASIRi"->.2" = • $9.00/106Btu • 17.77

0.55 • 106

i ($4,095 - $2,250)

= 1.23.

Conclusion: The ASIR is greater than 1, indicating that the additional

expense of the added insulation thickness is more than offset hy the extra

energy savings, such that the 2" size is more cost effective than 1" if there

is no budget limitation.

[Cautionary Note: The SIR computed on total investment and total savings data

does not provide a reliable technique for sizing projects. The SIR for the

1" thickness, for example, is 17.47, substantially higher than the SIR for

the 2" thickness of 10.15, yet the incremental investment _is^ cost effective.

(The discounted payback technique has the same type of shortcoming for sizing

projects as the SIR.)]

Step 9. Answer the question, "What Priority Should This Project Receive

Relative to Other Projects if the Budget is Insufficient to Allow

Acceptance of All Available Cost-Eff ective Projects?"

Approach: The economic objective in setting priorities is to choose the

projects that will result in the greatest net benefits from the available

budget. Assigning project priorities based on the descending order of project

sir's provides a workable approach for achieving (or closely approximating)

this objective.

5-16
When there is a budget constraint, project sizing can often be accomplished in

conjunction with project ranking by breaking projects into their size

increments, computing SIR's on those increments, and ranking the increments

relative to other potential projects. Assume, for example, that the

illustrative pipe retrofit project using a 1" thickness of insulation is

designated Project A, and the project increment required to increase thickness from 1" to 2" is designated Project B. Projects A and B can then be

assigned priority relative to other projects C, D, E, F, and G—all of which

are competing for the limited funds available—according to their SIR's, as

shown in table 5-3.

Table 5-3. Joint Sizing and Ranking of Projects

Potential Project Ranking

Projects SIR for Priority

2

5

6

3

1

4

not acceptable

A (0^1" of Insulation) 17.47

B (1>2" of Insulation) 1.23

C 1.15

D 15.50

E 25.00

F 12.52

G 0.75

5-17
Since it is cost effective to choose all projects with SIR's greater than 1,

2" of insulation will be selected over 1" if sufficient funds remain

after Projects E, A (1" of insulation), D, and F are funded.

In practice, the sizing decision and the project priority decision are often

treated separately, rather than jointly as shown above. A project may first

be sized as though there were no budget constraint (i.e., 2" thickness of

insulation), and then assigned priority relative to other projects based on

the SIR computed on the size selected. Using this approach in the above

example. Project A (1" of insulation; SIR = 17.47) and Project B (the

increment from 1" to 2" of insulation; SIR = 1.23) would not be separately

identified in the ranking. Rather a single project entry (designated A)

would be made, based on total values for 2" of insulation (SIR= 10.15), as

shown in table 5-4.

Table 5-4. Ranking of Projects of Predetermined Size

Potential Project Ranking

Projects SIR for Priority

4

5

2

1

3

not acceptable

A (2- of Insulation) 10.15

C 1.15

D 15.50

E 25.00

F 12.52

G 0.75

5-18
This latter approach results in a different relative priority of the projects

than the former approach. A disadvantage of this approach is that if funds

are very limited, the project may not be done at all, even though its first

increment (1") is estimated to be more cost-effective than projects D and F

which now receive higher priorities. An advantage of the approach is that the

projects which are selected will be sized so as to avoid the loss of potential

net benefits. For example, if 1" thick pipe insulation is installed, there

will not likely be another opportunity to capture the additional net benefits

that would have resulted from the additional thickness of 2". The relative

merits of the approaches depend to a large extent on (a) the severity and

duration of funding shortages and (b) the costs of later additional retrofit.

5-19

Section 6

Sensitivity Analysis

Some of the costs and most of the benefits of capital investment projects

occur in the future, necessitating forecasting of their values. Since forecasted data are usually uncertain, the findings of the economic evaluation

will also tend to be uncertain. In addition, there are often unknown elements

even in the very short run which may cause estimated values to deviate from

actual values. Sensitivity analysis is one approach for taking into account

uncertainty in economic evaluations. This section briefly treats the

technique in three parts:

( 1

)

Approach

(2) Applications

(3) Examples

Approach

Sensitivity analysis is performed by simply repeating a project evaluation,

with each repetition based on a different value of the factor in question.

Applications

Sensitivity analysis is used in three main ways: (1) to identify critical

parameters, (2) to address "what if" questions, and (3) to establish upper and

lower bounds for the estimated outcome. Sensitivity analysis is used to

identify the factors that are critical to a project's success by changing in

turn or in combination the values of factors in the analysis by given

percentages and observing the corresponding percentage changes in the measure

of economic performance.

6-1
Sensitivity analysis is used to address "what if" questions (such as how

worthwhile will the project be if a certain component lasts only half as long

as the manufacturer claims) by finding the outcome under the hypothesized

condition. The technique is used to set upper and lower bounds of estimated

outcome by repeating the analysis for the worst case and the best case.

Examples

Figure 6-1 illustrates a project choice that is sensitive to the length of

time over which the project will be required. For a study period of less than

about 10 years, B has the lower life-cycle cost, but for a study period

greater than 10 years, A has the lower life-cycle cost.

Figure 6-2 illustrates the sensitivity of present value energy savings to the

rate of energy escalation. Given a fixed discount rate of 7 percent and no

escalation, present value savings rise only slightly over time. But as the

escalation rate increases to 7 percent and then 14 percent, the present value

savings rise sharply over time.

References

:

See Workbook Section 13, Problem Set C, "Sensitivity Analysis Problem:

Insulation," and Workbook Section 12, Problem Set B, "Computer Room Waste Heat

Recovery Problem."

6-2
LCC

In

PV

$

Figure 6-1 Sensitivity Analysis

A = Project A

B = Project B

Time Horizon

10 15

Years

20 25

6-3
Figure 6-2

Sensitivity Analysis

$60 r D = .07, E = .14

= .07, E = .07

= .07, E =

15 20

Years

Note: Base-year Savings = $1,000

6-4
Section 7

Probability Analysis

Probability analysis is another technique for taking into account uncertainty

in economic evaluations. It relies on the use of probabilities rather than

repetition of the evaluation. Probability analysis is a useful approach when

(a) there is more than one possible condition, or "state of nature," which can

occur, (b) the project outcome may differ depending on the state that occurs,

and (c) the probability, or relative frequency, with which each possible state

is expected to occur can be used to calculate the average, or "expected,"

value of possible outcomes weighted according to their frequency of

occurrence. The following four sections provide a brief treatment of the

topic:

(1) Approach

(2) Problem Illustration—Calculating Expected Values

(3) Decision Trees

(4) Computer Simulations

Approach

(1) List the alternative courses of action under consideration for which a

decision is to be made. For example, which of two project alternatives.

Project A or Project B, should be selected?

(2) List the possible states which may be significant to the project decision.

For example, a component may function without failure (state 1), or it may

fail during the project study period (state 2).

7-1
(3) For each state, estimate in turn the outcome if that state occurred and

each of the alternative courses of action were taken. For example, what is

the estimated life-cycle cost of Project A if state 1 occurs; what is the

life-cycle cost of Project B if state 1 occurs; and what are the life-cycle

costs of each project if state 2 occurs? [Note that this is in effect

sensitivity analysis using the conventional evaluation techniques considered

previously.

]

(4) For each possible state, it can now be determined which course of action

would be best if it were known with certainty that the state in question would

occur. Project B might be found to be the more cost-effective project if

state 1 occurred with certainty, and Project A the more cost-effective project

if state 2 occurred with certainty. [Note that one course of action might be

preferred, or "dominant," for all states, in which case the desired course of

action is clear. This means that the decision is not sensitive to the state

which occurs. But if the best course of action does depend on the state that

occurs, further analysis is required as described in steps 5-7 below.]

(5) Assign a probability to the likely occurrence of each state, making sure

that the probabilities of all of the states sum to 1.0. (The previous

statement assumes one and only one of the states occurs). For example, state

1, no component failure, may be expected to occur 60 percent of the time, and

state 2, failure, 40 percent of the time. [Note that these probabilities may

be based on statistical observation of the frequency of failure in like or

similar components, or they may be based on a measure of the degree of belief

that the respective states will occur.]

7-2
(6) Calculate the expected value of each course of action. This is done for

a course of action by multiplying the value which would result from that

course of action under each state of nature by the probability that the state

of nature will occur, and summing the results. For example,

EVa = PI XAl + P2 XA2 + ••• + Pn ^An .

where EV^ = expected value of a given course of action. A,

Pj^ = the probability of a given state occurring, where the subscript

indicates states 1 to n, and

x^j^ = the estimated value associated with the given course of action. A,

if the state designated by the subscript n were to occur with certainty.

(7) Choose the course of action according to the expected value criterion, i.e.,

minimize the expected value of cost or maximize the expected value of net

benefits. This decision process, based on expected values, is illustrated in

the hypothetical example which follows.

7-3
Problem Illustration—Calculating Expected Values

[Note: This is a hypothetical problem intended only to illustrate the

technique.

]

The problem is whether or not to install an emergency power generator for

refrigerated storage in a Federal warehouse facility. The generator costs

$5,000 to purchase and install, and is expected to have no other significant

costs over its estimated 10 year life. Two courses of action are to be

considered: Course A, do not install the generator; and Course B, install the

generator.

The rationale for installing the emergency generator is to protect against

losses of stored goods which will result if there is a power failure lasting

more than four hours. Based on past experience, the electric utility predicts

the probability of a single occurrence within the period of a year of power

failure exceeding four hours to be .005. The Federal agency estimates the value

of losses per event of major power failure to be $50,000 without the generator,

and $0 with the generator.

The decision maker wishes to make the decision on the basis of minimizing the

expected value of the overall cost of the operation. Should the generator be

installed? (Assume that a 10 percent discount rate applies.)

7-4
SOLUTION

Table 7-1. Annualized Cost of Alternative Actions Under Possible States of

Nature

Annualized Cost, Given State

State 1 State 2 No Power Failure Power Failure

Courses of Action (p = .995) (p = .005)

A (Do Not Install Generator) $0 $50,000

B (Install Generator) $815^ $815^

^ The annualized cost of installing the generator is $5,000 x .163 = $815,

where $5,000 is the initial cost and .163 is the Uniform Capital Recovery

Factor for 10 years and 10 percent.

Expected Value Calculations ;

EV^ = [(0) (.995)] + [($50,000) (.005)]

= $250.

EVg = [($5,000) (.163) (.995)] + [($5,000) (.163) (.005)]

= $815.

(Note that EVg can be found simply as ($5,000) ( .163) , because according to

problem assumptions the cost of installing the generator is $5,000 regardless of

the state. The calculation is shown broken down into elements for each state of

nature to portray the more general case. For example, if a power failure would

result in partial losses despite the installation of the generator, then the

cost of Action B would be a function of the State of Nature.)

Decision :

Do not install the emergency generator.

7-5
Decision Trees

Decision trees are useful schematic forms for depicting in a decision framework

alternative outcomes resulting from probabilistic events. A decision tree for

the illustrative problem is shown below. Decision trees are constructed from

left to right and are analyzed from right to left. Boxes are used to indicate

controllable (decision) points and circles for uncontrollable (chance) events.

DECISION TREE

do not install generator

$250

$250

install generator

$815

power failure $50,000

(.005)

no power failure $0

(.995)

power failure $5,000x.l63

(.005)

no power failure $5,000x.163

(.995)

Computer Simulation

Computer simulation is generally required when probability distributions are used for a number of input values. The computer is programmed to select a value

at random from each of the Input distributions, and to compute a measure of

7-6
economic performance (such as net savings) for each set of data so selected.

This operation is repeated many times, generating a probability distribution of

the output. Statistical analysis of the output distribution can then be used to

provide the decision maker with a measure of the degree of dispersion, the risk

associated with the project, as well as the expected value.

Reference ; See Workbook Section 13, Problem Set C, "Problem in Probability

Analysis: Heat Pump Versus Solar Energy System."

7-7

Section 8

Break-Even Analysis

Break-even analysis Is a technique used to solve for the value of a selected

parameter which will equate heneflts and costs. It Is useful In a variety of

decision making applications, usually in a supporting or supplementary role to

other evaluation techniques. This section provides a brief introduction to

the use of break-even analysis in the following three parts:

(1) Approach

(2) Applications

(3) Break-Even Analysis Problem Illustration: Make-Buy Decision

Approach

Select a critical parameter, the value of which is uncertain, and treat that

parameter as an unknown. Construct an equation which sets present value

benefits equal to present value costs (or the costs of alternatives equal to

one another, depending on the nature of the problem), entering into the

equation the unknown parameter. Solve for the value of the parameter. The

solution value is the minimum or maximum value which that parameter can take

and still have the project be minimally cost effective. For example, the

break-even purchase and installation cost would indicate the maximum amount

that a project could cost initially and be minimally acceptable, other things

being equal. To evaluate project acceptability, the decision maker must

consider the likelihood that the actual value of the parameter will be greater

or less than the solution value.

8-1
Applications

One type of application for the break-even technique is in making decisions

that result in the substitution of costs that are relatively fixed for costs

that are relatively variable. Examples include decisions to own versus to

lease buildings and equipment; to produce an item internally versus to buy it

outside; and to use labor-intensive versus capital-intensive production

techniques.

Break-even analysis is useful to address the problem of uncertainty associated

with many different kinds of projects by helping to establish the boundaries

within which a project will be cost effective. For example, the technique can

be used to find break-even investment cost, break-even energy savings,

break-even system life, and the minimum or maximum required value of

practically any other parameter critical to project success.

The break-even technique is widely used by private business to estimate the

minimum requirements necessary for successful operations, such as the minimum

sales required to cover total costs.

8-2
Break-Even Analysis Problem Illustration: Make-Buy Decision

[Note: This hypothetical problem is intended only to illustrate the

technique.

]

Problem Statement : A temporary Federal facility in Pennsylvania, now in the

planning stage, will have a demand for steam. But at this time only a very

rough estimate of the quantity demanded is available.

An outside source has expressed interest in supplying the steam requirements

at an initial price (PP) of $10.00 per Mlb of steam supplied at the building

boundary, with a subsequent annual escalation of price equal to the annual

change in the GNP price deflator index plus 5 percent. The source appears

reliable and compatible with other aspects of the facility's plan.

