i

U.S. Department of Commerce

National Bureau of Standards

National Engineering Laboratory

Center for Building Technology

Washington, D.C. 20234

Rosalie T. Ruegg

Stephen R. Petersen

Harold E. Marshall

NBSIR 80-2040

Recommended Practice

for Measuring Life-Cycle

Costs of Buildings and

Building Systems

June 1 980

NBSIR 80-2040

RECOMMENDED PRACTICE

FOR MEASURING LIFE-CYCLE

COSTS OF BUILDINGS AND

BUILDING SYSTEMS

BATIONAL BUREAU

OF STANDARDS

LIBRARY

SEP 1 9 1980

Hoi acoCtr

u

Rosalie T. Ruegg

Stephen R. Petersen

Harold E. Marshall

Building Economics and Regulatory

Technology Division

Center for Building Technology

National Engineering Laboratory

National Bureau of Standards

Washington, D.C. 20234

June 1980

U.S. DEPARTMENT OF COMMERCE, Philip M. Klutznick, Secretary

Luther H. Hodges. Jr., Deputy Secretary

Jordan J. Baruch, Assistant Secretary for Productivity. Technology, and Innovation

NATIONAL BUREAU OF STANDARDS. Ernest Ambler, Director
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PREFACE

Life-cycle cost (LCC) analysis, when applied to building decisions, provides an economic

evaluation of the net dollar effect, over time, of purchasing, constructing/installing

,

maintaining, operating, repairing, and replacing buildings or building systems. Rising

prices of labor, material, and particularly energy have forced builders, architects,

engineers, building owners and operators, and code writers to turn to LCC analysis to identify building designs and building systems that will be cost effective in the long run. A practical, standardized approach for evaluating the LCC of building decisions is needed

for widespread acceptance, understandability , and comparability of the results of LCC analysis. Reflecting this need in the public sector, the National Energy Conservation Policy

Act of 1978 and an earlier Executive Order by President Carter mandated that a practical

and uniform set of LCC methods and procedures be established and used by all Federal

agencies in making decisions about energy projects in Federal buildings. A comparable

set of guidelines which includes the treatment of taxes and other effects influencing

building decisions in the private sector would further promote sound investment decisions

as well as aid in the transfer of information among the many parties that together comprise

the building community.

This National Bureau of Standards report has been prepared in response to an ongoing standards development activity in the American Society of Testing and Materials (ASTM E-6 —

Performance of Building Constructions) and in response to requests from the building com- munity for assistance in applying life-cycle cost analysis in a uniform and practicable

manner. This document has been submitted to ASTM E-6. 81, the Building Economics Subcommittee, for its consideration in the development of a "recommended practice for measuring

the total life-cycle costs of buildings and building systems." The technical material is

presented in such a manner that the Subcommittee can use it to develop either a single or several recommended practices or standards.

This report describes how to measure the total life-cycle costs of an investment. Its

preparation is one of a series of steps towards developing a comprehensive set of standard

recommended economic practices that will meet the diverse needs of the building community

for measures of economic performance. Specifically, this report provides the technical

base for the development of a standard method or recommended practice for measuring total

life-cycle costs of investments in buildings and building systems. Applying standardized

LCC methods to building investment decisions will help to assure that the cost effectiveness of alternative building projects can be compared in a consistent and technically

correct manner. This will assist the building community in making cost-effective building

inves tments

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The members of ASTM who attended the Building Economics Subcommittee meeting in October

1979 in Champsign-Urbana agreed upon the basic elements that should be included in an initial life-cycle cost recommended practice. That meeting helped determine the framework

of this paper, and therefore special thanks are due those ASTM attendees, including

Raymond Albrecht, Donald Carr, Susan Christmas, Earl Ferguson, Selwyn Fox, J. Heslip,

David Jeanes, Morris Lleff, Frederick Pneuman, George Ratliff, John Ryan, Jerry Severson,

John Smith, and Christopher Tyson.

Thanks are also due our colleagues at the National Bureau of Standards who assisted in the

preparation of this report. Special appreciation is extended to James Gross for his

reviews and guidance in this project, to Stephen Roberts for his work on the sample

investment problem, and to Wayne Stlefel, Charles Mahaffey, and Barry Jackson for their

excellent reviews of earlier drafts. Appreciation is also due Mary Ramsburg who typed

the manuscript.

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ABSTRACT

Rising prices of labor, material, and particularly energy have forced builders, architects,

engineers, building owners and operators, and code writers to identify building designs

and building systems that will be cost effective in the long run. This report describes

how to measure the life-cycle costs of buildings and building systems. Life-cycle cost

analysis, when applied to building investment decisions, provides an economic evaluation

of the net dollar effect, over time, of purchasing, constructing/installing, maintaining,

operating, repairing, and replacing buildings or building systems. This recommended

practice for making life-cycle cost evaluations will assist the private and public building

communities in making cost-effective decisions.

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TABLE OF CONTENTS

Page

PREFACE ill

ABSTRACT v

LIST OF FIGURES vii

LIST OF TABLES vii

1. INTRODUCTION 1

1.1 Scope and Organization 1 1.2 Definitions 2 1.3 The Life-Cycle Cost Method and Evaluation Techniques 6 1.4 Procedures for Total Life-Cycle Cost (TLCC) Evaluation: An Overview 7

2. IDENTIFY OBJECTIVE, ALTERNATIVES, AND CONSTRAINTS 8

3. ESTABLISH BASIC ASSUMPTIONS 9 3.1 Time Horizon 9 3.2 Discount Rate 10

3.3 Level of Comprehensiveness 10

4. COMPILE DATA 12

4.1 Data Requirements 12

4.2 Cash Flows 12

4.3 Inflation 14

5. DISCOUNT ALL CASH FLOWS TO A COMPARABLE TIME BASIS 16

7 6. COMPUTE TLCC°s AND COMPARE ALTERNATIVES 20

7. RECOMMENDED APPLICATIONS 25

8. ELEMENTS OF A TLCC REPORT 26

APPENDICES

A. DISCOUNT FACTORS 27

B. COMPUTER PROGRAM TO CALCULATE TOTAL LIFE-CYCLE COSTS (TLCC) 36 1

C. TLCC EVALUATION FOR A SAMPLE INVESTMENT PROBLEM 55

D. SELECTED LCC REFERENCES 66

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LIST OF FIGURES

Page

FIGURES

1. ILLUSTRATION OF A CASH FLOW DIAGRAM 13

2. ILLUSTRATION OF DISCOUNTING CASH FLOWS TO PRESENT VALUE 19

LIST OF TABLES

1. DISCOUNT FORMULAS 17

2. ILLUSTRATION OF DISCOUNTING CASH FLOWS 18

A-l 6% DISCOUNT FACTORS 27

A-2 8% DISCOUNT FACTORS 28

A-3 10% DISCOUNT FACTORS 29

A-4 12% DISCOUNT FACTORS 30

A-5 15% DISCOUNT FACTORS 31

A- 6 20% DISCOUNT FACTORS 32

A-7 8% UPW* FACTORS MODIFIED FOR ENERGY PRICE ESCALATION 33

A-8 10% UPW* FACTORS MODIFIED FOR ENERGY PRICE ESCALATION 34

A-9 12% UPW* FACTORS MODIFIED FOR ENERGY PRICE ESCALATION 35

B-l SAMPLE TLCC COMPUTER PROGRAM OUTPUT 50

B-2 SAMPLE INPUT DATA FILE FOR TLCC COMPUTER PROGRAM 51

B-3 INPUT VARIABLES TO TLCC COMPUTER PROGRAM 52

B-4 INTERMEDIATE CALCULATION VARIABLES USED IN TLCC COMPUTER PROGRAM 53

B-5 DATA FORMAT FOR TLCC COMPUTER PROGRAM 54

C-l SAMPLE INVESTMENT PROBLEM: DATA AND ASSUMPTIONS 55

C-2 ALTERNATIVE 1: FUEL COSTS WITHOUT ADDITION OF THE WASTE HEAT RECOVERY

SYSTEM 57

C-3 ALTERNATIVE 1: OPERATION AND MAINTENANCE COSTS WITHOUT ADDITION OF THE

WASTE HEAT RECOVERY SYSTEM 58

C-4 ALTERNATIVE 1: TLCC OF CONTINUING USE OF THE EXISTING FURNACE WITHOUT

ADDITION OF THE WASTE HEAT RECOVERY SYSTEM 59

C-5 ALTERNATIVE 2: FUEL COSTS WITH THE WASTE HEAT RECOVERY SYSTEM 60

C-6 ALTERNATIVE 2: PURCHASE AND INSTALLATION COST OF THE WASTE HEAT RECOVERY

SYSTEM 61

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LIST OF TABLES (Continued)

Page

C-7 ALTERNATIVE 2: DEPRECIATION ALLOWANCES FOR THE WASTE HEAT RECOVERY SYSTEM ... 62

C-8 ALTERNATIVE 2: RESALE VALUE, NET OF CAPITAL GAINS TAX, FOR THE WASTE

HEAT RECOVERY SYSTEM 63

C-9 ALTERNATIVE 2: NON-FUEL OPERATION AND MAINTENANCE COSTS WITH ADDITION OF THE

WASTE HEAT RECOVERY SYSTEM 64

C-10 ALTERNATIVE 2: TLCC WITH ADDITION OF THE WASTE HEAT RECOVERY SYSTEM 65

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1 . INTRODUCTION

The term "life-cycle costing" (LCC) encompasses several techniques of economic evaluation

which are similar to the extent that they provide a measure of economic performance of an investment over some period of time extending into the future. These techniques differ

primarily in their units of measure—dollars, percent, and ratio—and, to some extent, in

their applicability to particular types of problems. One of these techniques, referred to

herein as the total life-cycle cost (TLCC) technique, means the summing, in either present

value or annual value dollars, of all relevant costs associated with an investment or project during an appropriate time period. The TLCC technique is the focus of this

recommended practice.

Other LCC techniques, which are closely related to the TLCC technique, are the net benefits

technique, which provides a dollar measure of an investment's net profitability; the

benefit/cost or savings-to-investment ratio technique, which indicates by a numerical ratio

the size of the gross dollar return relative to the size of the investment; and the internal-rate-of-return technique, which gives the percentage yield from an investment. Another

related technique which measures economic performance over time is the payback technique,

which gives the time required for an investment to recover its costs. These other LCC

techniques will be the focus of later efforts to develop a comprehensive package of recom- mended practices for economic analysis.

1.1 SCOPE AND ORGANIZATION

This report establishes a technical base for the development of a recommended practice for

evaluating the total life-cycle costs (TLCC) of buildings and building systems. The TLCC

technique measures in present value or annual value dollars the total of all relevant costs

associated with an investment decision.

Following a section on relevant definitions, a brief overview of the life-cycle costing

(LCC) concept and specific LCC techniques is given in part 1 for perspective. In parts 2 through 6, the procedures for using the TLCC technique are described step by step. The

major categories of costs typically treated in a TLCC evalution are identified. Major

assumptions required for measuring TLCC are listed and guidelines for making assumptions

and selecting parametric values to be used in the measurement are suggested. The "discounting" technique for converting costs and savings spread over time to their equivalent

values at a common time is described and equations for calculating TLCC are provided.

Following the procedures for performing TLCC analysis, part 7 describes potential applications of the TLCC technique, as well as its limitations. Part 8 identifies the information

that should be included in a report of a TLCC analysis. In support of applying the technique, appendix A gives discount factors for making present value and annual value calculations. Appendix B lists a computer program for performing TLCC calculations to further

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facilitate the use of this technique. This same appendix gives an example of the use

of the computer program to solve a building investment problem. Appendix C gives another

example of TLCC evaluation—this one solved step-by-step manually with the solution

displayed in tabular form. References on LCC analysis are listed in appendix D.

1.2 DEFINITIONS

The following are definitions of common terms relating to LCC analysis.

(1) Annually Recurring Costs - Those costs which are incurred each year in an equal amount

or in an amount that is increasing at a constant rate throughout the study period.

(2) Annual Value (Worth) - Project costs or benefits expressed as an equivalent uniform

annual amount, taking into account the time value of money.

(3) Annuity - see "Annual Value."

(4) Base Period - The time to which all future and past costs are converted when a present

value method is used, usually the beginning of the study period (time zero).

(5) Benefit-Cost Analysis - A method of evaluating projects or investments by comparing

the discounted present value or annual value of total expected costs and benefits.

(6) Benefit-Cost Ratio (B/C) - Benefits expressed as a proportion of costs, where both

are discounted to a present or annual value. The ratio must be greater than one

for an investment to be economically justified on the basis of dollar measurable

benefits and costs.

(7) Cash Flow - The stream of dollar values—costs and benefits—resulting from a project

or investment. Cash flow analysis accounts for both dollar amounts and their time

of occurrence.

(8) Constant Dollars - Values expressed in terms of the purchasing power of the dollar

at a given time, usually the base period; i.e., constant dollars do not reflect

price inflation.

(9) Cost Effective - Estimated benefits (savings) from an investment project are equal

to or exceed the costs of the investment, where both are assessed over the life of

the project and discounted to reflect the time value of money.

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(10) Current Dollars - Values expressed in terms of the actual prices of each year; i.e.,

current dollars reflect inflation.

(11) Differential Cost - The difference in an item of cost or in the total cost of two

alternatives

(12) Differential Price Escalation Rate - The expected difference between a general rate

of inflation and the rate of increase assumed for a given item of cost, such as

energy.

(13) Discount Factor - A multiplicative number, calculated from a discount formula for a given discount rate and interest period, used to convert costs and benefits occurring

at different times to a common basis.

(14) Discount Rate - The rate of interest reflecting the investor's time value of money,

used in discount formulas or to select discount factors for converting benefits and

costs occurring at different times to a common time.

(15) Discounted Payback Period (DPB) - The time required for the cumulative benefits from an investment to pay back the investment cost and other accrued costs, considering

the time value of money.

(16) Discounting - A technique for converting cash flows that occur over time to equivalent

amounts at a common point in time.

(17) Economic Life - That period of time over which an investment is considered to be the

least-cost alternative for meeting a particular objective.

(18) First Cost - The sum of the planning, design, and construction costs necessary to

provide a finished building or building component ready for use, sometimes called

initial investment cost.

(19) Future Value (Worth) - The value of a dollar amount at some point in the future, considering the time value of money.

(20) Inflation - A rise in the general price level, or, put another way, a decline in the

general purchasing power of the dollar.

(21) Internal Rate of Return (IRR) - The compound rate of interest which, when used to discount the life-cycle costs and benefits of a project, will cause the two to be

equal

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(22) Initial Investment Cost - The sum of the planning, design, and construction costs

necessary to provide a finished building ready for use, sometimes called first cost.

(23) Life Cycle - The period of time between the starting point and cutoff date for analysis, over which the costs and benefits of a certain alternative are incurred, sometimes called the study period or time horizon.

(24) Life-Cycle Costing (LCC) - A general method of economic evaluation which considers

all relevant costs associated with an activity or project during its time horizon,

comprising the techniques of total life-cycle cost, net savings, internal rate of

return, and savings-to-investment or benefit/cost ratio analysis.

(25) Maintenance and Repair Cost - The total of labor, material, transportation, and other

related costs incurred in conducting corrective and preventative maintenance and

repair on a building and/or its systems, components, and equipment.

(26) Net Benefits (NB) - The difference between the benefits and the costs—evaluated in

present or annual value dollars—of a project, activity, or design alternative.

(27) Net Present Value of Investment-Related Costs - The present value of the initial

investment costs, plus the present value of replacement costs, less the present value

of salvage

(28) Net Savings (NS) - The difference between the savings and the costs—evaluated in

present or annual value dollars—of a project, activity, or design alternative.

(29) Nominal Discount Rate - The rate of interest reflecting the time value of money

stemming both from inflation and the real earning power of money over time. This is

the discount rate to use in discount formulas or to select discount factors when

future benefits and costs are expressed in current (i.e., inflated) dollars.

(30) Non-Annually Recurring Costs - Those costs which do not occur each year in an equal

amount nor in an amount that increases at a constant rate throughout the study

period.