Preliminary estimates of the administrative, space, equipment, and maintenance

costs required for in-house production are as follows:

Allocated Space (S): $20,000

Administrative (A): $10,000/yr.

Equipment, Purchase and Installation (E) : $200,000

Equipment, Maintenance (M) : $5,000/yr.

(These are rough estimates because they are dependent to some extent on the

quantity of steam to be generated which is not known at this time. However,

the cost analyst thinks the cost estimates are relatively accurate because of

the large element of fixed costs involved.)

Additional information required to determine the cost of in-house production

is as follows:

1-3
Price of Coal per ton (PC): $45.00

Anticipated Plant Efficiency (Eff): 65%

Required Length of Service (N) : 8 years

Anticipated Salvage at the End of 8 Years (S):

Btu Content per Thousand Pounds (Mlh) of Steam: 1.05 x lO^Btu

Btu Content per Ton of Coal: 22.5 x lO^Btu

The facility planners are trying to decide whether to recommend that the steam

requirements be met through the outside supplier or by in-house production.

They believe life-cycle cost differences should be the deciding factor.

However, they are having difficulty with this comparison due to the

uncertainty regarding the amount of steam that will be demanded.

To do:

Assist them with their decision by estimating the minimum quantity of annual

steam demand necessary for cost-effective in-house production.

Solution;

Step 1. Equate the cost of purchase with the cost of production, entering

the quantity of steam demanded as the unknown variable; i.e.,

PP .Zbab . UPW*8yr,7%,5% = S + E + [(Am) • UPW8yr,7%] +

• PC . UPW*8yr,7%,DoE3

ZMlb • 1.05xl06Btu/mb

0.65 • 22.5xl06Btu/ton

8-4
Step 2. Solve for break-even level of steam, Mlb; i.e..

$10.00 - ZMlb

1+0.05

0.07-0.05

1.97]

^l+0.05\8

1-

1+0.07

= $20,000 + $200,000 + [(10, 000+5,000)

ZMlb ' 1.05xl06Btu/Mlb "'

0.65 • 22.5xl06Btu/ton

$45/ton • 7.37

$73.56 • ZMlb = $220,000 + $89,550 + 23.81 ZMlb

$49.75 ZMlb = $309,550

Z = 6,222 Mlb.

Step 3. Draw Conclusion, i.e..

For cost-effective production of steam in-house, the annual demand must be

greater than about 6,000 Mlb. Due to the large component of fixed cost for

in-house steam production, less steam consumption could more economically be

purchased from outside. Higher consumption, on the other hand, would help

reduce the cost per pound for in-house production and thereby likely make it

cheaper than the fixed price per pound of steam purchased from the outside.

References

Other Problem Examples: See Workbook Section 12, Problem Set B, "Computer

Room Waste Heat Recovery Problem," and Workbook

Section 14, Problem Set D, "Team Problem—BreakEven Orders for a Computerized Procurement System.

8-5

Section 9

Replacement Decisions

Replacement Theory or Analysis is a methodology for finding the economic life,

that is, the service interval for equipment and facilities for which

life-cycle costs for a given level of service will be minimum or net benefits

will be maximized. It is briefly treated here in the following two parts

because replacement decisions go hand-in-hand with other project investment

decisions:

( 1

)

Approach

(2) Illustrative Problem: Determining Optimal Replacement of Like

Equipment

Approach

The customary approach for determining the optimal service interval is to

compute the annualized costs for different service intervals and select the

interval that minimizes annual cost. For certain kinds of problems such as

those involving relatively short, well-defined time periods, it may be more

convenient to minimize present value costs.

9-1
Illustrative Problem: Determining Optimal Replacement of Like Equipment

[Note: This hypothetical example is intended only to illustrate the

technique.

]

Question : How frequently should a given piece of equipment (E^) be replaced?

Data and Assumptions:

o Identical constant dollar costs (C) for present and future replacement

units of E^ of $20,000

o Uniform benefits

o Long duration of service

o The following are resale values (S) and operation, maintenance, and repair

costs (0+M+R) for each year the equipment is in service:

Year Resale 0+M+R

in Value Cost

Service (constant $) (constant $)

1 12,000 2,000

2 10,000 3,000

3 8,000 4,000

4 6,000 5,000

5 2,000 6,000

Approach: Find the number of years until replacement (n) for which the

annualized cost (AC(n)) is minimum, where

n AC(n) = [C - (S(n) x SPW(n)) + I [ (0+M+R) j x SPWj ]

] x UCR(n)

j = l

Solution:

9-2
Step 1. Calculate annual costs for different val ues of n.

n

AC (n) = [C -(S(n) x SPW(n)) + i [(O+Mj+Rp x SPW|]] (UCR(n))

i = 1 AC (1) = [[$20,000 - (12,000 x 0.93)] + (2,000 x 0.93)] (1.07) = $11,449

AC (2) = [[$20,000 - (10,000 x 0.87)] + [(2,000 x 0.93) + (3,000 x 0.87)]]

(0.553) = $8,721

AC (3) = [[$20,000 - (8,000 x 0.82)] + [(2,000 x 0.93) + (3,000 x 0.87) +

(4,000 X 0.82)]] (0.381) = $8,073

AC (4) = [[$20,000 - (6,000 x 0.76)] + [(2,000 x 0.93) + (3,000 x 0.87) +

(4,000 X 0.82) + (5,000 x 0.76)]] (0.295) = $7,962

AC (5) = [[$20,000 - (2,000 x 0.71)] + [(2,000 x 0.93) + (3,000 x 0.87) +

(4,000 X 0.82) + (5,000 x 0.76) + (6,000 x 0.71)]] (0.244) = $8,391

9-3
Step 2. Compare the annual costs for different replacement times and

identify the replacement time for which annual cost is lowest

YEAR RESALE ANNUAL O&IVI EQUIVALENT

IN VALUE COSTS ANNUAL COST

SERVICE $ $ $

20,000

1 12,000 2,000 11,449

2 10,000 3,000 8,721

3 8,000 4,000 8,073

4 6,000 5,000 7,962*

5 2,000 6,000 8,391

9-4
AC

($)

8,000

Step 3. Establish replacement schedule,

RESULTING REPLACEMENT POLICY

Scheduled

replacement

Scheduled

replacement

1980 1981 1982 1983 1984 1985 1986 1987 1988

9-5
New Information; Now assume that It is approaching the scheduled time in 1984

for replacing the equipment (E^) , based on the preceding analysis. However,

new information has been received that an improved piece of equipment (Eg)

will be available in 1985. An analysis of Eg indicates that its annualized

costs will be about $5,000 if it is replaced every six years. This new

scenario is illustrated by figure 9-1.

Question: What decision do we make for 1984?

Approach: Identify alternative actions that might be taken, and compare

present value costs for the period 1984-1988 under the alternative actions.

Then select the action that is estimated to result in the lowest present

value. (It is only necessary to consider the period 1984-1988, because the

new equipment Eg will be introduced no later than 1988 and, once introduced,

it will have a replacement schedule of every six years).

Solution ; Three alternative actions are identified and their present value

costs estimated, as shown in figure 9-2. The third action listed, "Keep

existing equipment until 1985, then innovate," is estimated to be the

cost-effective decision.

References: Also see Workbook Section 14, Problem Set D, "Team Problem:

Determining Optimal Retirement of Equipment."

9-6
Figure 9-1

DETERMINING REPLACEMENT WITH UNLIKE EQUIPMENT

AC

($)

8,000

5,000 -

Scheduled

replacement

Ea

Scheduled

replacement

Ea(4)

Eb(6)

1983 1984 1985 1986 1987 1988

I Improved

equipment is

expected to

become available

What decision do we make for 1984 ?

9-7
Figure 9-2

SOLUTION: COMPARE PV COSTS FOR 1984-1988

UNDER ALTERNATIVES

• Replace in 1984 with E^ and wait until 1988 to innovate

PV = $8,000 X 3.39 = $27,120

• Replace in 1984 with E^ and innovate in 1985

4^ A -^ -VK -vv5^

PV = [$20,000 - ($12,000 X 0.93)] + ($2,000 x 0.93) + ($5,000 x 2.62 x 0.93) = $22,883

* • Keep existing equipment until 1985, then innovate ^

<aV^^ <^<^ <}*^ 6?^^ <f*^ ^o^* <f^'' <^^ .<s°^ ,^ ^y <^ s<s°o* «? v^ >y <y PV = [$6,000 - ($2,000 X 0.93)] + ($6,000 x 0.93) + [$5,000 x 2.62 x 0.93] = $21,903

'This is the decision that minimizes present value costs. After Eg is adopted in 1985, it would then be replaced every 6 years.

9-8
Section 10

Worksheets

This section contains six sets of worksheets for solving retrofit building

problems and one set for selecting among alternative new building designs.

They are provided as aids in organizing the data and performing the

calculations to solve problems presented in Sections 11 and 12. Problem 2

in Section 11 and problems 1 and 3 in Section 12 require one set of

retrofit worksheets each. Problem 2 in Section 12 requires three sets of

retrofit worksheets. Problem 3 in Section 11 uses the set of new building

design worksheets.

10-1
RETROFIT LCC WORKSHEETS

Identifying Information

Building Description;

Location

DoE Region

Functional Use

Building type ( ) Residential

( ) Commercial

( ) Industrial

R.emaining Life of Building

Project Description

Expected Project Life

Length of Study Period (Not to Exceed 25 years)

10-2
RETROFIT LCC WOfCJCSHEET (Concinuad)

>,. Calculating the Prasant Value of Enargy Coato Without th« Retrofit

TYPE

(1)

ANHUAL UNITS 0? £NERCT PURCHASED

(2) EASE-TEAR

ENERGY PRICE PER UNIT

(l)x(2)=

(3)

3.\SB-YEAR ENERGY COSTS

(4)

DPW* FACTOR

(3)^x^(4)^

PRESENT VALUE

OF ENERGY COSTS

KLECTRICITT $ aASE CHARGE

DEMAND CHARGE

$ TIKE C? lAY CHARGE

$ CONTRACT CAPACITY CHARGE

OTHER

CHARGE COMPONENT

s

$

$

$

$

or.

CKS

(misz

B.

TOTAL

Calculating lavestaent

^^rxr:^

Costa for the Existing

><c

Syateia Without

]XI

the Retrofit

X

(1) Base-Yir^r xesale. Salvage, or Reuse Value of the Existing Syecea to be Replaced $

(2) Baae-Year Renovatloa Costs for the Existing Systea If the Retrofit Project is Not laplecented $

C. Calculating Annually Recurring Honfuel Operation and Malntenauce (OSM) Coats Without

K'ne Retrofit

(1)

Amoiiat of Atmuall?' Recurring

Co«t3 in Base Year

(2)

niV Factor

(i)x(2) =

<3) Present Value of Annually

Kacurrlng Costs

10-3
RETR07IT LCC V0?XS't{lZT5 (Continued)

D. C«lculaclng Honttiaually Recurring MM (Nonfuel) Co»C», Repl»coa«at Co«ca, *nd Salvaga Valii* Wlchoue Che Racroflc-

<1) TEAR IH WHICH

13 HXPECT2D TO OCCtTR

(2)

AMOtTHT OF NOSAK>i'OALLT RZCCUPJ.INC 04H

COSTS (LH BASETEAR. 5)^

(3) AMOUNT 0? RSPLACEXENT

COSTS (IN EASE-YEAR $)1

(4)

AMotjyr OP SALVAGE

VKLim (IfJ BASE-YZAR S)^

(5) SPW FACTORS PR23ENT

VALLTE 0? NCH- AKKCALLT RECURRING

O&M COSTS

(3)^.p) =

PRESENT VALUS CP REPLACEMENT

(8)

PRESEhfT

VAL'JH 0? SALVAGE

VAUtS

'

TOTTAl ^xC^>><^ ^>><;^><

r, Calculaclnj TLCC Without the Retrofit

(1) Present Value of Energy Co»t» ; A(5) Total '

(2) Pr»3ent Valoe of Investaent Coats : B(l) OT (2) + '

(3) Prea^Qt Value of Annually Recurring (Noniuel) OSH Costs : C(3) "*" '

(A) Fresent Value o£ Nonaunually Recurring (Nonfuel) (KM Coat*: D(6) Total + 5

(3) Present Valua of ReplacaranC Coats : D(7) Total + 5

(6) Present Valu* of Salvage : D(8) Total ~ '

(7) Tix;c without th« Retrofit: (l)+(2)+(3)f(A)+(5)

(6) " '

' 7or exaapl

and you at vlthout fu

e. If nonannually r< a ualng 1982 as the turn Inflation.

scurrlng (nonfue

l>aae year, baaa

1) WH coots, ref -year dollars oej

LO-4

)laceoent

kna statin

coats, or aalvaga value occur In 1990

S the 1990 co«t» In 1982 dollars , I.e.
K:T:;<,OFrr LCC WORKSHHZTS (ConClau«d)

Parti F through J CaLculata TLCC vlth th« Retrofit

f. Calculating tha Prcstnt Value of Fuel Cones With Ch« Ratroflc

TiFZ

(1)

ANNUAL 0HITS 0? ENEKGT PTOCHASED

(2) BASI-YEAR

ENTRCY PRICE

PER UNIT EASE-YZARES-ERGY COSTS

(4)

tJPW* FACTOR

PRESENT VALUE

OF EMERGY COSTS

ziBcraicrrr ? BASE CHAZGS

? DEHA.VD CHARGZ

TIKE G?

tiKZ CHARCK

9 COXTRACT CAPAcmr

CHARCK

5 OTdjU

CHARCE

ccH?o>(!iyr

3

3

3

3

3

OIL

GAS

OTHEE

TOTAL ^xC^^rx^ XX C. Calculating InvesCaenC Coot* v^lth the Retrofit

(1) Estlaated Acttial laveaCaonC Codt» for tha Retrofit Project

(2) InveotnenC Co3t Adjuatacnt Factor

(3) Adjusted Invootneut Costa for the Retrofit Project : (l)x(2)

(4) Baae-Year ReQOvatloo Coata for the Exlatlag Sjrstexi If the Retrofit Project la inplemcated

(5) Total Adjusted Preaent Value Iivestrjoat Coats Actrlbucabla

Co the Retrofit Project: (3) + (4)

10-5
RETROFIT LCC VOIIXSHEETS (Concinuad)

H, Calculating Annually Rocurrlag (Nonfunl) Oporation and HilnC«a*Qc« (OtM) Co»tt With tha Rocroflt