(31) Operating Costs - The expenses incurred during the normal operating of a building or a building system, component, or equipment, including costs of labor, materials, and

utilities

(32) Opportunity Cost of Capital - The rate of return available on the next best available

investment, indicative of the appropriate value of the discount rate.

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(33) Present Value (Worth) - The value of a benefit or cost at the present time (i.e., as

of the base period), found by discounting future cash flows to the present.

(34) Present Value (Worth) Factor - The discount factor by which a future value may be

multiplied to find its value at the present time.

(35) Real Discount Rate - The rate of interest reflecting the real earning power of

money over time. This is the discount rate to use in discount formulas or to select

discount factors when future benefits and costs are expressed in constant dollars.

(36) Replacement Cost - Any significant future component replacement, included in the

capital budget, which is expected to be incurred during the study period in order

to maintain the investment at a functional level.

(37) Resale Value - The net sum to be realized from disposal or sale of an asset at the

end of its economic life, at the end of the study period, or whenever it is no longer

to be used.

(38) Salvage Value - For the purpose of calculating depreciation expenses, the value estimated to remain at the end of the depreciation period.

(39) Savings-to-investment Ratio (SIR) - Either the ratio of present value savings to

present value investment costs, or the ratio of annual value savings to annual value

investment costs.

(40) Sensitivity Analysis - Testing the outcome of an evaluation by altering the value of

one or more parameters from the initially assumed value(s).

(41) Simple Payback Period (SPB) - A measure of the length of time required for the

cumulative benefits, net of cumulative future costs, from an investment to pay back

the initial investment cost, without taking into account the time value of money.

(42) Study Period - The length of time over which an investment is analyzed, sometimes

referred to as the time horizon or life cycle.

(43) Sunk Cost - A cost which has already been incurred and should not be considered in

making a subsequent investment decision.

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(44) Time Horizon - The length of time over which an investment is analyzed, sometimes

referred to as the study period or life cycle.

(45) Time Value of Money - The time-dependent value of money that may stem both from changes

in the purchasing power of money (i.e., inflation or deflation), and from the real

earning potential of alternative investments over time. The time value of money

is indicated by the rate of interest which will cause the value of a dollar received

at some future time to be equivalent in value, from the standpoint of the investor,

to a dollar received today.

(46) Total Life-Cycle Costs (TLCC) - A technique of life-cycle costing which finds the sum

of the costs of the initial investment (less salvage value), replacements, operations

including energy use, and maintenance and repair, over the life-cycle of an investment,

expressed in present or annual value dollars.

(47) Useful Life - The period over which an investment continues to generate benefits or savings.

1.3 THE LIFE-CYCLE COST METHOD AND EVALUATION TECHNIQUES

The basic premise of the LCC method is that to an investor or decision maker all costs

arising from an investment decision are potentially important to that decision, including

future as well as present costs. The LCC method applied to buildings, building systems,

and building practices results in an economic evaluation that encompasses the net effect, over time, of purchasing, constructing/installing, maintaining, operating, repairing, and

replacing buildings or building systems. This method is referred to herein as the LCC

method. (1-8)^

A number of alternative economic evaluation techniques exist. Those techniques which are consistent with the LCC method are referred to as LCC techniques. LCC techniques are more comprehensive in their coverage than are economic evaluation techniques which do not encompass all relevant costs over time, and, therefore, conceptually provide the more accurate measures of economic performance. LCC techniques include the Total Life-Cycle Cost (TLCC)

Technique (the focus of this report and of the ASTM's initial recommended practice for LCC

analysis), the Net Benefits or Net Savings (NB or NS) Technique, the Benefit/Cost or Savings-to-Investment Ratio (B/C or SIR) Technique, and the Internal-Rate-of-Return (IRR)

Technique.

1 Numbers in the parentheses refer to the list of references appended to this report.
Related techniques are the Discounted Payback (DPB) and Simple Payback (SPB) Techniques.

These two techniques are not fully consistent with the LCC concept because they evaluate

costsor partial costs in the case of Simple Payback—over a time period limited to the

time required to recover investment costs, which may be shorter than the time relevant to

the investor or decision maker.

1.4 PROCEDURES FOR TOTAL LIFE-CYCLE COST (TLCC) EVALUATION: AN OVERVIEW

I The recommended procedures for measuring the TLCC of a building or building system can be

summarized in five basic steps as follows:

1. Identify Objective, Alternatives, and Constraints

2. Establish Basic Assumptions

3. Compile Data

4. Discount All Cash Flows to a Comparable Time Basis

5. Compute TLCC's and Compare Alternatives

In the following sections 2 through 6, each of these steps is addressed further.

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2. IDENTIFY OBJECTIVE, ALTERNATIVES, AND CONSTRAINTS

First, establish the specific objective of the investor or decision maker, identify alternative ways of accomplishing that objective, and bring out any constraints that limit the

available options to be considered. This sets the framework for the TLCC analysis.

An example of a building-related objective that might be addressed by TLCC analysis is the

objective of reducing the total costs of the interior furnishings of a building over its

useful life. Examples of constraints in meeting this objective are that neither the functional use of the building can be altered nor the productivity of its occupants lowered.

For instance, if a certain level of illumination is required, all alternative lighting

systems should provide the required level of illumination. General examples of potential

ways of accomplishing the cost-reduction objective are to change the quality of the furnishings, to change the maintenance on the furnishings, or to change the length of time the

furnishings are kept in service.

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3. ESTABLISH BASIC ASSUMPTIONS

Second, set the basic assumptions that are to be followed in applying the TLCC technique

to the investment problem at hand. Assumptions usually include, among other things, the

time period over which the evaluation is to be made, the value of the discount rate, and

the level of comprehensiveness of the TLCC evaluation.

3.1 TIME HORIZON

The selection of a time horizon, the study period over which an investment is analyzed,

depends on the personal time perspective of the building investor. It may be much shorter

than either the economic life or useful life of the building investment. While there are generally no fixed time horizons for investment projects, the following general guidelines

can be given for selecting a time horizon:

(1) When analyzing an investment from the standpoint of determining the economically

efficient decision for society, a relatively long time horizon, close or equal to

the useful life of the investment, is recommended.

(2) When analyzing an investment from the standpoint of predicting the investment

decision that a certain type or group of investors might make—the view a marketing researcher, for instance, might take—an estimate of the "subject's"

time horizon is recommended.

(3) When analyzing an investment from a personal or individual investor's standpoint,

the use of the specific investor's time horizon is recommended. For a speculative

investor, the time horizon might be based on the holding period that is expected

to maximize speculative profits. For a homeowner, the time horizon for houserelated investments might equal the remaining life of the mortgage, the length

of expected occupancy, or the time until resale. For a non-speculative business,

the time horizon for an investment in an owner-occupied building might be the

economic or useful life of the building or building system, and for an investment

property, the time horizon might be selected on the basis of the depreciation

period, the financing period, or the intended holding period. For investments by government agencies and large corporations, specific guidelines often

direct the choice of time horizons.

(4) Regardless of the type of investor or purpose of the analysis, a general guideline for selecting a time horizon when calculating the present value of all

costs associated with an investment is to use the same time horizon for each

cost category.

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(5) Furthermore, when comparing investment alternatives on the basis of their TLCC's

in present value dollars, the same time horizon must be used for each investment

alternative.

3.2 DISCOUNT RATE

The discount rate is selected to reflect the investor's time value of money. The discount

rate is used to convert costs occurring at different times to a common time. The discount

rate should reflect the rate of interest which makes the investor indifferent between

paying or receiving a dollar now or at some future time. Discount rates may be expressed

in "nominal" (market) terms, where both the effects of inflation and the real earning

power of money invested over time are reflected, or in "real" terms, where only the real

earning power of money is reflected and inflation is not included.

As in the case of time horizons, there is no single correct discount rate for all investors.

However, again some general guidelines can be given:

(1) The discount rate should be selected to reflect the investor's particular time

preference for money (5,9). This appropriate rate may be guided by the level of

return on alternative investment opportunities, on the cost of borrowing money,

or, in the case of public organizations, on mandated or legislated requirements.

The earning rate available on alternative investments should take precedence over

the borrowing rate as an indicator of the appropriate discount rate if that

earning rate exceeds the borrowing rate.

(2) A nominal discount rate should be selected if estimates of future costs and

benefits include inflation.

(3) A real discount rate should be selected if estimates of future costs and benefits

do not include inflation.

3.3 LEVEL OF COMPREHENSIVENESS

A TLCC evaluation is usually performed to one o.J three levels of comprehensiveness: Before

taxes and before inflation (BTBI), after taxes and before inflation (ATBI), and after taxes

and after inflation (ATAI) (6). The level of comprehensiveness selected for a TLCC evaluation depends chiefly on (1) the degree of complexity of the problem, (2) the intended

purpose of the evaluation, (3) the level of monetary and non-monetary impacts contingent

on the investment decision, (4) the cost of the evaluation, and (5) the evaluation resources available to the investor or decision maker.

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Following are some general guidelines for establishing when to undertake an economic

evaluation and the level of comprehensiveness for the evaluation:

(1) When costs of investment, operation, repair, and replacement are negligible, and

there are expectations of savings, project cost effectiveness can generally be

presumed without a formal economic evaluation.

(2) For a government or non-profit investment, a BTBI evaluation will usually

suffice. (The BTBI approach does not preclude the inclusion of differential

price escalation rates to adjust for price changes faster or slower than general

price inflation).

(3) For a private investment subject to taxes, either an ATBI or an ATAI evaluation

is usually recommended. If significant items of cost are anticipated to be

fixed in amount or to rise at a rate faster or slower than general price inflation, the ATAI evaluation is recommended.

11
4. COMPILE DATA

4.1 DATA REQUIREMENTS

Third, compile the basic data required to measure the TLCC of the potential alternatives

for meeting the objective. For measuring the TLCC of an alternative building design, building system, or building practice, typical cost categories for which data will be needed are investment costs, including the costs of planning, design, engineering, construction, purchase, installation, and financing; non-fuel operating and maintenance costs, including

the materials and labor costs for routine upkeep and operation other than energy; repair

and replacement costs, including future costs to repair or replace a building system or component thereof which wears out; energy costs; and property and capital gains taxes.

Data will also be needed for any cost-reducing items, such as resale values, tax deductible

expenses, tax credits, and grants or other subsidies (10,11). Other data requirements

are for tax rates, depreciation methods and periods, and financing terms. As the time

horizon considered becomes shorter than the expected useful lifetime, it becomes more

critical to include the proper assessment of salvage or resale value in the TLCC analysis,

and, hence, greater attention to this value is recommended when time horizons are short.

Costs and offsetting benefits which are not relevant to the decision can be omitted from

the TLCC evaluation. For example, sunk costs, as well as those present and future costs

which are not affected by the investment decision in question, need not be included in the

TLCC evaluation.

4.2 CASH FLOWS

In addition to compiling the dollar amounts of the relevant costs and benefits, determine

when each will occur. This information is essential for discounting dollars in past or

future years to a common point in time.

A convenient and widely used diagrammatical aid for describing cash flows is a cash flow

diagram such as the one illustrated in figure 1. Figure 1 shows the cash flows for a hypothetical project over 10 years. The initial investment is $6,000; the yearly non-fuel

operating and maintenance cost is $100 in constant dollars; the yearly energy cost is $1,000

evaluated at present prices and is expected to increase each year at a compound rate 5 percent faster than general price inflation; the fifth year's replacement cost is $500 in

constant dollars; the salvage value at the end of the 10 year time horizon is $1,200.

The initial investment is assumed to occur at the beginning of the first year, i.e., the

base period, and all other amounts are assumed to occur at the end of the year in which

they accrue.

12
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Inflows).
4 . 3 INFLATION

When all costs and benefits over the time horizon of an investment can be reasonably

assumed to inflate at about the same rate as prices in general, and the income tax bracket

of the investor is not expected to change significantly as inflation pushes prices (and

nominal profits) higher, a "real" discount rate can be used to convert future constant

dollar cash flows to present value.

When all costs over the time horizon cannot reasonably be expected to increase at the same rate, inflation should be included in a life-cycle cost analysis (1,6). Taking this

approach, the following guidelines apply:

(1) Future costs that are fixed in amount and therefore are not responsive to inflation should not be adjusted to include inflation. Examples are loan payments

and contracted future costs not subject to a price escalation clause.

(2) Future costs that are expected to change at rates significantly different from

the general rate of price increase (e.g. energy costs) should be estimated on

the basis of the specific rate of price change expected, be it faster or slower

than the general rate of price increase.

(3) All other future costs should be estimated to reflect the rate of general price

inflation.

(4) A "nominal” discount rate which includes inflation should be used.

As an alternative to including inflation in each cost category and in the discount rate,

the general rate of inflation may be omitted from all cost escalation rates and from the

discount rate, and only the differential rate of price change should then be included in

each cost category. Taking this approach, the following guidelines apply:

(1) Those future costs expected to change faster than the rate of inflation should

be Increased only to reflect the rate of price escalation in excess of general

inflation.

(2) Future costs expected to change slower than the general rate of inflation should

be reduced to reflect the difference between the rate of price escalation for

the particular cost category and the general rate of inflation.

(3) Those costs expected to increase approximately at the general rat6 of inflation

should not be adjusted.

14
(4) Costs fixed in amount by contract should be reduced by exactly the rate of

inflation in each year prior to discounting.

(5) A real discount rate should be used to convert future cash flows to present

value.

15
5. DISCOUNT ALL CASH FLOWS TO A COMPARABLE TIME BASIS

1

Fourth, discount all cash flows to a comparable time basis—either to present values or annual values. This step is necessary before the various costs can be summed to derive

the TLCC measure.

Discounting is performed by applying discount formulas, or corresponding discount factors

calculated from these formulas, to the estimated data associated with a given investment

alternative. Table 1 depicts the most commonly used discounting formulas, indicates their

use, and gives their algebraic form. Appendix A gives discounting factors based on the

formulas in table 1 for selected discount rates and time periods.

Apply the appropriate formula or factor to a cash amount to convert it to its equivalent

value at a selected time. Select a common time to adjust all cash amounts—either (1) the

present, whereby all cash amounts are converted to an equivalent value occurring now, i.e.,

to a present value , or (2) annually, whereby all cash amounts are converted to a time

equivalent value occurring in a uniform amount each year over the time horizon, i.e., to an annual value .

Table 2 illustrates the use of the discount formulas and factors to find present value and

O annual value equivalents for the same set of cost data given in figure I. Figure 2 illustrates graphically the relationship between these data and their equivalent present

values. The sum of the present values shown at the top of the vertical axis is $15,048.

1 The adjustment of all cash flows to a common-time equivalent value is necessary because

a dollar received or expended in the base year does not have the same value as it would

if it were received or expended in the future. One causal factor in the time dependency

of value Is the earning potential of money in hand (actually the resources money can

buy). That is, a dollar received now can be put to use to generate additional income,

whereas a dollar to be received in the future offers no earning potential in the interim

Similarly, an expense that must be paid now draws resources from the investor which

cannot be used for other productive purposes. If the funds to meet the expense are

borrowed, the investor must pay a borrowing charge to compensate the lender for the loss

of Income from falling to invest those funds in other endeavors. This earning potential

of money is often called the opportunity cost of capital, and it occurs independently

of Inflation or deflation. The second causal factor in the time dependency of value is

the change in the purchasing power of the dollar reflected in price inflation or price

deflation.

2 For any given set of cost data and assumptions, the present value of an investment and

the annual value of the same investment are time equivalent values.

16
TABLE 1. DISCOUNT FORMULAS

Formula Name Illustration Use Algebraic Form

Single Compound

Amount Formula (SCA) -0 To find F when

P is known

F - P • (1 + i) N

Single Present Value

Formula (SPW) To find P when P - F . 1 D -E F is known (Th^

Uniform Sinking Fund

Formula (USF) dU + [Af] till — 0

To find A when

F is known A - F. 1 (1 + i)R-l

Uniform Capital Recovery

Formula (UCR) _ [Af] + dH**'* [at]

To find A when

P is known A - p-iq +

(i + i)"-i

Uniform Compound

Amount Formula (UCA) Q + 0 s- 0

To find F when A is known

F - A • (1 + i) N-l

i

Uniform Present To find P when P - A (1 + i)J-l

Value Formula (UPW) 0 -0 + cs A is known i(l + i)"

/ x f

Uniform Present Value 0 • • To find P when A is P - A /1 + e\ | 1 Formula Modified (UPW*) p? *-L— + escalating at rate e

5 U

~ *) l

Where:

P - a present sum of money.