(I) Aoouat of Annually Recurring

CosCs 1q Base tear

(2) UPW Factor

ajx(2)=

(3) PraaeaC V»lua of Annually

R^curricg Coses

I« Calculatiag Nonacnually Recurring (Nonfuel) OiM Costs, Replacerusat Cojcs, and Salvaga Value Vlth the Retrofit

(I)

TZA-R IH

V-HXCH EXPENDITURE

IS EXPECTED TO OCCUR

(2)

AMOujrr 0? No:i- A^•NUALLT RECURRING 04M COSTS (IN BASE- TEAR 5)1

(3)

AMOCTIT OF REPIACEKEOT

COSTS (IS BASE-YEAR $)1

(i)

AhOtr»rr of SALVAGE

VALUE (IN EASE-TEAR $)1

(5) SPJ' FACTORS

PRESEJfT VALCE OF KOSAK>rtH.LLT RECORRING

06H COSTS

PRESEin:

VAUj-S 0? aEPLACEMENT

(4)x(5)=

(o) PRESENT VALL^ 0? SALVAGE VAXUE

1

TOTAL XXI^x^X

J. Calculating TLCC With the Retrofit Project

(1) PrescQt Value of Energy Coata : F(5) Total

(2) ?re3ect Value of Adjusted Inv.-staeat Coots; G(5)

(3) Present Value of f^zxunllj Recurring (Nonfuel) OiM Costs ; H(3)

(4) Preseat Value of Konannually Recurring (Nonfuel) O&H Costs; 1(6) Total

(5) PToBent Value of Replaceaent Costs ; 1(7) Total

(6) Present Value of Salvage ; I (8) Total

(7) TLCC With the Retrofit Project: (l) + ( 2 ) + (3 )+ (A ) + (5) - (6)

I £eo footnote on Part U for explanat Ion. 10-6
ITETP.OFIT LCC UORKS^ECTS (Contlnuod)

K. Not Savings or Excisaa Cost of tho P.eCrofiE Project

(1) TLCC wlchouC the Retrofit : E(7) $

(2) TLCC with the Retrofit ; J(7) - 5

(3) Net Savings (+) or net losses (-) . (l)-(2) " W 5

L. SIE. Calculation

(1) SIR Ji'uaerator

(a) Energy Cose Savings froa the Retrofit : E(l)-j(l) 5

(b) Change iu Noafuel. 06M Co3t3;. [ J C3) + C'^) ] -[ E(3) + C4) ] - '

(c) SIR Nuneracor : (a) -(b) •• S

(2) SIR Deaoaiaator

(a) Adjusted DlffereaCiaL luvestaecit Cost : j(2)-E(2) $

(b) Change la ReplaceaeaC Costs ; JC5)-E(5) + $

(c) Change la Salvage Value ; J(6)-EC6) - $

(d) SIR Denocilaacor : (a)+(b)-(c) > $

(3) SIR for Ranking the Retrofit Project : (1) (c)* (2) (d)

10-7
RETROFIT LCC WORKSHEETS

Identifying Information

Building Description:

Location

DoE Region

Functional Use

Building type ( ) Residential

( ) Comiuercial

( ) Industrial

Remaining Life of Building

Project Description

Expected Project Life

Length of Study Period (Not to Exceed 25 years)

10-8
R2TR0?IT LCC WORKSHEET (Coacinuad)

A. Calcul*ting the Pre»ant Value of Eaergy CosCs UlthouC Cha Retrofit

TTPe

(1)

ANNUAL TOITS 0? ENERGY PURCHASED

(2) BASE-YEAR

ENERGY PRICE PER UNIT

(l)x(2)=

(3)

BASE-TEAR

ENERGY COSTS

(4)

UPW* FACTOR

PP^SENT VALUE

OF ENERGY COSTS

ELECTRICnX s BASE CHARGE

3 DEMAND CHARGE

3 TIKE 0?

IVlY CHARGE

s CONTRACT CAPACITY

CHARGE

$ OTHER

CHARGE COMPONENT

$

$

$

$

$

OIL

CKS

OTHii

B.

TOTAL

Calculating Investaect 2;::xcr

Coats for the Existing

X

Syateca Without

^x^

the Retrofit

X

(1) Baae-Year Resale, Salvage^ or Reuae Value of the Ezistlng Syatea to be Replaced $

(2) Base-Year Renovaclon Costa for the Existing Systen if the Retrofit Project is Not Laplecented $

C. C?i.culatl-a2 Annually Recurring Konfuel Operation and Mainteaance (O^M) Coats Without

the Retrofit

<1) Anounc of Annually Recurring

Costs in Base Year

(2) OFW Factor —" a)x(2)=(3) Present Value of Annually

Recurring Coats

10-9
RETROFIT LCC WOaXSHESTS (Coaciaued)

D, Calculating NonannuaLly Recurring MM (Nonfuel) Co»c», Repl»cai»»at Co»t«, «nd Salv«g« 7«lu« Without th» Retrofit.

<1) TEAR Df VHICR EXPENDITb-^

IS EXPECTED TO OCCCR

(2) AMOUNT 0? NON- ANNUALLT

RECCURRINC O&H

COSTS (m BASE- YEAR $)1

(3)

AMOinJT 0? REPLACEMENT

COSTS (IN

BASE-YE.'LR 5)^

(4) AMOUNT OF SALVAGE VALUE (IN BASE-YEAR S)^

(5) SPW FACTORS

??-ESEST VALUE 0? NCH- AKKUALLT

RECURRING

06M COSTS

C3)^xp) =

PRESENT

VALL^S 0? R2PLACE>iENT

(8)

PRESE.ST VALUE 0? SALVAGE VAU^

TOTAL ^x^^x^^>><;^X r 1

S. CalcMlatlr.g TLCC Without the Ratroflt

(1) Present Valco of Energy Co»t3 ; Af5") Total 5

(2) Praaent Value of Investneat Coats ' "&(!) OT (2) + $

(3) Present Value of Annually Recurring (Nonfuol) OSM Costs : f!(l) +9

(4) Present Vslua of Nonannually Recurring (Honfuel) C&H Cost*: D(6) Total + $

(5) Present Value of Replaceroent Costa : D(7) Total -f 5

(6) Preaent Valu« of Salvage : D(8) Total - *

(7) TLCC Without the Retrofit: (l)-\- (2) + (3) + (^^ + ( "^^ - ( f,) - 9

* 7or sxanpli

•nd you an

without fu

s. If nonannually r«

: using 1982 its the

Lure Inflation.

currlng (nonfueJ baoe year, base1(

.) CiM coats , rep

-yeir dollar* nea

3-10

l.icenent c n« StJlClE; oaca» or aalvago vmluc occur In 1990

: Chfi 1990 co»t» tn 1982 dollars. I.e.
ESTHOrrr LCC worksheets (Concinusd)

Parti 7 through J Calculata TLCC vlth Ch« Retrofit

F. Calculating the Present 7alue of Fuel Costa With tha Rotroflt

TiYi

(1)

ATWOAL ONTTS 0?

SHESiCX PraCHA5ED

(2) BASZ-YEAR

ENERCT PRICE

PER UNIT

Cl)x(2)=

6)

BASE-TEAR

ENTRCt COSTS

trpw* FACTOR

PRESENT VALOE

OF EhfERGY COSTS

zizcrs-icLzt BASE CHARGE

CSIAM) CHARCZ

TIKE Q? CAY CHARC2

CONTRACT CAPAcrrr

CHARry.

9 OTHER CHARGE

CCH?0*iii.vr

5

9

$

9

9

OIL

GAS

CTH£a

1 i

•:or.«x ^!!l^^^--^^"^^^Cir ^'-— ~'""~--. XX G, CAlculatlag lavesCsent Costs vlth the RetroJlt

(1) Estiaated Actual laveatnetit Coats for tha Retrofit Project

(2) Inveatcient Co3t Adjust=i*nt Factor

(3) Axdjijsted lav^stnent Costs for the Retrofit Project : (l)x(2)

(A) Base-Tear Renovation Coats for the Exiatlag Syotea If the Retrofit Project Is Ii:plea«at«til

(5) Total Adjusted Present Value Iive9t:aent Cojta ACtrlbutablo

Co the Retrofit Project: (3) + (A)

10-11
?^TRO?IT LCC WCRKSKEETS (Conclnuad)

R. CttlculiCiag Annually Racurring (Nouiual) Oparatloa a.cd >UtaC8n«nc« (CiM) Co»t» Vlth tha Xacrofl:

(1)

Aiaouat of Annually Recurring

Cosca In Base Tear

(2) XnV Factor

UJ.x(2) =

(3) Pr«»eQt Valua oi Annoally

ELecurxlc^ Coses

I. Calculating Nonannually Racurring (Noaiual) OSM Costs, Replacement Coats, and Salvaga Value Vlth the Retrofit

TZ-VR IN

'rfHICH EXPEN-DITURE

IS EXPECrZO

TO OCCUR

(2) AMOUNT 0? HOSANNTJAU-T RECURRING oan

COSTS (IN 3ASETEAR. S)^

(3) AMOUNT 0? RSPIACZMZNT

COSTS (.IS BASE-YEAR S)^

AHOKiT 0? SAL7AGZ VALUE (Df

3ASE-^AR 5)1

(5) SJ'V FACTORS FZZSENT VALCE 0?

A.VMLALLY R^CURRIKG

OiH COSTS

PRESEHT

7AL;r2 0? EEPIACEKEhT

(4)x(5)==

(o) P°2SEliT VALUE 0? SAL7ACZ

7ALCE

Torij. ><^^xCX

J. Calculating TLCC With the Retrofit Project

(1) Present Value of Energy Costa : F(5) Total

(2) Predent Value of Adjusted XnvesCa-ent Coats; G (5) +

(3) Preaent Value of Annually Recurring (.'fonfuei) C&H Costs ; H(3) +

(4) Present Value of Nonannualiy Recurring (Sonfuel) 0>^M Coats - 1(6) Total +

(5) Praaent Value of Re?lac±aenc Coats : 1(7) Total +

(6) Pr=»cnt Value of Salvage ; I (8) Total

<7) TLCC With the Retrofit Project : (l)+(2 )+ (3 )+ (4 )-f-(5) - (6)

^ Sco footnote on Part D (or explanation.

10-12
E£T?.0?IT LCC WORKSHEETS (Concinuod)

K. Hoc Savings or Hxceao CoaC o' the RoCroflc Project

(1) TLCC ulchouC the Retrofit : E(7) 5

(2) TLCC -^th the Retrofit ; J (7) - 5

(3) Net Savings (+) or net lossea (-) . (l)-(2) ** ("'^ ^

L. SIR CAlcuLatton

(1) SIR. Kuorfrator

(a) Energy Cost Savings froa the Retrofit : E(l)-j(l) ^

(b) Change In Nonfuel. O&M Costs ; [ J (.3)+ C"^) ] -[ E (3) + C4) ] " ^

(c) SIR Nuoeratoc : (a)-(b) - $

(2) SIR Daoonlaato-

(a) Adjusted Differencial Investaent Cost ; j(2)-E(2) 5,

(b) Change In ReplaceaenC Coats ; JC5)-E(5) + ?

(c) Cp.ar.ge la Salvage Value ; J(6)--EC6) - $

(d) SIR DenoEilnator : (a) + (b)-(c) - $

(3) SIR for Ranking the Retrofit Project : (1 ) (c) - (2) (d)

10-13
RETROFIT LCC WORKSHEETS

Identifying Information

Building Description:

Location

DoE Region

Functional Use

Building type ( ) Residential

( ) Commercial

( ) Industrial

R-emaining Life of Building

Project Description

Expected Project Life

Length of Study Period (Not to Exceed 25 years)

10-14
RETROFIT LCC WORKSHEET (Conclnuad)

X. Calcul»tlQg the Pro»ent Value of Enorgy CosCs Without the P.etrofit

TYPE

(1)

t-amjAL TOTTS or ENERCT PURCHASED

(2) BASE-YEAa

ENERGY PRIC2 PER UNIT BASE-TEAR ENZRCT COSTS

(4)

CPU* FACTOR

<•>,!>""

PRESENT VALUE

0? ENERGY COSTS

EL^CTRICITT $ BASE CHARGE

DEMAND OURGE

3 TIXE OF

Hk-Z CHARCE

$ CONTRACT CAPACITY

CHARGE

s OTHER

CHARGE CCM50NHNT

5

5

S

OIT,

GAS

aiiiKii

B.

TOTAL

C/iloilailag Iavest3«aC

^^:rxd

Coats for the Exlatlng

^>><^

Systea Without

^Xl

the Retrofit

X

(1) BB8e-Yt;'jr Resale, Salvage, or Reuse Value of the Existing Systea to be ReplaciMl $

(2) Baoe-Tear RenovatloQ Coats for the Existing Systea If the Retrofit Project Is Not InpLeiienCed ?

C. Calculating Annually Recurrlag Nonfuel Operatlou aod Maintenance (OfiM) Costs Without

the Retrofit

(1)

AaoiiQt of AntiualLy Recurring

Co«ts la B.Aae Year

(2) DIV Factor r£WU~F(3) Present Value of Annually

Recurring Coats

10-15
RETR07IT LCC WORKSKESTS (CoQCiauad)

D. Calculating Konaonuallx Recurring 0AM (Nonfuel) Co»c», Repl»coM*nt Co«ca, and SAlvaga Valu« Without tha RotroflC-

(1)

WHICH EXPEHDITURE

13 EXPSCTTD TO OCCOR

(2) AMOUNT OF NON- AKNUALLT

P^CCURRING OSfi COSTS (IN BASE-

(3)

A.MOUNT 0? REPLACSXZNT

COSTS (IN

BAS2-YEAR $)1

(4) AMOONT 0? SALVAGE

VALtre (IN BASE-TEAK S)^

(5) SPU FACT0K3

(2).(5)-

p?J:sz^^r VAL'JE 0? SOHA^-KUALLT RZCURRISG

OiM COSTS

PP-ESENT 7ALK C? JiePLACEMNT

(3) FRES2NT

VAL'JZ 0? SALVAGE

VAUfZ

•

TOTAL ^XC XX 2. Calculating TLCC Without the Rar:roflt

(1) ?Teaent Valua of Enargy Coata ; A(5) Total

(2) Present Value of Invastaeat Co.jtn ' B(l) Or (2)

(3) Preaect Value of Annually Recurring (Nonfunl) OSH Coats : C(3)

(<) Present Value of Noneunually Recurring (Noafuel) OSM Costa : D(6) Total

(5) Present Value of Replacerwat Costs : D(7) Total

(6) Present Vaiu* of Salvaga : D(8) Total

(7) TLCC WlthouL the Retrofit: (l) + (2) + (3)-f-(A)+ (5) - (6)

9 + $ + 5 + $ + 5 - 9

3

^ for oxauple, if nonannually recurring (nonfucl) OSM coats, replacetaenc costs, or tslvage value occur In 1990

»Tid you are using 1982 e.i% the Iwiae year, baoa-yeor dollar* aean» stating the 1990 costs la 1982 dollars. I.e. vlchout futiira Inflation.