F “ a future sum of money.

i - an interest or discount rate for the period being considered.

N - number of interest or discounting periods.

A - an end-of-period payment (or receipt) in a uniform series of payments (or receipts) over N periods at i interest or discount rate.

e 3 rate of escalation of A in each of N periods.

F? - indicates a future value to be found; P?, a present value to be found; and A?, an annual

value to be found.

To find P when A is escalating at a different rate over each of k escalation periods,

where n^ = the length of the period for a given escalation rate in a given period, and the subscript h indicates the escalation period; and

17
TABLE 2. ILLUSTRATION OF DISCOUNTING CASH FLOWS

(Based on a Time Horizon of 10 Years, a Real Discount Rate of 8%, and End-of-Year Payments)

Description of Cash Flow Discounting to Present Value Equivalents Discounting to Annual Value Equivalents

(1)

Discount

Formula®

(2)

Corresponding

Discount

Factor*5 (3)

Present

Value,

Dollars0 (A)

Discount

Formula

(5)

Corresponding

Discount Factor

(6)

Annual

Value,

Dollars**

(7)

Initial Investment cost of $6,000 n.a.

e

1 6,000 UCR 0.903 894

Replacement Cost in 5th

year of $500, constant $ SPW 0.6806 340 UCR 0.14903 51

Yearly (non-energy) O&M Cost

over 10 years of $100, Constant $ UPW 6.710 671 UCR 0.14903 100

Yearly Energy Cost over 10 years, beginning at $1,000,

in base period dollars, and

escalating at a rate of 5Z per year UPW* 8.5923 8,593 UCR 0.14903 1,281

Salvage value of $1,200 at end of 10th year, constant $ SPW 0.4632 556 UCR 0.14903 83

a From table 1.

b From appendix A.

c Col. 4 - amount In col. 1 x discount factor in col. 3.

** Col. 7 - amount in col. 4 x discount factor in col. 6.

e No discounting necessary.

18
$15,048

Figure 2. Illustration of Discounting Cash Flows to Present Value
6. COMPUTE TLCC's AND COMPARE ALTERNATIVES

After all cash amounts relevant to a given investment have been discounted to present value

or annual value dollars, combine them to obtain a measure of TLCC. Then compare the TLCC measures for the various investment alternatives to determine the alternative with the

minimum TLCC. Other things being equal, the alternative with the lowest TLCC is preferred

on economic grounds.

On a before-tax basis, the TLCC of a building or building system can be formulated in simple

terms as

TLCC =C+R-S+A+N+E, (1)

where C = investment costs,

R = capital replacement costs,

S - resale value of investment at end of study period,

A annually recurring operating maintenance and repair costs (except fuel

costs),

N « non-annually operating recurring maintenance, and repair costs,

E * fuel costs,

and all costs are in life-cycle present value or annual value dollars.

A more comprehensive TLCC analysis will include adjustments for financing of investment

costs as well as tax adjustments.^ That is,

TLCC =D+F+P+R-S-Tj-Tj dlcg -T_+T„+A+N+E+Tpo- T„ (2) v/

* Note that all tax credits and tax deductible items are assumed to result in end-of-year

cash flows. In computing income taxes, a composite marginal income tax rate (Tl) com- prising Federal, State, and local taxes is used. This rate may be calculated as follows:

Tl - T

p

<1 - T

s - Tl

) + T

g +Tl ,

where Tp marginal Federal income tax rate,

Tg ** marginal State income tax rate, and

T

y = marginal local income tax rate.

20
where D - down payment on project,

F all finance costs and principal payments,

P any principal remaining at end of study period,

R = capital replacement costs,

S = resale value of investment at end of study period,

= tax savings from depreciation allowance,

= tax savings from interest payments,

T

c = tax credits,

T = capital gains taxes,

O

A ** annually recurring operating, maintenance and repair costs,

N = non-annually recurring operating, maintenance and repair costs (except

fuel costs),

E = fuel costs,

Tp = property taxes,

T

q = tax savings for all operating-related costs (i.e., for A, N, E, T

p

),

and all costs are in life-cycle present value or annual value dollars.

The cost components of this more comprehensive TLCC can be calculated in present value

dollars as follows*:

D " C

l - Fl (1 - F5

) (3)

F = (FjXFyXFg) (4)

P = X

1 jNl 7 ^ 1 + n> Nl

C12 Y

R = z (Rk ) ((l + c7 )/(l + il)) k

(6)

k=l

C

S = (C

L

) (C U)((1 + c7 )/(l + II)) 13 (7)

Nl

T

d = Z ^ Za

,

+ 11 > j (8)

j=l

All notation to right of "equals” sign is consistent with variables used

in the TLCC computer program given in appendix B.

21
N1

T

i = Z ( x

2 , j) (Tl)/(1 + Il) j (9)

j=l

T

c - (C

9

) (C 1 )/(l-t-Il) (10)

C T

g - [ (D7 - ((^ - D

x )) (T3) + (D2 - D

x

) (Tl)]/(1 + II) 13 if D7 > (Cj_ - D

x ), (11)

or

C T

g = [ (D7 - (C

x - D2 )) (Tl)]/(1 + II) 13 if (Cj_ - > D7 > (C^ - D

2

)

A = (Ml) (M3)

M4 M

N = l ( m

2 ^ j) (d + M5)/(l + II))

( 12 )

(13)

(14)

E - (E

x

) (E 3) (15)

C

13 T =2 (C

L - D8) (C

g

) (T2) ((1 + C

? )/(l + II)) 3 "1 (16)

j=l

(Property tax in the first year is calculated as a percentage of the assessed value of the

asset, which in turn is a percentage of the first cost. In order to determine the base

value for estimating assessed value in future years, the asset is "depreciated" over its

actual expected useful life on a straight-line basis. The resulting depreciated value is

then adjusted upwards each year by the rate of cost inflation for that asset category.)

T

q

= (A + N + E + T

p

) (Tl) (17)

where:

C^ = total purchase cost,

Cy = cost inflation rate,

Cg = first year assessed value for property tax basis (% of Cj),

Cg = investment tax credit (% of C^),

C^q = actual expected useful life,

Cfi = estimated resale value at end of useful life or end of study period,

whichever comes first (% of in base-year dollars),

^12 = nurn ber °f replacements during study period,

C^

3 = actual expected life of capital investment or study period, whichever is shorter,

22
D

1 = accumulated depreciation using straight-line method,

D

2 - accumulated depreciation using alternative method,

C

D7 = actual selling price = (C^) (C^

(1 + Cy)

E^ = annual fuel costs in base-year prices.

Eg = UPW* factor based on cost inflation rates for the fuel type used, study period,

and discount rate,

= amount borrowed,

F

2 = life of loan,

Fg = loan interest rate,

F^ = number of payments per year,

Fg = "points" paid (% of F^),

Fy = uniform capital recovery (UCR) factor for given interest rate (Fg) and loan life

(f2 ),

Fg = loan life (F 2

) or study period length (Nl), whichever is shorter,

Fg = uniform present value factor for given discount rate (II) and time period (Fg),

II = discount rate,

Ml = annually recurring operation, maintenance and repair costs (except fuel costs),

in base-year dollars,

M2 = cost inflation rate for operation, maintenance and repair cost (except fuel costs),

M3 = UPW* factor based on study period (Nl), cost inflation rate (M2), and discount rate

(ID,

M4 = number of non-annually recurring operation, maintenance and repair costs (except

fuel costs),

M5 = cost inflation rate for non-annually recurring operation, maintenance and repair

costs,

Nl = study period length,

= kth capital replacement cost, in base-year dollars,

XI = marginal income tax rate (composite Federal, State and local),

T2 = property tax rate,

T3 = capital gains tax rate.