10-16
RETROFIT LCC WORKSHESTS (Conclnund)

P«rt» 7 through J C«lcul»to TLCC vlth th« Retrofit

7. Calculmtlng the Prcstat Value of Fuel Costa Ulth tho Retrofit

TYPS

(1)

ANNUAL UNITS 0? ENESCT PORCKASED

(2) BASZ-YEAR

ENtP.CT PRICE PER IWIT SASE-TEAR

E.VERGT COSTS

(4)

CTPW* FACTOR

"•li"-

PRESENT VALUE

OF EKESCY COSTS

EucnLrcrrr 9 B-\SE CHARGE

? DS^iAND CHARGE

5 TIKE G? lAT CKARCB

$

$

9

$

3 CCSTSLKCr CAPACm

CHARGK

$ OTHilX CHARGE COtPONEST

$

OIL

GAS

OrHEH;

TOTAI. ^I^xC ^;::xd XX G. CalcuJLaClng lavescaenc Coata vlth the Retrofit

(1) Eotltaated Actu*l InveataenC Coflta for the Retrofit Project

<2) Investnent Cost AdJustaenC Factor

(3) Adjusted lavoflCncnt Coat« for che Ratroflt Project : (l)x(2)

(4) Base-Tear Rcnovntloti Costa for the Exiatlag Syatea If the Retrofit Project la ImpleBented

(5) Totil Adjusted Preaent VaIus laveatmout Coata Attrlbutabla

to the Retrofit Project: (3) + (4)

10-17
E2TR0FIT LCC WORXSHEETS (Coutinuad)

H. CAlculaclrig Annually Xacurrlos (Noafual) OpsrttloQ and Mdlntaniucn (OiH) Co»ci Vlth cha i^BCroflC

(1) Amount of Annually Recurring

Coats In Base tear

(2)

tJTrf Factor

aj,x(2)=

(3) PraseoC Vilua cf Acnoally

Jlecurrliig Coats

I, Calculating Noaanaually ilecurrlag (Nonfuel) O&M Costs, Replace=<*ac Coats, artd Salvaga V.^lue With the Retrofit

(1) TEAR IN WHICH

EXPENDITURE

IS EXPECTED

TO OCCC?.

(2) AMOUNT 0? No:;- ANTrtTALLY RECURRING aSH

COSTS (IN BASE- TSAR $)1

(3)

AMOOTIT OF REPLACEKENT

COSTS (IS

3A5E--fHAR S)^

(4) AWOLfNT 0? SALVAGE

Y.UX'E (IN SASS-TEAR 5)^

(5) sp-v ?ACT0?3

FRESZ>fr VALTE 0? KONAifS-CUI-T REC!j?-RD;G

OiH COSTS

(3)^(5).

pRESsyr

VAJOj'E 0? REPLACEMENT

PRESENT VALUE 0? SALVAGE VALUE

TOT.U- ^xT^ ^^X^^x:^Xj

J. Calculaclag TLCC Ulth tl\e Retrofit Project

(1) Present Value of Ener37- Coats : F(5) Total

(2) rresent Value of Adjusted InveataenC Costs: G(5)

(3) Preuent Value of Anaually Recurring (Noofuel) O^M Costs ; H(3)

(4) Present Value of Ko-.iannually Recurring (Nonfu»l) OiM Coats ; 1(6) Total

(5) trosent Value of Replaceaent Coats ; 1(7) Total

(6) Present Value of Salvage ; 1(8) Total

(7) TLCC With the Retrofit Project : (1 ) + (2 )+ (3 ) + (4 ) + ( 5) - (6)

» Sea footnotn on Part D for cxplanaclc

10-18
KEIROFIX LCC V03XSHZF.T3 (Concitiued)

K. Mac Savlaga or Sxceso CobC of tha ^aCroflC Project

(1) TLCC without the Retrofit : E(7)

(2) TIXC vith the Retrofit ; J (7)

(3) Met Savings (+) or net losses (-) . (l)-(2)

L. SIR Calculation

5 - 5

- (+) S

(1) SIR };-ua<»r3tor

(a) Energy Cose Savings froa the Retrofit : E(l)-J(l) 5

(b) Change in Nonfuel. OiH Costs i [ J (3) + C4) J - [ E (3)+(4) ] - ?

<c) SIR Numerator : (a)-(b) - $

(2) SI?» Deoonlaator

(a) Arijuatcd DiffereatiaL Investaent Cost ; j(2)-E(2) $

(b) Change la Replacene^C Costs ; JC5)-E(5) + $

(c) Char.se ta Salvage Value ; J(6)-EC6) - $

(d) SIR Denooioator : (a)+(b)-(c) - $

(3) SIK for Raking the Retrofit Project : (1) (c)-r (2) (d)

10-19
RETROFIT LCC WORKSHEETS

Identifying Inf orniatioii

Building Description:

Location

DoE Region

Functional Use

Building type ( ) Residential

( ) CoLiiaercial

( ) Industrial

P-etQaining Life of Building

Project Description

Expected Project Life

Length of Study Period (Not to Exceed 25 years)

10-20
RSraOFIT LCC WOPJCSKEET (Conclnued)

A. CaJLcul»Clag thi Prooant Valua of Enargy Coats Without Cho Retrofit

TTPE

(1)

ANNUAL UNITS OF ENERGY POKCHASCD

(2) BASE-TEAR

ENERGY PRICE PER UNIT

Cl)x(2)=

(3)

BASE-TSAR

EN-ERCY COSTS

(4)

UPW* FACTOR

PRESENT VALUE

0? ENERGY COSTS

ELECTRICITT $ BASE

CH-fRG^

$ DEtiAND CHARGE

3 TIKE 0? IKT CHARCK

S CONTRACT

CAPACn-T CHARGE

s OTHER. CHARGE CCMPOHENT

$

$

$

$

OIL

GAS

anuis.

TOTAL ^::xc^ ^x^ ^xC^X^

B. Calculating lavescaenc Costa for the Existing Systen Vlthout the Retrofit

(1) Baae-Yeir Resale, Salvage, or PvCuse Value of the Existing Systea to be Replaced S

<2) aase-Year Renovation Coats for the Existing Systea if the Retrofit Project is Not Inplecented i

C. Calculating AnnuaJ.ly Recurring Nonfuel Operation and Maintenance (OiM) Coot3 Without

tha Retrofit

(1)

AaoiinC of Annually Recurring

Costs in Base Tear

(2) UPW Factor(3) Present Valua ot Annually

Recurring Costs

10-21
B2TR07IT LCC W0RXSH2ET3 (Coatlnuad)

D, Calculating Nonaonoally Recurring O&M (Nonfusl) Co(it», Repl»co-!»«nt Coacs, *nd Salvsgu Valu« Without tha Racrofit.

(1) THAR IN WHICH EXPENDITURZ

IS EXPKCTZD

TO cxrcuR

(2) AMOUNT 0? NON- ANKUAU.T

RECCURRINC OSM COSTS (IN BASE- YEAR $)1

(3) AMOUNT 0? repiach:>ent COSTS (IN BASE-YEAR $)1

(4) AMOUNT OP SALVAGE

VALUE (IN BASE-YEAR $)1

(5) SPW FACTORS

(2Jx(5)=

PRESENT

VALUE 0? NOHANKIIALLY RECURRING

OSM COSTS

PRESENT

VALL^E OF REPLACEMENT

(A)x(5)=

(8) PRESENT

VALUE OF SALVAGE

VAUiE

TOTAL ^><:C ^x^^>><;^\x

Calculating TLCC Without the Retrofit

(1) Present Valua of Enorgy CoaCa ; A(5) Total

(2) Prasent Value of InveataenC Costs • B(l) or (2)

(3> Presftnt Value of Annually Recurring (Nonfuol) OSM Coeca : CC3)

<A) Preaent Value of Nonannually Recurrli\g (Noafuel) OSM Coat*: D(6) Total

(5) Preaent Value of RcplacsTSdat Coats : D(7) Total

(6) Preaent Valu* of Salvage : D(8) Total

(7) TLCC Without the Riitroflt: (l) + (2) + C3) + (4) + (5) - (6)

+ 5 + $ + $

- >

^ Tor eicJtaple, If nonannuelly recurring (nonfuel) CAM conts, replactoenc coats, or aalvaga value occur In 1990 •nd you are using 1982 as the baae year, baaa-year dollara cseans statiog Che 1990 coats in 1982 dollirs, i.e. vlthout future Inflation. 10-22
RETROFrr LCC WORXSHZETS (ConClnuad)

p*rt« ? through J Calcul*to TLCC vlch tha R«troflc

F. C«lcul*ciiig tha ?rc3eat Value of Fuel Coscb With cha Ratrofit

TTPg

(1)

ANWUAL UNITS 0?

EhfSSCT PtrRCRA5ED

(2) BAS:;-YEAR ENERCT PRICE PER LTjrr BASE-TEAR

ENERGY COSTS

(4)

DPW* FACTOR

PRESS>r: VALUE

0? ENERGY COSTS

ELSflitlCITr 5 BASE CHARC3

DSMAKD CHARGE

EAT CHASC5

9 COSTRACT CAPACITT

CHARGK

$ OTHER

CHARGE CCH?OHSHT

OIL

CAS

OTHEK

TOTAL ^>^d ^^:::x::^ XX C. CilculAClng lavasc^enc Cost* with the Retrofit

(1> Eotlaated Actual laveataent Coats for tha Ratroflc Project

(2) t:ve9ta<r.t Cost AdJu3ta>enC Factor

(3) Axijuated Investnent Coata for the Retrofit Project : (l)x(2)

(4) Bane-Tear RenovaCloo Coats for the Exlatlag Systen if the Retrofit Project la Imple-aeatwi

(5) ToCul Adjusted Present Value X:ive3t3aQt Costa ActrlbuCabla

to the Retrofit Project: (3) + (4)

10-23
RETROFIT LCC WORKSHEETS (Conclnuad)

H. CalculaClng Axinually Recurring (>fonfual) OperaCloQ and MjilnCen»ac« (OiM) CsaCa Vlth tha Retrofit

<1)

AziOUQt of Annually Recurring

Co9C» la Base Tear

(2) DPW Factor a)x(2)=

(3)

Pr«»eQt 7ilu8 of Acnu-illy

S^curricg Coats

I, Calculating Nonanauaily Recunrlag (Noafuel) C&H Coats, Replace=«aC Coats, aod SaJLvoga Value With the Retrofit

(I) TEAR Df VHICH

EXPENDITURE

IS EXPECTED

TO OCCUR

(2) AMOUNT OF N'ON- ANNUALLY

RECURRING 04M COSTS (IN SASE- TEAR 5)^

(3) AMOUNT OF

REPLAC-EKEirr COSTS (IN BASE-YEAR 5)^

AMOUNT OF SALVAGE

VAXUE (IN

5A5E-'23AR $)1

C5) SFJ' FACTORS PRESENT VALUE OF KONAKS'UAU.Y P^CURRING

OSH COSTS

PRESENT VALUE 0? ZEPUCZKENT

(4)3X(5)=

PRESEirr VALUE 07 SALVAGE VAXDE

TOTAL ^x:;^ ><^XX

J. Calculating TLCC With the Re'troflt Project

(1) Proseat Value of Energy Costs: F(5) Total

(2) Present Value of Adjusted Inveatseat Coats; G(5) +

(3) Present Value of Annually Recurring (Nonfuel) GSM Costs : H(3) +

(4) Present Value of Nonannually Recurring (Nonfuel) OiH Costa; 1(6) Total +

(5) Present Value of Replaceaent Costs : 1(7) Total +

(6) Present Value of Salvage ; I (8)' Total

(7) TLCC With the Retrofit Project : (1)+ ( 2 ) + ( 3 ) + (4 ) + (5) - (6)

' Seo footnote on Part D (or explanation.

10-24
3£T?vO?IT IXC WORKSHEETS (Continued)

K. Hoc Savings or Sxceaa Cosc o* the Retrofit Project

(1) TLCC without the Retrofit : E(7) S _

(2) TTXC vlth the Retrofit : J(7) - 5_

(3) Net Savings (+) or net Icssea (-) . (l)-(2) - (+) 5 _

L. SI?. Calculatloa

(1) SIS. Vuoerator

(a) Ecergy Cosc Savings froa the Retrofit : E(l)-j(l) 5

(b) Change In NonfuelOiH Costs;. [ J (3) + (4) ] -[ E (3) + (4) ] - ?

(c) SIR Nunerator : (a)-(b) - $

(2) SIR. Deaoolnator

(a) Adjusted Differential Investartnt Cost : j(2)-E(2) 5,

(b) Change la ReplaceaecC Costs ; JC5)-E(5) + $

(c) Change in Salvage Value ; J(6)-EC6) ~ . $

(d) SIR Denomtoacor : (a) + (b)-(c) - $

(3) SIR for Ranking the Retrofit Project : (1) (c ) -^ (2) (d)

10-25
RETROFIT LCC WORKSHEETS

Identifying Information

Building Description:

Location

DoE Region

Functional Use

Building type ( ) Residential

( ) Commercial

( ) Industrial

R.emaining Life of Building

Project Description

Expected Project Life

Length of Study Period (Not to Exceed 25 years)

10-26
RETROFIT LCC WORiCSHEET (Conclnuad)

A. Calculating the Present Value of Enarjy Coats Without tha Retrofit

TYPE

(1)

ANNUAL UNITS OF

ZlJZKGr PDRCHASED

(2) BASS-TCAa

ENERGY PRICE PER UJJIT

(l)x{2)=

(3)

EASE-YE.AR ENERGY COSTS

(4)

DPW* FACTOR

PRESENT VALUE

OF ENERGY COSTS

ZL2<;rKICITT $ BASE CHARGE

3 DEMAND CHARGE

3 TIME OF M.Y CHARGE

$ CONTRACT

CAPACITY CHARGE

s OTHER CHARGE CCMPONENT

$

$

s

OIL

C^S

OTHER.

B.

TOTAL

CAlculatlng laveatsent

^:^xcr

Costa for the Existing

><C

Syatea Without the Retrofit

X

(1) Baae-Ye%r Resale, Salvage, or Reuae Value of the Existing Syscea to be Replaced

(2) 3>a8e-Year Renovation Costs for the Existing Systen if the Retrofit Project is Not Inplecenttid

C. Calculating Annually Recurring Nonfuel Operation and Maintenance (O&H) Coats Without

the Retrofit

(1)

AaouQt of Annually Recurring

Coats in Rase Year

(2) DTW Factor

(3) Present Value of Annually

Kocurring Costs

10-27
SLSTR07IT LCC W0RXSHE2T3 (Coctlnuad)

D. Calculating Non*aau*ll7 Recurring OiM (Nonfuel) Co»ca, Repl»C8?»«nt Coac», »n<i 3Alv«g« Valu« Without Che R«tro£lC.

<1) TZAR IS WHICH zxFZSDXrmz

IS EXPECljiD TO OCCUR

(2) AMOlThT OF NONANNTJALLT RECCURRISC OiM

COSTS (IN BASS- TEAR $)1

(3) AMOUNT 0? REPLACEKENT

COSTS (IN BASE-YEAR $)1

(4) AMOUNT OP SALVAGE VALUE (IN BASE-YEAR S)^

(5) SPW FACTORS

(2^x(5)=

??j:sent VALUE 0? ycNA^-yUALLT RZCuRRING

06M COSTS

PRESENT VALUE C? R£PLACI?1ENT

(8) FRESENT

VAL'JE 0? SALVAGE

VAUIE

1

TOTAL X^^^X^XX

E. CAlculatlng TLCC Without Che Retrofit

(1) Present Valua of Ecocgy Co»t3 ; A(5) Total

(2) Prasenc Value of Icveatment Costs ^ B(l) Or (2)

(3) Present Value of Annually Recurring (Noofuel) OSH Costa : C(3)

(4) Present Valua of Nonannually Recurring (Nonfuel) OSM Costa : D(5) Total

(5) Present Value of P.eplaCeioenC Costs ; D(7) Total

(6) Present Valu« of Salvage : D(8) Total

(7) TLCC Without the Retrofit: (l) + (2) + (3) + (4) + (5)- (6)

9 .

$ + 9 + 5 + J - >

^ Tor exaaple. If nonannually recurring (nonfuel) OiM costs, replaccoent costs, or salvage value occur In 1990

and you aro using 1982 as the Ixioe year, base-year dollars aeans stating the 1990 costs In 1982 dollars, i.e.,

without future Inflation. 10 — ?8
R2TR0Frr LCC WORKSHEETS (Conclnusd)

Part* T through J Calcul*ta TIjCC vlth th« Retrofit

r. (Ulculatlns tha ?rc3tnt Tiluft of Fuel Costs With the Retrofit

TY?".

(I)

AKNHAL UNITS 0?

ENEE.CT PCROL^SED

(2) BAS:^-YZAR ntmcx PRICE

PER UNIT BASE-YEAR

ENEUG? COSTS

(4)

Ij?V* FACTOR PRESEOT VALUE

OF EHERCY COSTS

zizcmiciu 3 BA£E

CRA3.cz

D£MA.SD CHARGZ

9 TDC G? QiY CHARCS

9 CONTRACT CAPACITY

CHARO?,

$ CTHZX CHARCZ

ccKPONZzrr

3

5

$

9

OIL

GAS

OTHZa

TOTAL

JI^^^-^^*^^--Cl ^^^xCCl X>><^

C. Calculating luvesCaenC Coats vith the Retrofit

(1) Estloated Actu^il laveacaent Coats for tha Retrofit Project

(2) laveataent Coat AdjuaCaenc Factor

(3) Adjusted laveatnent Coata for the Retrofit Project : (l)x(2)

{4) Base-Tear Renovatloa Coota for the Exlatln^ Systers If the Retrofit Project la Impleaeated

(5) Total AJjuated Present Value Inveatnaat Coats Attrlbutabla

Co the Retrofit Project: (3) + (4)

10-29
B2TP.0?IT LCC VCKKSHEETS (CoaClnuad)

H, CalcuLatlag Annually Rocurrlag (N'onfu<»l) Operitlon mod Halatan»ac« (OiM) Coat* With tho Retrofit

(1) Aaouat of Annually Recurring

Costa In aase Year

(2) DPW Factor

a).x(2)=

(3) Praaent Value of Annually

Recurring Costs

I, Calculating Nonannually Recurring (Nonfuel) OiM Coats, Replaeeacnt Coats, and Salvage Value Wifcn cna Retrofit

(1)

TEA?. LM

WrllCH

EXPSSTIIT'JHi: IS E.XPECTZD TO OCCOR

(2) AMOUNT 0? NON- ANNOAIXT

RECURRING OSM

COSTS (IN BASS- YEAR S)^

(3) AMOUNT 0? R£PLACEHZNT

COSTS (IK

BASZ-YZAS. S)^

(4) AMOUNT OF SALVAGE

VALPZ (Di

(5) SW

FACTORS

P2JSSSNT VALTE 0? NON- AKVnAU.Y RZCURRINC

OttM COSTS

PRESENT VALUE OF MPLACZMENT

(A)^xC5).

PRESENT

VALUE 0? SALVAGE VAXUE

TOTAL ^xC ^><^X

J. Calculating TLCC With the Retrofit Project

(1) Present Value of Energy Coats: F(5) Total

(2) Present Value of Adjusted Inveataent Coats; G(5)

(3) Present Value of Annually Recurring ('JonfueJL) OiH Costa ; H(3)

(4) Pieoent Value of Xonannually Recurring (Nonfuel) O&M Costs; 1(6) Total

(5) Prsuent Value of Replaceaent Costs : 1(7) Total

(6) Present Value of Salvage ; 1(8) Total

(7) TLCC With Che Retrofit Project: (l)+ (2 ) + (3) + ('i ) + (5) - (6)

^ Sea footnote on Part U for explanation. 10-30
EETROfIT LCC yORKSKIETS (Coaciouod)

K, H«C Savings or Exceao Coat of tha RoCroflC Project

(1) TLCC wlthouC the Retrofit : E(7) 5 _

(2) TLCC with the Retrofit ; J(7) - 5_

(3) Net Savings (+) or net losses (-) . (l)-(2) - (+> 5 _

SIR Calculattca

(1) SIR Kuc«ritor

(a) Energy Cose Savings froa the Retrofit : E(l)-J(l) 5

(b) Change in Nonfuel. MM C03t3. [ J (.3) + C4) ] - [ E(3) + (4) ] " ?

(c) SIR Nuneracor : (a) -(b) - ?

(2) SIR Deaonlaator

(a> Adjusted Differential InvestoenC Coat : j(2)-E(2) $

(b) Change in Replacenenc Costs ; JC5)-E(5) + $

(c) Change in Salvage Value ; J(6)—£(6) - $

(d) SIR Denodtnator z fa)4-(b)-(c) » $

(3) SIR for Ranking the Retrofit Project : (1) (c)-t- (2 ) (d)

ia-31
RETROFIT LCC WORKSHEETS

Identifying Information

Building Description;

Location

DoE Region

Functional Use

Building type ( ) Residential

( ) Comnercial

( ) Industrial

P.emaining Life of Building

Project Description

Expected Project Life

Length of Study Period (Not to Exceed 25 years)

10-32
8ETR0?rr LCC WORKSHZET (Conclnuad)

A. Calculmtlng the Pro9«nt Value of Energy Coata WlChouC Che Retrofit

TYPE

<1)

ANNUAL UNITS OF ENERGY PraCHASED

(2) BASE-TEAK

ENERGY PRICE PER UNIT

(l)x(2)=

(3)

BASE-YEAR

E^fERGT COSTS

(4)

UPW* FACTOR PRESENT VALUE

OF EKERCY COSTS

ELZCTRICITT $ BASE CHARGE

3 DEKAXD CHARGE

3 TIMZ OF VAX CHARGE

$ CONTRACT CAPACITT CHARGE

$ OTHER

CHARGE

COMPOJfENT

S

s

s

s

s

OIL

GAS

aivjot

B.

TOTAL

Calculating InvesCaenC ^Ill^xd^

Coats for Che Existing

^xC

SysCea Without

^><^

the Retrofit

X

(1) Baas-Year Resale, Salvage, or Reuse Value of the Existing Syscea to be Replaced $

(2) Base-Year Renovation Costs for the Existing SysCea if the Retrofit Project Is Kot Inpleuenced 3

C. Calculating Aanually Recurring Nonfuel Operation and Maintenance (O&H) Coats Without

ti« Retrofit

(1) Aaount of Annually Recurring

Costs In Bade Year

(2)

trPW Factor

a)x(2)"

(3) Present Value of Annually

Recurring Costs

10-33
R2TR0T1T LCC WORKSHEETS (ConCinuftd)

D. Culculattng Nonannually Recurring OiM (Nonfuel) Coaca, Repl«.c8a«nC Co»C», and S«jLv«g« Valu« Without the RaCroflt.

(1) TEAR IH VHICH EXPENDITURE

IS EXPECTED

TO OCCUR

(2) AMOUNT OP NONAJfNUALLY RECCURRING O&H

COSTS (IN BASE- YEAR 5)1

(3)

A.MOUNT 0? REPIACEJCyr

COSTS (IN BASZ-YEAR S)l

(4) AMOUNT 0? SALVAGE

VALUE (IH BASE-YEAR S)^

(5) SPW

FACTORS PRESENT

VALUE 0? NOHAii-KCALLY RECURRING

06M COSTS

PRESErrr VALUE CP

REPLACE?2:;rr

(8) PRESENT VALUE 0? SALVAGE VAUC

TOrrXI. ^x^x^^><^U:

K. Cilculattrtg TljCC Without the Rotroflt

(1) Present Valua of Energy Coats ; A(5) Total

(2) Fraseat Value of Inveatncot Costa : B(l) Or (2)

(3) Present Value of Annually Recurring (Nonfuel) 06M Costs : C(3)

(A) Preaent Valun of Nonannually Recurring (Honfuel) QSM Coat» : D(6) Total

(5) Proseat Value of Replaceraaot Costa ; D(7) Total

(6) Present Valun of Salvago : D(8) Total

(7) TLCC Without the Retrofit: (l) + (2) + (3) + (4) + (5) - (6)

3 + $ + 3 + $ + i

I 7or txaaple, if nonannually recurring (nonfuel) OiM coats, replaceoent costa, or aalvago value occur In 1990 •nd you »ro using 1982 aa the haae year, ba»a-ye«r dollar* Qe»n» stating the 1990 coata In 1982 dollars. I.e. without future Inflation. 10—34
RETROFIT LCC WORXSH^STS (Contlnutd)

Part» ? through J Calcul»co TLCC with th« Retrofit

t. C*lcul«tlng tha Present 7alue of Fuel Coats With th* Rotroflt

TYP2

(1)

ANNfUAL DNTTS 0? ENEKGY PURCHASED

(2)

BAS^-YEAR

ElfERGT PRICE PER imrr

BA.SZ-XZAR

ES-SRGT C05TS

(4)

UPV* FACTOR

FRESZOT VALUZ

OF ENERGY COSTS

ELScL'iircrrT 5 BASE CHARC3

«

CiEMAND CHARGZ

5

9

TIffi C? D&t CHARCS

9 COSTRACr CAPAcrrr

CHARCK

9 OTHHjt

CHARC2

CCHPONiiKT

s

9

9

OIL

GAS

•

OTHZS

TOTAL ^>xd ^^^xC ^X^X C. Calculating lavesCneat Co«t» with the Retrofit

(1) Eatlcuited ActuJil InveatacnC Coats for the Retrofit Project

(2) Inveataent Coflt AdJuaCaent Factor

(3) Adjuated lavcstneat Costa for the RstroflC Project : (l)x(2)

(4) Baaa-Year Renovation Coata for the EilaClaa S/»taa If the Retrofit Project la lapleaeated

(5) Total Adjusted Present Value Tiveat^aant Coats Attrlbutabla

Co the Ratroftt Project: (3)+(4)

10-35
UETROrrr LCC worksheets (Coaclnuod)

H. Calculating Annually Rocucrlug (Noafuftl) Oparatloo and HatnCanaaca (OiM) Co»t» Vlth th« ReCrofiC

<1) Anouat of Annually Recurring

Costs In Base Tear

(2) UPW Factor

aix(2)=

(3) Pr««eaC Value of Annually

Sjecurrlos Coats

I. Calculating ^foaatlaually Recurring (Nonfuel) 06M Costs, Replacp-v»nc Coats, and Salvaga Talua Vtth the Retrofit

(I) TZAR IN WHICH

EXPESDITtJRE

IS EXfECTED TO OCCDR.

(2) AMOUNT OF N'OM- ANNUAIXT

RECURRING 04M COSTS (IN BASEYEAR, 5)1

(3) AMOUNT OF REPLACEHEWr

COSTS (IN BASE-YEAR S)l

(4) AMOUNT OF SALVAGE VALUE (IN BASE-ISAR $)1

(5)

FACTORS PRESENT VALUE 0? KOM- ANNUALLY

RECURRING 04H COSTS

PRESENT VALUE OF RZPUCZMENT

PRESENT VALUE 0? SALVAGE VALUK

TOTAL ^>><^^xZ ^s^^

J. Calculating TLCC With the Retrofit Project

(1) Present Value of Energy Coats! F(5) Total

(2) Present Value of Adjusted Inveatment Coats; G(5)

(3) Present Value of Annually Recurring (Nonfuel) O&M Coats : H(3)

(4) Preoent Value of Nonannually Recurring (Nonfuel) OiM Costs; 1(6) Total

(5) Present Value of Replacenent Coats ; 1(7) Total

(6) Present Value of Salvage ; 1(8) Total

(7) TLCC With the Retrofit Project: (l) + (2) + (3) + (4) + (5)- (6)

1 See footnote onPSTt U for explanation.

10-36
KETROnt LCC WOH-KSHEETS (Conclnusd)

K. tiac Saviago or Exceaa Cost of the RaCrojtlC Project

(1) TLCC wlchout the Retrofit : E(7) 5

(2) TLCC vlth the Retrofit ; J (7) - 5

(3) Net Savings (+) or net lossea (-) . (l)-(2) - C+) S

L. SIR. Calculation

(i) SIR Kuoerator

(a) Energy Cose Savings froa the Retrofit : E(l)-J(l) 5

(b) Change in Noafuel. OSM C09t3; [ J (.3) + C4) ] - [E(3) + C4) ] " ^

(c) SIR Nuoerator : (a)-(b) - $

(2) SIR Deaoaiaator

(a) Adjusted Differeacial Investnent Coat : j(2)-E(2) $

(b) Change la ReplacenenC Costs ; JC5)—E(5) + $

(c) Change ia Salvaga Value ; J(6)—EC6) — $

(d) SIR Denominator : (a) + (b)-(c) $

(3) SIR for Ranking the Retrofit Project : (1) (c)-^ (2) (d)

10-37
PROJECT SELECTION

Priority Project Net

Ranking Project Cost SIR Savings

Totals N.A.