23
*

2,3

Y

k

z 2,3

j

interest paid in year *,

year of kth capital replacement, and

amount of depreciation taken in year j.

* Assuming equal loan payments in each time period.

F

4 *

2,3 " ^

^ x

3 ,k-l^ (F2 /F4>

where X

2 ^ remaining principal after each loan payment, k = 1 , 2 . P

4 ; q remaining principal at end of previous year

24
7 . RECOMMENDED APPLICATIONS

The TLCC measure can be used to determine whether or not to make an investment. For

example, if the addition of insulation to a building reduces the TLCC (i.e., the reduction

in energy costs outweighs the increase in the investment costs), then it is economical to

make that investment.

The TLCC technique can also be used to determine the efficient level of investment (i.e.,

scale or size of investment). For example, as long as the TLCC falls with added insulation, it is profitable to increase the insulation level. If the TLCC increases with added

insulation, it is not profitable to increase the insulation level. The economically

efficient (or optimal) level of insulation is the level for which TLCC is minimized.

Substitutable investment projects for a given purpose can be compared by examining their

TLCC's, provided they are evaluated over the same time horizon. For example, if a building

owner has a choice between a conventional heating/cooling system and a solar energy

system with a conventional system backup, both of which meet thermal performance requirements, the system with the lower TLCC would be the more cost effective as long as other

things were equal (11-13).

A limitation on the application of the TLCC technique is for allocating a limited budget

among investment projects. Because it does not provide a measure of the return per investment dollar, choosing investment projects on the basis of their TLCC measures alone will

not necessarily result in the largest possible cost reductions for a given budget. The

benefit/cost or savings-to-investment ratio technique or the internal-rate-of-return

technique are preferred to the TLCC technique for allocating limited budgets among multiple

investment opportunities for maxi mum economic efficiency.

25
8. ELEMENTS OF A TLCC REPORT

A report of a TLCC analysis should state the objective, the constraints, the alternatives

considered, and the key assumptions and data. Items whose values should be made explicit

include the discount rate, the time horizon, and the main categories of cost data, including

initial costs, recurring and non-recurring costs, resale values, and grants, tax deductibles, credits, and expenses, as well as financing terms if applicable. The tax status of

the investor should be given, together with the method of treating inflation, and the level

of comprehensiveness of the analysis. Any significant effects that remain unquantified

should also be described in the TLCC report.

Two examples of applying the TLCC technique to building investment problems are given in

appendices to this report. Appendix B, which contains a computer program for calculating

TLCC, gives an illustrative case example solved by the computer program. The computer

printout includes a display of the key elements that are necessary for an understanding

of the problem and its solution. Appendix C presents an additional problem example—this

one solved manually step by step in tabular form. Again, the objective, the alternatives,

and the key data and assumptions are set forth, as well as the conclusions.

26
APPENDIX A

Discount Factors

Table A-l 6% Discount Factors

Single Single Uniform Uniform Uniform

Compound Present Sinking Capital Compound Present

amount value fund recovery amount value

factor factor factor factor factor factor

n SCA SPW USF UCR UCA UPW

1 2 3 4 5 6 7 n

1 1.0600 0.9434 1.00000 1.06000 1.000 0.943 1 2 1.1236 0.8900 0.48544 0.54544 2.060 1.833 2 3 1.1910 0.8396 0.31411 0.37411 3.184 2.673 3 4 1.2625 0.7921 0.22859 0.22859 4.375 3.465 4

5 1.3382 0.7473 0.17740 0.27340 5.637 4.212 5

6 1.4185 0.7050 0.14336 0.20336 6.975 4.917 6 7 1.5036 0.6641 0.11914 0.17914 8.394 5.582 7 8 1.5938 0.6274 0.10104 0.16104 9.897 6.210 8

9 1.6895 0.5919 0.08702 0.14702 11.491 6.802 9 10 1.7908 0.5584 0.70587 0.13587 13.181 7.360 10

11 1.8983 0.5268 0.06679 0.12679 14.972 7.887 11 12 2.0122 0.4970 0.05928 0.11928 16.870 8.384 12 13 2.1329 0.4688 0.05296 0.11296 18.882 8.853 13

14 2.2609 0.4423 0.04758 0.10758 21.015 9.295 14

15 2.3966 0.4173 0.04296 0.10296 23.276 9.712 15

16 2.5404 0.3936 0.03895 0.09895 25.673 10.106 16

17 2.6928 0.3714 0.03544 0.09544 28.213 10.477 17

18 2.8543 0.3503 0.03236 0.09236 30.906 10.828 18

19 3.0256 0.3305 0.02962 0.08962 33.760 11.158 19 20 3.2071 0.3118 0.02718 0.08718 36.786 11.470 20

21 3.3996 0.2942 0.02500 0.08500 39.993 11.764 21

22 3.6035 0.2775 0.02305 0.08305 43.392 12.042 22 23 3.8197 0.2618 0.02128 0.08128 46.996 12.303 23

24 4.0489 0.2470 0.01968 0.07968 50.816 12.550 24

25 4.2919 0.2330 0.01823 0.07823 54.865 12.783 25

26 4.5494 0.2198 0.01690 0.07690 59.156 13.003 26

27 4.8223 0.2074 0.01570 0.07570 63.706 13.211 27

28 5.1117 0.1956 0.01459 0.07459 68.528 13.406 28

29 5.4184 0.1846 0.01358 0.07358 73.640 13.591 29

30 5.7435 0.1741 0.01265 0.07265 79.058 13.765 30

31 6.0881 0.1643 0.01179 0.07179 84.802 13.929 31

32 6.4534 0.1550 0.01100 0.07100 90.890 14.084 32 33 6.8406 0.1462 0.01027 0.07027 97.343 14.230 33

34 7.2510 0.1379 0.00960 0.06960 104.184 14.368 34 35 7.6861 0.1301 0.00897 0.06897 111.435 14.498 35

40 10.2857 0.0972 0.00646 0.06646 154.762 15.046 40

45 13.7646 0.0727 0.00470 0.06470 212.744 15.456 45

50 18.4202 0.0543 0.00344 0.06344 290.336 15.762 50

55 24.6503 0.0406 0.00254 0.06254 394.172 15.991 55 60 32.9877 0.0303 0.00188 0.06188 533.128 16.161 60

65 44.1450 0.0227 0.00139 0.06139 719.083 16.289 65

70 59.0759 0.0169 0.00103 0.06103 967.932 16.385 70

75 79.0569 0.0126 0.00077 0.06077 1300.949 16.456 75

80 i io.7960 0.0095 0.00057 0.06057 1746.600 16.509 80

85 141.5789 0.0071 0.00043 0.06043 2342.982 16.549 85

90 189.4645 0.0053 0.00032 0.06032 3141.075 16.579 90

95 253.5463 0.0039 0.00024 0.06024 4209.104 16.601 95

100 339.3021 0.0029 0.00018 0.06018 5638.368 16.618 100

27
Table A-2 8% Discount Factors

Single Single Uniform Uniform Uniform

Compound Present Sinking Capital Compound Present

amount value fund recovery amount value

factor factor factor factor factor factor n SCA SPW USF UCR UCA UPW

1 2 3 4 5 6 7

1 1.0800 0.9259 1.00000 1.08000 1.000 0.926 1 2 1.664 .8573 0.48077 0.56077 2.080 1.783 2 3 1.2597 .7938 .30803 .38803 3.246 2.577 3 4 1.3605 .7350 .22192 .30192 4.506 3.312 4 5 1.4693 .6806 .17046 .25046 5.867 3.993 5

6 1.5869 .6302 .13632 .21632 7.336 4.623 6 7 1.7138 .5835 .11207 .19207 8.923 5.206 7 8 1.8509 .5403 .09401 .17401 10.637 5.747 8 9 1.9990 .5002 .08008 .16008 12.488 6.247 9 10 2.1589 .4632 .06903 .14903 14.487 6.710 10

11 2.3316 .4289 .06008 .14008 16.645 7.139 11 12 2.5182 .3971 .05270 .13270 18.977 7.536 12 13 2.7196 .3677 .04652 .12652 21.495 7.904 13 14 2.9372 .3405 .04130 .12130 24.215 8.244 14