10-38
NEW BUILDING DESIGN LCC WORKSHEETS

Identifying Information

Building Description:

Location

DoE Region

Functional Use

Building type ( ) Residential

( ) Commercial

( ) Industrial

Project Description

Expected Project Life

Length of Study Period (Not to Exceed 25 years)

10-39
VEM BUILDING DESIGN LCC WORKSHEETS (Continued)

A. Calculating the Present Value of Energy Costs

TYPE

(1)

AliNUAL UNITS OF ENERGY PURCHASED

(2) BASE-YEAR

ENERGY PRICE PER UNIT

(l)x(2)=

(3)

BASE-YEAR

EtfERGY COSTS

(4)

UPW* FACTOR

PRESENT VALUE

OF ENERGY COST

ELECTRICirr $ BASE CHARGE

$ DEMAHD CHARGE

$ TIME 07 TAX CHARGE

$ CONTRACT

CAPACITY

CHARGE

$ OTHER CHARGE COMPONENT

$

' $

$

$

$

Oil.

CAS

OTHHR

TOTAL ^^xC ^xiX B. Calculating Investaent Costs for the New Building Design

(1) Estimated Actual Investment Costs for the New Building Design

(2) Investment Cost Adjustment Factor

(3) Adjusted Investment Costs for the Retrofit Project; (l)x(2)

10-40
JJHW BUILDING DESIGN LCC WORKSHEETS (Continued)

C. Calculaclng Annually Recurring (Nonfuel) Operation and Maintenance (OiM) Costs

(1) Amount of Annually Recurring

Costs in Base Year

(2) UPW Factor

(l)x(2)=

(3) • Present Value of Annually

Recurring Costs

D. Calculating Nonannually Recurring (Honfuel) O&M Costs, Replacement Costs, and Salvage Value

(1) YEAR IN WHICH

EXPENDITURE

IS EXPECTED

TO OCCUR

(2) AMOUNT OF NON- ANNUALLY

RECUPJllNC O&M

COSTS (IN BASEYEAR 5)1

(3) AMOUNT- OF REPLACEMENT

COST (IN BASE-YEAR $)1

(4) AMOUNT OF SALVAGE

VALUE (IN BASE-YEAR $)^

(5) • SPJ FACTORS

(2)x(5)=

(6) PRESENT

VALUE 0? NON- ANNUALLY RECURRING

O&M COSTS

(3)x(S)=

(7) PRESENT VALUE OF REPLACEteNT

(A)xC5) =

(8) PRESENT VALUE OP SALVAGE VALUE

TOTAL ^;>><:^ ^^X^^x^x]

E, Calculating the TLCC

(1) Present Value Energy Costs : A(5) Total

(2) Present Value Adjusted Investnent Coats; B(3)

(3) Present Value of Annually Recurring (Honfuel) O&M Costs t C(3)

(4) Present Value of Nonannually Recurring (Nonfuel) O&M Costs; D(6)

(5) Present Value of Replacement Costa T D(7)

(6) Present Value of Salvage : I)(8)

(7) TLCC of the New Bullditrg or System Design; (l) + (2) + (3) + (4) + (5) - (6)

$ + $

+ $ + $ + $

- $ -> $

* For example, if nonannually recurring (nonfuel) O&M costs, replacement costs or salvage value occur in 1990

and you are using 1982 as the base year, base-year dollars means stating the 1990 costs in 1932 dollars,

i.e., without future inflation.

10-41

Section 11

Problem Set A

This section contains simple discounting problems and simple building and

energy conservation problems arranged in the following order:

(1) 6 Problems: Discounting and LCC Analysis Using Discount Factor

Tables

(2) Programmable Time Clock Problem

(3) New Building Design Problem

Solutions to these problems are provided at the end of the section.

11-1
Problem Set A

6 Problems: Discounting and LCC Analysis Using Discount Factor Tables

[These are hypothetical examples intended only to illustrate the techniques.]

1

.

What is the estimated present value today to the Federal Government of a $10,000 cost to be incurred five years from now in conjunction with an energy conservation project? What is the equivalent annual value?

2. What is the estimated present value today to the Federal Government of

a uniform annual cost of $1,000 (in constant dollars) that recurs over

the next 20 years? (The cost stems from a renewable energy project).

What is the equivalent annual value?

3. What is the estimated present value today of electricity costs for

powering a motor in a Washington, D.C. Federal office building over the

next 15 years, given that today's price of electricity is (ii. per kWh, and

the annual energy consumption is 8,000 kWh? What is the equivalent

annual value?

4. What is the estimated present value of a reduction of 10,000 gallons/

year in distillate fuel oil consumption for heating a Federal office

building in Boston, given that the current price per gallon is $1.30,

and the savings are expected to continue over the remaining life of

the building, estimated at 50 years? What is the equivalent annual

cost?

5. What is the DoE-projected average U.S. price per cubic foot of natural

gas for commercial-type use in raid-1983?

6. What is the total pres'ent value cost over its useful life of purchasing,

installing, operating, maintaining, and, finally, disposing of a heat

pump for a house on a military base in Washington, D.C. given the

following assumptions:

o Initial purchase and installation cost = $1,500

o Annual maintenance cost, constant $ = $50

o Compressor replacement in year 8, constant $ = $400

o Salvage value (net of disposal costs) at end of life = $250

o Useful life = 15 years

o Annual electricity costs, valued at the beginning of the study

period = $800

11-2
Problem Set A

Programmable Time Clock Problem

[Note: This is a hypothetical example intended only to illustrate the

technique.

Problem Statement : An energy-conserving retrofit is being considered for the

Federal office and courthouse building in Houston, Texas (DoE Region 6). The

remaining life of the building is expected to be 20 years or more.

At present, the building has a mechanical time clock that turns building HVAC

equipment on and off. This clock runs all HVAC equipment during overtime

hours. A programmable time clock could reduce after-hours equipment usage by

turning on only needed HVAC equipment. It is estimated that the programmable

clock would reduce by 80 percent the current after-hours electricity

consumption of 323,220 kWh per annum.

The price of electricity to the agency is $0.0373 per kWh. The programmable

clock would last for 20 years and cost $9,000 to purchase and install. There

are no other sizable costs or salvage values associated with either clock.

Determine: Is the proposed time clock retrofit cost effective?

11-3
Problem Set A

New Building Design Problem

[Note: This is a hypothetical example intended only to illustrate the

technique.

]

Problem Statement ; An energy-conserving building design is being considered

as an alternative to a conventional building design for a Federal office

building in Madison, Wisconsin (DoE Region 5). The two designs are approximately equivalent in total assignable and auxiliary spaces and in

functional performance with respect to the purpose of the building. Each has

two underground levels for parking and seven office floors, plus a mechanical

house. Each has a floor area of approximately 176,000 ft (gross).

The two designs differ primarily in the envelope, building configuration,

orientation, and lighting systems. The energy-conserving design is slightly

elongated on the east-west axis for greater exposure of the south side to

solar radiation. The window area of the energy-conserving design is 25

percent of the wall area and most of that is located on the south side; in the

conventional building, it is 40 percent. More massive exterior surfaces are used and insulation is increased, reducing the wall U value from 0.16 to 0.06,

and the roof U value from 0.15 to 0.06. Horizontal window fins reduce the

summer cooling load of the energy-conserving design. The north wall of the

first floor of the energy-conserving design is earth bermed. It is assumed

that both designs will last at least 25 years, and, for lack of a good basis

for projecting differences in their salvage values, they are both assumed to

have no salvage value remaining at the end of the 25-year study period.

Following is a listing of the major relevant costs for each design:

(a) Site acquisition costs: (To

ensure adequate exposure of

south-facing windows, an additional acquistlon cost of

$100,000 is necessary for the

energy-conserving design.

Other site costs are assumed

to be identical for both

designs, and hence are not

shown.

)

Energy-Conserving

Design

$100,000

Conventional

Design

(b) Architectural and Engineering

Design Fees and Construction

Costs

$9,780,000 $9,130,000

(c) Annual Energy Consumption:

Natural Gas

Electricity

2,290 X lO'^Btu

3,866 X lO^Rtu

4,980 X lO^Btu

7,277 X lO^Btu

11-4
New Building Design Problem, Continued

(d) DoE Energy Prices:

Natural Gas

Electricity

(e) Nonfuel O&M Costs:

Recurring Annual Cost:

Repairs to External Surfaces

Every 10 Years:

Energy-Conserving Conventional

Design Design

$ 3.84/lO^Btu

15.67/lO^Btu

$70,000

$60,000

$ 3.84/lO^Btu

15.67/lO^Btu

$90,000

$100,000

\fhich design has the lowest life-cycle cost?

11- 5
6 Problems: Solution

1. P = $7,130

A = $1,739

2. P = $10,590

A = $1,000

3. P = $5,314

A = $583

4. P = $231,010

A = $19,821

5. Mid-1983 = $0.004/ft3 (i + .0885)2 = $0.0047/ft3

6. LCC = $10,954

11-6
Programmable Time Clock: Solution

Schedule A -- Electricity: (1) 323220kWh; (2) $0.0373/kWh; (3) $12056.11;

(4) 12.92; (5) $155765; Total $155765.

Schedule B ~

Schedule C —

Schedule D —

Schedule E — (1) $155765; (2)-(6) 0; (7) $155765.

Schedule F — (1) 64644kWh (323220 x 0.2 = 64644); (2) $0.0373/kWh;

(3) $2411.22; (4) 12.92; (5) $31153; Total $31153.

Schedule G — (1) $9000; (2) 0.9 (1 - 0.1 = 0.9); (3) $8100; (4) 0;

(5) $8100.

Schedule H ~

Schedule I ~

Schedule J — (1) $31153; (2) $8100; (3)-(6) 0; (7) $39253.

Schedule K — (1) $155765; (2) $39253; (3) $116512.

Schedule L — (1) (a) $124612; (b) 0; (c) $124612; (2) (a) $8100; (b)-(c) 0;

(d) $8100; (3) 15.38.

11-7
New Building Design Problem: Solution

Schedule A — Electricity: (1) 3,866 x 10^ Btu (7,277 x 10^ Btu);

(2) $15.67/106 Btu; (3) $60,580.22 ($114,030.59); (4) 14.23;

(5) $862,057 ($1,622,655).

Gas: (1) 2,290 x 10^ Btu; (4,980 x 10^ Btu); (2) $3.84/106 Btu;

(3) $8,793.60 ($19,123.20); (4) 18.68; (5) $164,264 ($357,221).

Totals: $1,026,321 ($1,979,876)

Schedule B -- (1) $9,880,000 ($9,130,000); (2) 0.9; (3) $8,892,000

($8,217,000).

Schedule C— (1) $70,000 ($90,000); (2) 11.65; (3) $815,500 ($1,048,500).

Schedule D — For 10 years: (2) $60,000 ($100,000); (5) 0.51; (6) $30,600

($51,000). For 20 years: (2) $60,000 ($100,000); (5) 0.26;

(6) $15,600 ($26,000).

Totals: (6) 46,200 ($77,000)

Schedule E -- (1) $1,026,321 ($1,979,876); (2) $8,892,000 ($8,217,000);

(3) $815,500 ($1,048,500); (4) $46,200 ($77,000); (5)-(6), 0;

(7) $10,780,021 ($11,322,376).

11-8
Section 12

Problem Set B

This section contains more comprehensive building investment problems,

presented as follows:

(1) Water Conservation Problem

(2) Team Problem^—Planning an Energy Conservation Package

(3) Computer Room Waste Heat Recovery Problem

Solutions to these problems are provided at the end of this section.

12-1
Problem Set B

Water Conservation Problem

[Note: This is a hypothetical example intended only to illustrate the

technique.

]

Problem Statement : A Federal office and courthouse building is part of the

Oklahoma City Federal Complex in Oklahoma City, Oklahoma. It is expected to

be continued in use indefinitely. An energy-conserving retrofit has been

proposed.

Data and Assumptions : Currently, water consumption of the 8 showers and 105

faucets in the building totals 28,056 gallons per month. It is estimated

that by installing flow restricting shov;erheads and faucet aerators on these

fixtures, water consumption would decrease by 30 percent. In addition, these

devices would reduce the quantity of steam required for heating water, since

less would be heated. It is estimated that steam consumption of the fixtures

would be lowered from 60,583 to 42,408 pounds per year, and the maximum hourly

consumption rate of 20.2 pounds per hour would be reduced to 14.2 pounds per

hour.

The local water utility charges the agency $0.65 per 1000 gallons of

consumption. The purchased steam (produced from natural gas) has two separate

charge components: (1) $0.0049 per pound of consumption, and (2) a monthly

charge of $0.09 per pound per hour for the maximum hourly consumption rate.

The flow restricting showerheads would cost $7.00 each, and the faucet

aerators $1.14 each. It is assumed that there are no other significant costs or salvage values associated with these devices. Both devices are expected to

last for 5 years.

There is a limited sum of $10,000 that has been budgeted for the retrofit of

the building. Other retrofit project opportunities are as follows:

(1) A group of small projects, R, S, T, and U, costing a total of $2,000

and saving a total of $10,000 in present value dollars.

(2) Project V, having a first cost of $1,600 and a total present value

saving of $12,000.