15 3.1722 .3152 .03683 .11683 27.152 8.559 15

16 3.4259 .2919 .03298 .11298 30.324 8.851 16

17 3.7000 .2703 .02963 .10963 33.750 9.122 17 18 3.9960 .2502 .02670 .10670 37.450 9.372 18 19 4.3157 .2317 .02413 .10413 41.446 9.604 19 20 4.6610 .2145 .02185 .10185 45.762 9.818 20

21 5.0338 .1987 .01983 .09983 50.423 10.017 21 22 5.4365 .1839 .01803 .09803 55.457 10.201 22 23 5.8715 .1703 .01642 .09642 60.893 10.371 23

24 6.3412 .1577 .01498 .09498 66.765 10.529 24

25 6.8485 .1460 .01368 .09368 73.106 10.675 25

26 7.3964 .1352 .01251 .09251 79.954 10.810 26

27 7.9881 .1252 .01145 .09145 87.351 10.935 27 28 8.6271 .1159 .01049 .09049 95.339 11.051 28

29 9.3173 .1073 .00962 .08962 103.966 11.158 29

30 10.0627 .0994 .00883 .08883 113.283 11.258 30

31 10.8677 .0920 .00811 .08811 123.346 11.350 31 32 11.7371 .0852 .00745 .08745 134.214 11.435 32

33 12.6760 .0789 .00685 .08685 145.951 11.514 33

34 13.6901 .0730 .00630 .08630 158.627 11.587 34

35 14.7853 .0676 .00580 .08580 172.317 11.655 35

40 21.7245 .0460 .00386 .08386 259.057 11.925 40

45 31.9204 .0313 .00259 .08259 386.506 12.108 45

50 46.9016 .0213 .00174 .08174 573.770 12.233 50

55 68.9139 .0145 .00118 .03118 848.923 12.319 55

60 101.2571 .0099 .00080 .08080 1253.213 12.377 60

65 148.7798 .0067 .00054 .08054 1847.248 12.416 65

70 218.6064 .0046 .00037 .08037 2720.080 12.443 70

75 321.2045 .0031 .00025 .08025 4002.557 12.461 75

80 471.9548 .0021 .00017 .08017 5886.935 12.474 80

85 693.4565 .0014 .00012 .08012 8655.706 12.482 85

90 1018.9151 .0010 .00008 .08008 12723.939 12.488 90

95 1497.1205 .0007 .00005 .08005 18701.507 12.492 95

100 2199.7613 .0005 .00004 .08004 27484.516 12.494 100

28
Table A-3 10% Discount Factors

Single Single Uniform Uniform Uniform

Compound Present Sinking Capital Compound Present

amount value fund recovery amount value

factor factor factor factor factor factor

n SCA SPW USF UCR UCA UPW

1 2 3 4 5 6 7 n

1 1.1000 0.9091 1.00000 1.10000 1.000 0.909 1 2 1.2100 0.8264 0.47619 0.57619 2.100 1.736 2 3 1.3310 0.7513 0.30211 0.40211 3.310 2.487 3 4 1.4641 0.6830 0.21547 0.31547 4.641 3.170 4 5 1.6105 0.6209 0.16380 0.26380 6.105 3.791 5

6 1.7716 0.5645 0.12961 0.22961 7.716 4.355 6 7 1.9487 0.5132 0.10541 0.20541 9.487 4.868 7 8 2.1436 0.4665 0.08744 0.18744 11.436 5.335 8

9 2.3579 0.4241 0.07364 0.17364 13.579 5.759 9 10 2.5937 0.3855 0.06275 0.16275 15.937 6.144 10

11 2.8531 0.3505 0.05396 0.15396 18.531 6.495 11 12 3.1384 0.3186 0.04676 0.14676 21.384 6.814 12

13 3.4523 0.2897 0.04078 0.14078 24.523 7.103 13

14 3.7975 0.2633 0.03575 0.13575 27.975 7.367 14

15 4.1772 0.2394 0.03147 0.13147 31.772 7.606 15

16 4.5950 0.2176 0.02782 0.12782 35.950 7.824 16

17 5.0545 0.1978 0.02466 0.12466 40.545 8.022 17 18 5.5599 0.1799 0.02193 0.12193 45.599 8.201 18

19 6.1159 0.1635 0.01955 0.11955 51.159 8.365 19

20 6.7275 0.1486 0.01746 0.11746 57.275 8.514 20

21 7.4002 0.1351 0.01562 0.11562 64.002 8.649 21 22 8.1403 0.1228 0.01401 0.11401 71.403 8.772 22

23 8.9543 0.1117 0.01257 0.11257 79.543 8.883 23

24 9.8497 0.1015 0.01130 0.11130 88.497 8.985 24

25 10.8347 0.0923 0.1017 0.11017 98.347 9.077 25

26 11.9182 0.0839 0.00916 0.10916 109.182 9.161 26

27 13.1100 0.0763 0.00826 0.10826 121.100 9.237 27

28 14.4210 0.0693 0.00745 0.10745 134.210 9.307 28

29 15.8631 0.0630 0.00673 0.10673 148.631 9.370 29

30 17.4494 0.0573 0.00609 0.10608 164.494 9.427 30

31 19.1943 0.0521 0.00550 0.10550 181.943 9.479 31

32 21.1138 0.0474 0.00497 0.10497 201.138 9.526 32

33 23.2252 0.0431 0.00450 0.10450 222.252 9.569 33

34 25.5477 0.0391 0.00407 0.10407 245.477 9.609 34

35 28.1024 0.0356 0.03369 0.10369 271.024 9.644 35

40 45.2593 0.0221 0.00226 0.10226 442.593 9.779 40

45 72.8905 0.0137 0.00139 0.10139 718.905 9.863 45

50 117.3909 0.0085 0.00086 0.10086 1163.909 9.915 50

55 189.0591 0.0053 0.00053 0.10053 1880.591 9.947 55

60 304.4816 0.0033 0.00033 0.10033 3034.816 9.967 60

65 490.3707 0.0020 0.00020 0.10020 4893.707 9.980 65

70 789.7470 0.0013 0.00013 0.10013 7887.470 9.987 70

75 1271.8952 0.0008 0.00008 0.10008 12708.954 9.992 75

80 2048.4002 0.0005 0.00005 0.10005 20474.002 9.995 80

85 3298.9690 0.0003 0.00003 0.10003 32979.690 9.997 85

90 5313.0226 0.0002 0.00002 0.10002 53120.226 9.998 90

95 8556.6760 0.0001 0.00001 0.10001 85556.760 9.999 95

100 13780.6123 0.0001 0.00001 0.10001 137796.123 9.999 100

29
Table A-4 12% Discount Factors

Single Single Uniform Uniform Uniform

Compound Present Sinking Capital Compound Present

amount value fund recovery amount value

factor factor factor factor factor factor n SCA SPW USF UCR UCA UPW

1 2 3 4 5 6 7 n

1 1.1200 0.8929 1.00000 1.12000 1.000 0.893 1

2 1.2544 0.7972 0.47170 0.59170 2.120 1.690 2 3 1.4049 0.7118 0.29635 0.41635 3.374 2.402 3 4 1.5735 0.6355 0.20923 0.32923 4.779 3.037 4 5 1.7623 0.5674 0.15741 0.27741 6.353 3.605 5

6 1.9738 0.5066 0.12323 0.24323 8.115 4.111 6

7 2.2107 0.4523 0.09912 0.21912 10.089 4.564 7 8 2.4760 0.4039 0.08130 0.20130 12.300 4.968 8

9 2.7731 0.3606 0.06768 0.18768 14.776 5.328 9 10 3.1058 0.3220 0.05698 0.17698 17.549 5.650 10

11 3.4785 0.2875 0.04842 0.16842 20.655 5.938 11 12 3.8960 0.2567 0.04144 0.16144 24.133 6. 194 12