(3) Project W, having a first cost of $10,000 and a total present value

saving of $80,000.

(4) Project X, having a first cost of $2,000 and a total present value

saving of $25,000.

(5) Project Y, having a first cost of $3,000 and a total present value

saving of $36,000.

(6) Project Z, having a first cost of $1,000 and a total present value

saving of $9,000.

(Note: Assume 10% adjustment factor to investment costs does not apply to

projects R-Z.)

Determine ; Is the proposed water conservation retrofit cost effective? Do

you recommend that the water conservation project be included in

the projects funded by the $10,000 budget?

12-2
Problem Set B

Team Problem—Planning an Energy Conservation Package

[Note: This is a hypothetical example intended only to illustrate the

technique.

]

Problem Statement : Plan an energy conservation package for military base

housing that will maximize net savings, given the following conditions and

candidate retrofit projects. The housing is located in Washington, D.C. Its

remaining life is expected to be 15 years. The agency has a limited budget of

$2,000 to spend on each house.

Each house has been weatherstripped and caulked. It has R-11 insulation in

the attic, as well as all the insulation that can be accommodated in the

floors and walls without making major structural modifications. A jacket has

been added to the domestic water heater, and thermal draperies have been added

to the windows.

Each house is currently heated by an electric resistance system that is in

good condition and could reasonably be expected to last over the remaining 15

year life of the house with only negligible maintenance and repair. The

efficiency of the system is assumed to be 100 percent. The annual space

heating load is 100 x 10"Btu per house. The base now pays $16.89 per 10"Btu

($0.06 per kWh) of electricity. The annual domestic hot water load is 22 x 10°Btu per house. Hot water is currently supplied by an electric water heater

that is expected to last over the remaining 15 year life of the house with

only negligible maintenance and repair. The efficiency of the existing hot

water system is assumed to be 100 percent.

The following options are being considered for retrofit to each house:

(A) Addition of a solar domestic water heater. The system that has been

recommended as reliable and sufficiently durable to last the 15 years

without major maintenance or repair costs $1,600, and is expected to meet

80 percent of the annual hot water load. No net salvage value is

expected.

(B) Bieplacement of the existing electric resistance space heating system with

a higher efficiency (1.8 COP) heat pump. The replacement of the

existing system with the heat pump will cost $1,700. No net salvage

value is expected from disposal of the existing system. The heat pump is

expected to have about the same maintenance and repair costs and life

expectancy as the existing system.

(C) Addition of attic insulation to raise the current resistance (R) level

from R-11 to R-19. The insulation will cost $300 to purchase and Install

and is expected to reduce the energy consumption for space heating by 5 percent.

(D) Replacement of incandescent lighting with fluorescent lighting. The

fluorescent lighting will cost $300 to purchase and install and is

expected to reduce by 60 percent the 2000 kWh annual consumption rate of

the existing lighting. Over the 15 year project life, the economic

effects of the longer lives of the fluorescent tubes and their

higher replacement costs are expected to be offsetting. There are assumed to be no salvage values associated with either the incandescent

or fluorescent lighting.

12-3
Problem Set B

Computer Room Waste Heat Recovery Problem

[Note: This is a hypothetical example intended only to illustrate the

evaluation technique.]

Problem Statement ; Would you recommend the following retrofit project for a Federal office building in Washington, D.C. (DoE Region 3)? The proposed

project is to install a heat exchanger (with necessary piping and valves) for

recovery of heat from waste condenser water from a computer room chiller for

the purpose of preheating domestic hot water for the building.

Data and Assumptions:

(1) Condenser water at 95°F is currently delivered from the computer room water chiller to the cooling tower for dissipation of the thermal energy to

the atmosphere.

(2) Purchased steam at $9.00 per thousand lbs (Mlb) is currently used to heat

domestic hot water for the office building. The energy content of the steam

is 1.05 X lO^Btu/Mlb. The supplier of the steam uses coal to generate the

steam with a plant efficiency of 65%.

(3) Domestic hot water consumption averages 1 gallon per person per day (GPD).

The building is occupied 252 days per year and dally occupancy averages 3,000

people (P). The water Intake temperature averages 60°F and the supply

temperature is 120OF,

(4) Passing the BO^F domestic water supply through a heat exchanger through

which the 95°F waste condenser water is routed will preheat it to SO^F.

(5) The installed cost of the heat exchanger (including all piping and

insulation and values) is estimated at between $6,000 and $7,000, depending on potential problems that may be encountered in installation.

(6) Maintenance cost on the heat recovery system is estimated at $200 per

year.

(7) A replacement cost of $500 for retublng the heat exchanger is expected at

the end of 15 years.

(8) With proper maintenance and periodic replacements, the system is expected

to last at least 25 years.

Note: Annual Energy Consumption (Mlbs. of steam) = [GPD x P x Dy/Yr x 8.34 Ib/G X AT] V 1.05 X lOOBtu/Mlb.

Determine

(A) Net present value savings.

(B) SIR for ranking this project relative to other projects.

12-4
(C) The break-even purchase and installation price of the heat exchanger,

12-5
Water Conservation Problem: Solution

Schedule A -- Steam from Gas: (1) 605831b; (2) $0.0049/lb; (3) $296.86

(base), $21.82 (demand); (4) 5.18; (5) $1538 (base), $113

(demand); Total $1651

Schedule B ~

Schedule C — (1) $218.84; (2) 4.10; (3) $897

Schedule D ~

Schedule E — (1) $1651; (2) 0; (3) $897; (4)-(6) 0; (7) $2548

Schedule F -- (1) 424081b; (2) $0.0049/lb; (3) $207.80 (base), $15.34

(demand); (4) 5.18; (5) $1076 (base), $79 (demand); (6) $1155

Schedule G — (1) $175.70 [ ($7.00/showhd. x 8 show) + ($1. 14/aerator x 105

faucets) = $175.70]; (2) 0.9; (3) $158; (4) 0; (5) $158

Schedule H — (1) $153.19 [28056G/mo x 0. 7 x 12mo x $0.65/1000G =

$153.19; (2) 4.10; (3) $628

Schedule I ~

Schedule J — (1) $1155; (2) $158; (3) $628; (4)-(6) 0; (7) $1941

Schedule K — (1) $2548; (2) $1941; (3) $607

Schedule L — (1) (a) $496; (b) -$269; (c) $765; (2) (a) $158; (b) 0;

(c) 0; (d) $158; (3) 4.84

12-6
PROJECT SELECTION - LIMITED BUDGET

PROJECTS SIR

1 4.84

RANKING

NO BUDGET

CONSTRAINT

(7)

FIRST

COST

($)

176

NET

SAVINGS

($)

Water-saving

devices 607

R,S,T,U 5.0 (6) 2,000 8,000

V 7.5 (5) 1,600 10,400

W 8.0 (4) 10,000 70,000

X 12.5 (1) 2,000 23,000

Y 12.0 (2) 3,000 33,000

Z 9.0 (3) 1,000 8,000

OPTIONS Project W All project except W

WITHIN

BUDGET:

First cost = $10,000 or NS = $70,000

First cost = $9,776

NS = $83,007

12-7
Team Problem—Planning an Energy Conservation Package: Solution

Install Solar Domestic Water Heater:

Schedule A — (1) 22mmBtu; (2) $16 .89/mmBtu; (3) $371.58; (4) 11.07;

(5) $4113; Total $4113

Schedule B —

Schedule C —

Schedu le D —

Schedule E — (1) $4113; (2)-(6) 0; (7) $4113

Schedule F — (1) 4.4mmBtu; (2) $16 .89/mmBtu; (3) $74.32; (4) 11.07;

(5) $823; Total $823

Schedule G -- (1) $1600; (2) 0.9 (1.0 - 0.1 = 0.9); (3) $1440; (4) 0;

(5) $1440

Schedule H ~

Schedule I ~

Schedule J -- (1) $823; (2) $1440; (3)-(6) 0; (7) $2263

Schedule K — (1) $4113; (2) $2263; (3) $1850

Schedule L — (1) (a) $3290; (b) 0; (c) $3290; (2) (a) $1440; (b)-(c) 0;

(d) $1440; (3) 2.28

Install Heat Pump: »

Schedule A — (1) lOOmmBtu; (2) $16 .89/mmBtu; (3) $1689; (4) 11.07;

(5) $18697

Schedule B —

Schedule C —

Schedule D —

Schedule E — (1) $18697; (2)-(6) 0; (7) $18697

12-J
Schedule F — (1) 55.56inmBtu; (2) $16.89/inmBtu; (3) $938.41; (4) 11.07;

(5) $10388; Total $10388

Schedule G — (1) $1700; (2) 0.9 (1.0 - 0.1 = 0.9); (3) $1530; (4) 0;

(5) $1530

Schedule H ~

Schedule I ~

Schedule J — (1) $10388; (2) $1530; (3)-(6) 0; (7) $11918

Schedule K — (1) $18697; (2) $11918; (3) $6779

Schedule L — (1) (a) $8309; (b) 0; (c) $8309; (2) (a) $1530; (b)-(c) 0;

(d) $1530; (3) 5.43

Add R-U to R-19 Insulation:

Schedule A -- (1) lOOmmBtu; [ 55. 56mmBtu] ; (2) $16. 89/mmBtu ; (3) $1689

[$938.41]; (4) 11.07; (5) $18697 [$10388]; Total $18697

[$10388]

Schedule B ~

Schedule C ~

Schedule D ~

Schedule E -- (1) $18697 [$10388]; (2)-(6) 0; (3) $18697 [$10388]

Schedule F -- (1) 95inmBtu [52. 78mmBtu] ; (2) $16. 89/inmBtu ; (3) $1604.55

[$891.45]; (4) 11.07; (5) $17762 [$9868]

Schedule G -- (1) $300; (2) 0.9; (3) $270; (4) 0; (5) $270

Schedule H ~

Schedule I ~

Schedule J -- (1) $17762 [$9868]; (2) $270; (3)-(6) 0; (7) $18032 [$10138]

Schedule K— (1) $18697 [$10388]; (2) $18032 [$10138]; (3) $665 [$250]

12-9
Schedu le L — (1) (a) $935 [$520]; (b) 0; (c) $935 [$520]; (2) (a) $270;

(b)-(c) 0; (d) $270; (3) 3.46 [1.93]

Install Lighting:

Schedule A — (1) 2000kWh ; (2) $0.06/kWh; (3) $120; (4) 11.07; (5) $1328;

Total $1328

Schedule B —

Schedule C ~

Schedule D ~

Schedule E — (1) $1328; (2)-(6) 0; (7) $1328

Schedule F — (1) 800kWh ; (2) $0.06/kWh; (3) $48; (4) 11.07; (5) $531;

Total $531

Schedule G — (1) $300; (2) 0.9; (3) $270; (4) 0; (5) $270

Schedule H ~

Schedule I ~

Schedule J -- (1) $531; (2) $270; (3)-(6) 0; (7) $801

Schedule K — (1) $1328; (2) $801; (3) $527

Schedule L — (1) (a) $797; (b) 0; (c) $797; (2) (a) $270; (b) 0; (c) 0;

(d) $270; (3) 2.95

12-10
PROJECT SELECTION

PROJECT NET

PROJECT COST ($) SIR SAVINGS ($)

Heat pump 1700 5.43 6,779

Insulation

without HP 300 3.46 665

Lighting 300 2.95 527

Solar water

heater 1600 2.28 1850

Insulation

with HP 300 1.93 250

SELECTION

12-11
Computer Room Waste Heat Recovery Problem: Solution

Schedule A — steam: (1) 360.3 Mlb (IGPD x 3000? x 252Dy/Yr x 8.341b/G x

(120 - 60)) ^ 1.05 mmBtu/mb = 360.3Mlb; (2) $9.00/MIb;

(3) $3243; (4) 15.93; (5) $51654

Schedule B ~

Schedule C ~

Schedule D ~

Schedule E — (1) $51654; (2)-(6) 0; (7) $51654

Schedule F — (1) 240.2Mlb (IGPD x 3000P x 252Dy/Yr x 8.34lb/G x (120 - 80))

r 1.05mmBtu/Mlb = 240.2Mlb); (2) $9.00/Mlb; (3) $2162;

(4) 15.93; (5) $34436; Total $34436

Schedule G — (1) $6000 - $7000; (2) 0.9 (1 - 0.1 = 0.9); (3) $5400 - $6300;

(4) 0; (5) $5400 - $6300

Schedule H — (1) $200; (2) 11.65; (3) $2330

Schedule I — (1) 15; (2) 0; (3) $500; (4) 0; (5) .36; (6) 0; (7) $180;

(8) 0; Totals (6) 0, (7) $180; (8)

Schedule J — (1) $34436; (2) $5400 - $6300; (3) $2330; (4) 0; (5) $180;

(6) 0; (7) $42346 - $43246

Schedule K — (1) $51654; (2) $42346 - $43246; (3) $8408 - $9308

Schedule L — (1) (a) $17218; (b) -$2330; (c) $14888; (2) (a) $5400 - $6300;

(b) $180; (c) 0; (d) $5580 - $6480; (3) 2.30 - 2.67

Break-Even (with adj. factor): .9P&I(BE) = $17218 - $2330 - $180 =

$147087.9 = $16342, where P&I(BE) = break-even purchase and

installation cost.

12-12
Section 13

Problem Set C

This section contains problems related to the treatment of uncertainty in

project analysis, presented as follows:

(1) Sensitivity Analysis Problem: Insulation

(2) Problem in Probability Analysis: Heat Pump Versus Solar Energy System

Solutions to these problems are provided at the end of this section.

13-1
Problem Set C

Sensitivity Analysis Problem: Insulation

[Note: This is a hypothetical example intended only to illustrate the

technique.

]

Problem Description : Assume that you, as a homeowner, wish to insulate your

attic, which is currently uninsulated, to reduce your electricity cost. The

house is heated by an electric resistance system and the current price of

electricity is $.057/kWh ($ 16 .77/106Btu) . You expect to remain in the house

another 25 years. Your best alternative use of the money you have available

to spend on insulating the house is for a tax-free bond paying 10% compounded

annually. Current inflation is about 3% per year. The house is located in

Washington, D.C.

Using the Means Building Construction Cost Data Guide as a rough approximation

of costs,* you find the following cost data for this area for fiberglass

batts:

Material Cost Labor Ov erhead and Profit

($/ft2) ($/ft2)

.06

(Multiplier)

.14 1.25

.24 .07 1.23

.40 .08 1.17

.55 .09 1.15

R-11

R-19

R-30

R-38

In the past you have occasionally seen a 50% sale on installed insulation.

However, you haven't seen any sales recently and do not know if the lower

price will be available.

Further, you have noted a recent upswing in the local building industry which

may have driven labor rates sharply higher—as much as double those reported

by Means .

The area to be insulated is 1,200 ft2. You are basing your energy savings on DoE-proj ected price increases in energy, based on a recent research report by

the National Bureau of Standards which estimated the annual savings from attic

insulation for a house similar to yours as follows:

Change in Annual Heating Requirments

(lO^Btu)

O-R-U 12.913

O-R-19 14.987

O-R-30 16.315

O-R-38 16.833

Determine : How sensitive is the optimal level of attic insulation to these

potential variations in costs.

*R.S. Means assumes large job sizes so these costs will tend to be lower than

what the homeowner would face.

13-2
Problem Set C

Problem in Probability Analysis: Heat Pump Versus Solar Energy System

[Note: This is a hypothetical problem intended only to illustrate the

technique.

A heat pvunp and a solar energy system are two alternatives being considered

for retrofit to a number of similar Federal facilities. If the solar energy

system is installed, the existing heating system will be used as an auxiliary

system. The heat pump requires no auxiliary system. A major area of concern

is whether or not the existing system will provide reliable auxiliary service

without major overhaul costs. Expert judgment is that there is about a 30

percent chance that the existing system in a given facility will be found to

require major overhaul in order to provide auxiliary service to the solar

energy system, and a 70 percent chance that no major repairs or modifications

will be needed. If no major overhaul is needed, the combined life-cycle cost

of the solar/auxiliary system is estimated at $20,000; and if major overhaul

is needed, at $35,000. The life-cycle cost of the heat pump is estimated at

$25,000. Which system do you recommend on the basis of minimizing the

expected value of the life-cycle cost?

13-3
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13-4
»

Probability Analysis Problem: Solution

EV (Heat Pump) = $25,000

EV (Solar/Auxiliary) = ($20,000) • (.7) + ($35,000) • (.3) = C24,500

There is very little difference in the expected value of the outcomes; but the

solar/auxiliary system is expected to have a slightly smaller life-cycle cost

and could be recommended on that basis.

13-5

Section 14

Problem Set D

This section contains problems whose solutions utilize other analysis

techniques such as break-even analysis and replacement methodology. The

problems are presented as follows:

(1) Team Problem—Break-Even Orders for a Computerized Procurement System

(2) Team Problem—Determining Optimal Retirement of Equipment

Solutions to these problems are provided at the end of this section.

14-1
Problem Set D

Team Problem—Break-Even Orders for a Computerized Procurement System

[Note: This hypothetical problem is intended only to illustrate the

technique.

]

Problem Statement :

A Federal agency procurement office is considering the purchase of a new

computerized system that is expected to cut average labor time per order In

half. The number of orders has been identified as a key determinant of the

cost effectiveness of the system, and management wishes to make the decision

based on cost effectiveness.

Past trends in procurement orders have been analyzed, and a projection has

been made of future orders in terras of lower and upper boundary estimates.

Over the next three years, the average projected low estimate is 500 orders

per year and the average high is 800. Other data and assumptions are given

below:

Data and Assumptions:

System purchase and installation cost = $45,000

Annual maintenance cost = $2,000

(Fixed by contract in constant dollars)

Service charge per order = $1.00

(Fixed by contract in constant dollars)

System life = 10 years

Salvage =

Labor savings per order = $12.00

(Constant dollars)

14-2
To Do:

Based on the data and assumptions, perform a break-even analysis of the annual

procurement orders and, on this basis, advise management on the decision.

[Note: Assume the project is not regarded as an energy conservation project.]

14-3
Problem Set D

Team Problem—Determining Optimal Retirement of Equipment

[Note: This hypothetical example is intended only to illustrate the

technique.

]

Problem Statement : The existing motor-generator sets which power passenger

and freight elevators in a Federal building complex consume 2 million kWh's of

electricity per year. At the time of the analysis (early 1983) , electricity

costs $0.06/k:Wh, and the price is projected to increase over the next 5 years

at an annual compound rate 5 percent faster than general price inflation and

thereafter at a rate 1 percent faster than the general inflation rate.

With an extensive overhaul and modifications costing $50,000, it is estimated

that annual power consumption could be reduced by 15 percent and equipment

life extended to as long as 25 years. Without the overhaul, the equipment is

expected to last another 5 years, at which time overhaul will no longer be

feasible.

New elevator power equipment is available at a purchase and installation cost

of $400,000. It will cost $20,000 to remove and dispose of the old equipment

and to prepare the machine rooms to receive the new equipment. There is no resale or reuse market for this kind of equipment when it is removed from

service. The new equipment is expected to be 25 percent more energy efficient

than the existing equipment without the overhaul. The new equipment is

expected to last for the duration of the building life which is estimated to

be indefinite.

No appreciable difference is estimated in maintenance and repair costs of the

new and existing system, whether overhauled or not. The new equipment is

expected to continue to be "state-of-the-art" for the foreseeable future, and

its constant dollar costs are expected to remain the same over time.

Determine :

(1) Decision alternatives to be considered.

(2) The estimated least-cost alternative.

(3) The net savings estimated to be derived from making the cost-effective

decision.

14-4
Team Problem — Break-Even Orders for a Computerized

Procurement System: Solution

BREAK-EVEN: LABOR-MACHINE DECISION

SOLUTION - Find break-even no. of orders and compare with

projected no. of orders

PV costs = PV savings

S45,000 + (S2,000 x UPWio) + (S1.00 x no. orders x UPWiq)

S12.00 X no. orders x UPWio

S45,000 + (S2,000 x 6.145) + (S1.00 x no. orders x 6.145) = S12.00 X no. orders x 6.145

545,000 + $12,290 + 6.145 no. orders = 73.74 no. orders

67.60 no. orders = 57,290

Break-even no. orders = 847.49 annually

14-5
Team Problem — Determining Optimal Retirement of Equipment: Solution

KEEP EXISTING EQUIPMENT "AS IS" FOR 5 YRS,

THEN REPLACE

ENERGY COSTS, NEW EQUIP. COST,

YRS. 1-5 END OF YR. 5

PV = [2,000,000kWh x $0.06/kWh x UPW* y^ 70/^ 50/J + [($400,000 + 20,000) x SPW5 y^ 70/J

ENERGY COSTS,

YRS. 6-25 + [(1 -0.25) X 2,000,000 x $0.06 x SCA5 y, 50/, x UPW^q y, 7,/^ ,

»/, x SPW5 y, 70,^ ] = [2,000,000 xSO.06 X 4.73] -I- [$420,000 x 0.71 ] + [0.75 x 2,000,000 x

$0.06 X 1.28 X 11.53 X 0.71 ] = $1,808,862

14-6
RETIRE EQUIPMENT IMMEDIATELY

NEW EQUIPMENT ENERGY COSTS, YRS. 1-25

PV = [$400,000 + 20,000] + [(1-0.25) x 2,000,000 x $0.06 x [UPW* y^ ^o/^ 50/^ +

(SCA5 y^ 50/^ X UPW20 yr, 70/^ 10/^ X SPW5

y^ jo/J]] = $420,000 + [0.75 X 2,000,000 x $0.06 x [4.73 + (1.28 x 11.53 x 0.71)]] = $1,788,762

14-7
OVERHAUL EXISTING EQUIPMENT

OVERHAUL ENERGY COSTS,

COST YRS. 1-25

PV = [$50,000] + [(1-0.15) X 2,000,000 x $0.06 x [UPW5 y^ 70/^ 50/^ +

(SCA5 y^ 50/^ X UPW2O yr, 70/^^ 10/^ X SPW5

y^ 70/j]] = $50,000 + [0.85 X 2,000,000 x $0.06 x [4.73 + (1.28 x 11.53 x 0.71)]] = $1,601,263

14-8
COST-EFFECTIVE DECISION

• Overhaul existing equipment

• Net savings: — $207,599 Relative to keeping equipment ''as is" for

5 yrs, then replacing — $187,499 Relative to retiring existing equipment

immediately

14-9

TAB 15

PROBLEM SET 15

This tab contains a sample economic evaluation report.

15-1
Problem Set E

Team Critique of an Economic Evaluation Report

Critique this report as a team. Identify errors in problem formulation,

assumptions, analysis, and recommendations. Describe the nature of the errors

and how you would have avoided them. Select a representative of your team to

present to the class your version of an improved report.

15-2
Energy Conservation Feasibility Study

Federal Building I Washington, D.C.

Submitted by

XYZ Associates

Contractors Park, USA

[Note: This is purely a hypothetical example intended only as an instructional aid for illustrating important elements of an economic

evaluation report.]

15-3
1. Objective and Scope

This report analyzes six alternatives for reducing utility costs in Federal

Building I, an existing office building in Washington, D.C. The report

provides GSA decision makers with economic guidance as to which conservation

retrofits to select in light of the GSA objective of maximizing net savings

from energy conservation subject to budgeting constraints.

2. Alternatives

The six alternatives are time clocks for lighting control, additional roof

insulation, storm windows on the North side, flow restrictors for saving hot

water in restrooms, use of cool night air to precool the building during the

summer, and insulated window drapes. Other alternatives were considered, but

they were rejected because their savings were difficult to calculate.

3. Assumptions and Data

A study period of 25 years is used for energy retrofits, and a study period of

20 years is used for the flow restrictors.

A real discount rate of 10% is used for evaluating the roof insulation and

time clocks, and a real discount rate of 13% is used for the rest of the

retrofits.

All future costs that are discounted to present values are stated in current

dollars to account for inflation.

15-4
The report evaluates retrofits for the 1984 budget year. Since agency funding

for 1984 is not yet determined, three budget levels covering the range that

might be expected are assumed as follows: $92,000; $145,000; and $400,000.

An economically efficient set of retrofit projects is selected for each of the

three budget levels.

Occupant satisfaction with the building in terras of thermal comfort, lighting

levels, and water supply are assumed to be unaffected by the proposed

retrofits.

4. Analysis

The conservation retrofits are arranged in descending order of their cost

effectiveness. Since the objective is to maximize net savings from

conservation retrofits, column 4 (net dollar savings) determines the ranking

of the six projects.

All projects except using cool night air to precool buildings in the summer

are estimated to be cost effective in the sense that the SIR is greater than

1.0 and the payback is less than four years.

To maximize net savings under each of three budget scenarios, each project

should be selected in the order given by column 5 until net savings become

zero or negative, or until the budget is exhausted.

15-5
Table 1. Summary of Conservation Retrofits

Retrofit

Total Life-Cycle

Cost Savings ^

$

(1)

First Net

Cost Savings Economic

$ SIR $ Priority

(2) (3)=(1)^(2) (4)=(l)-(2) (5)

Storm Windows on North Side276,000 90,500 3.0 185,000

Time Clocks for

Lighting Control

226,000 53,400 4.2 172,600

Flow Restrictors

in Rest rooms 55,000 3,000 18.3 52,000

Roof Insulation 53,000 2,600 20.4 50,400

Insulated Window

Drapes

206,300 195,500 1.1 10,800

Cool Night Air

to Precool Building

i n Summe r

130,000 140,000 0.9 -10,000

^The data and calculations that underly the cost and savings figures in this table are available from a research assistant at XYZ Associates.

15-6
5. Recommendations

For a budget of $92,000, storm windows on the North side of the building

should be installed. Storm windows yield the greatest net benefits. The

$1,500 remaining is insufficient to undertake any of the other projects.

For a budget of $145,000, both the storm windows and the time clocks should be

installed. The $1,100 remaining is insufficient to undertake any other

project.

For a budget of $400,000, all of the projects except using cool night air to

precool the building in summer should be selected. Having a budget larger

than the cost of all available alternatives is equivalent to having no budget

constraint. Therefore any project with a relatively large SIR should be

undertaken. Using cool night air is rejected because its SIR is lower than

any of the other retrofits. For this reason it would not be acceptable

regardless of the budget size.

15-7
NBS-n4A IREV. 2-8CI U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO. NBS TN 1195

2. Performing Organ. Report No 3. Publication Date

June 1984

4. TITLE AND SUBTITLE

Seminar Workbook

Economic Evaluation of Building Design, Construction, Operation and Maintenance

5. AUTHOR(S)

Rosalie T. Ruegg

6. PERFORMING ORGANIZATION f/ f jom t or oth er thon N 8S, see instructions]

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

8. Type of Report & Period Covered

Final

JL

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State, ZIP)

Design Programs Branch

Public Building Service

General Services Administration

Washington, DC 20405

10. SUPPLEMENTARY NOTES

(^n Document describes a computer program; SF-185, FlPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less (actual summary of most si gnificant information. If document includes a significant

bi bliography or literature survey, mention it here) This workbook has been prepared for participants in the seminar, "Economic Evaluation of Building Design, Construction, Operation and Maintenance." It has two main

functions: (1) to provide basic resource materials, references, and introductions

to methods employed in the seminar and (2) to provide instructional problems for

solution by the participants. Specifically, it contains brief discussions of key

elements in performing economic evaluations: discounting, escalation, establishing

a study period, project selection techniques, and treatment of uncertainty; explanations of supporting analysis techniques: break-even analysis and replacement

theory; and problems, worksheets, and solutions. Cross references are given to

related sections of a reference manual (NBS Handbook 135) and to case studies which

illustrate the topics. The objectives of the seminar are to provide participants

with a working knowledge of economic evaluation procedures for making building

decisions, and to improve their decision-making abilities related to cost management

and to the design and selection of buildings and building systems. The seminar has

been developed for building design engineers and architects, project planning and

programming staff, managers of building programs, procurement officers and contract

coordinators, building construction estimators, and building analysts.

12. KEY WORDS (Six to twelve entries; alphabeti cal order; capitalize only proper names; and separate key words by semicolon s) cost effectiveness; economic evaluations; energy conservation; life-cycle costing;

public buildings; solar energy.

13. AVAILABILITY

[j^ Unl imi ted QH For Official Distribution. Do Not Release to NTIS

[v] Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C.

20402.

~~^ Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTED PAGES

183

15. Price

USCOMM-DC 6043-PeO

•U.S. GOVSBNMfNT PRINTING OFFICE : 1984 0-420-997/10000
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