13 4.3635 0.2292 0.03568 0.15568 23.029 6.424 13

14 4.8871 0.2046 0.03087 0.15087 32.393 6.628 14

15 5.4736 0,1827 0.02682 0.14682 37.280 6.811 15

16 6.1304 0.1631 0.02339 0.14339 42.753 6.974 16

17 6.8660 0.1456 0.02046 0.14046 48.884 7.120 17 18 7.6900 0.1300 0.01794 0.13794 55.750 7.250 18

19 8.6463 0.1161 0.01576 0.13576 63.440 7.366 19 20 9.6463 0.1037 0.01388 0.13388 72.052 7.469 20

21 10.8038 0.0926 0.01224 0.13224 81.699 7.562 21 22 12.1003 0.0826 0.01081 0.13081 92.503 7.645 22

23 13.5523 0.0738 0.00956 0.12956 104.603 7.718 23

24 15.1786 0.0659 0.00846 0.12846 118.155 7.784 24

25 17.0001 0.0588 0.00750 0.12750 133.334 7.843 25

26 19.0401 0.0525 0.00665 0.12665 150.334 7.896 26

27 21.3249 0.0469 0.00590 0.12590 169.374 7.943 27

28 23.8839 0.0419 0.00524 0.12524 190.699 7.984 28 29 26.7499 0.0374 0.00466 0.12466 214.583 8.022 29 30 29.9599 0.0334 0.00414 0.12414 241.333 8.055 30

31 33.5551 0.0298 0.00369 0.12369 271.292 8.085 31

32 37.5817 0.0266 0.00328 0.12328 304.847 8.112 32

33 42.0915 0.0238 0.00292 0.12292 342.429 8.135 33

34 47.1425 0.0212 0.00260 0.12260 384.520 8.157 34

35 52.7996 0.0189 0.00232 0.12232 431.663 8.176 35

40 93.0510 0.0107 0.00130 0.12130 767.091 8.244 40

45 163.9876 0.0061 0.00074 0.12074 1358.230 8.283 45

50 289.0022 0.0035 0.00042 0.12042 2400.018 8.305 50

CD — — — 0.12000 — 8.333 <30

30
Table A-5 15% Discount Factors

Single Single Uniform Uniform Uniform

Compound Present Sinking Capital Compound Present

amount value fund recovery amount value

factor factor factor factor factor factor

n SCA SPW USF UCR UCA UPW

1 2 3 4 5 6 7 n

1 1.1500 0.8696 1.00000 1.15000 1.000 0.870 1 2 1.3225 0.7561 0.46512 0.61512 2.150 1.626 2

3 1.5209 0.6575 0.28798 0.43798 3.472 2.283 3 4 1.7490 0.5718 0.20026 0.35027 4.993 2.855 4 5 2.0114 0.4972 0.14832 0.29832 6.742 3.352 5

6 2.3131 0.4323 0.11424 0.26424 8.754 3.784 6

7 2.6600 0.3759 0.09036 0.24036 11.067 4.160 7 8 3.0590 0.3269 0.07285 0.22285 13.727 4.487 8

9 3.5179 0.2843 0.05957 0.29057 16.786 4.772 9 10 4.0456 0.2472 0.04925 0.19925 20.304 5.019 10

11 4.6524 0.2149 0.04107 0.19107 24.349 5.234 11

12 5.3503 0.1869 0.03448 0.18448 29.002 5.421 12

13 6.1528 0.1625 0.02911 0.17911 34.352 5.583 13

14 7.0757 0.1413 0.02469 0.17569 40.505 5.724 14

15 8.1371 0.1229 0.02102 0.17102 47.580 5.847 15

16 9.3576 0.1069 0.01795 0.16795 55.717 5.954 16

17 10.7613 0.0929 0.01537 0.16537 65.075 6.047 17

18 12.3755 0.0808 0.01319 0.16319 75.836 6.128 18

19 14.2318 0.0703 0.01134 0.16134 88.212 6.198 19

20 16.3665 0.0611 0.00976 0.15976 102.444 6.259 20

21 18.8215 0.0531 0.00842 0.15842 118.810 6.312 21

22 21.6447 0.0462 0.00727 0. 15727 137.632 6.359 22

23 24.8915 0.0402 0.00628 0.15628 159.276 6.399 23

24 28.6252 0.0349 0.00543 0.15543 184.168 6.434 24

25 32.9190 0.0304 0.00470 0.15470 212.793 6.464 25

26 37.8568 0.0264 0.00407 0.15407 245.712 6.491 26

27 45.5353 0.0230 0.00353 0.15353 283.569 6.514 27

28 50.0656 0.0200 0.00306 0.15306 327.104 6.534 28

29 57.5755 ' 0.0174 0.00265 0.15265 377.170 6.551 29

30 66.2118 0.0151 0.00230 0.15230 434.745 6.566 30

31 76.1435 0.0131 0.00200 0.15200 500.957 6.579 31

32 87.5651 0.0114 0.00173 0.15173 577.100 6.591 32

33 100.6998 0.0099 0.00150 0.15150 664.666 6.600 33

34 115.8048 0.0086 0.00131 0.15131 765.365 6.609 34

35 133.1755 0.0075 0.00113 0.15113 881.170 6.617 35

40 267.8635 0.0037 0.00056 0. 15056 1779.090 6.642 40

45 538.7693 0.0019 0.00028 0.15028 3585.128 6.654 45

50 1083.6574 0.0009 0.00014 0.15014 7217.716 6.661 50

00 — — — 0.15000 — 6.667 00

31
Table A-6 20% Discount Factors

Single Single Uniform Uniform Uniform

Compound Present Sinking Capital Compound Present

amount value fund recovery amount value

factor factor factor factor factor factor n SCA SPW USF UCR UCA UPW

1 2 3 4 5 6 7 n

1 1.2000 0.8333 1.00000 1.20000 1.000 0.833 1 2 1.4400 0.6944 0.45455 0.65455 2.200 1.528 2 3 1.7280 0.5787 0.27473 0.47473 3.640 2.106 3 4 2.0736 0.4823 0.18629 0.38629 5.368 2.589 4 5 2.4883 0.4019 0.13438 0.33438 7.442 2.991 5

6 2.9860 0.3349 0.10071 0.30071 9.930 3.326 6

7 3.5832 0.2791 0.07742 0.27742 12.916 3.605 7 8 4.2998 0.2326 0.06061 0.26061 16.499 3.837 8

9 5.1598 0.1938 0.04808 0.24808 20.799 4.031 9 10 6.1917 0.1615 0.03852 0.23852 25.959 4.192 10

11 7.4301 0.1346 0.03110 0.23110 32.150 4.327 11 12 8.9161 0.1122 0.02526 0.22526 39.581 4.439 12 13 10.6993 0.0935 0.02062 0.22062 48.497 4.533 13

14 12.8392 0.0779 0.01689 0.21689 59.196 4.611 14

15 15.4070 0.0649 0.01388 0.21388 72.035 4.675 15

16 18.4884 0.0541 0.01144 0.21144 87.442 4.730 16

17 22.1861 0.0451 0.00944 0.20944 105.931 4.775 17

18 26.6233 0.0376 0.00781 0.20781 128.117 4.812 18 19 31.9480 0.0313 0.00646 0.20646 154.740 4.844 19

20 38.3376 0.0261 0.00536 0.20536 186.688 4.870 20

21 46.0051 0.0217 0.00444 0.20444 225.026 4.891 21 22 55.2061 0.0181 0.00369 0.20369 271.031 4.909 22 23 66.2474 0.0151 0.00307 0.20307 326.237 4.925 23

24 79.4968 0.0126 0.00255 0.20255 392.484 4.937 24 25 95.3962 0.0105 0.00212 0.20212 471.981 4.949 25

26 114.4755 0.0087 0.00176 0.20176 567.377 4.956 26

27 137.3706 0.0073 0.00147 0.20147 681.853 4.964 27

28 164.8447 0.0061 0.00122 0.20122 819.223 4.970 28

29 197.8136 0.0051 0.00102 0.20102 984.068 4.975 29

30 237.3763 0.0042 0.00085 0.20085 1181.882 4.979 30

31 284,8516 0.0035 0.00070 0.20070 1419.258 4.982 31

32 341.8219 0.0029 0.00059 0.20059 1704.109 4.985 32 33 410.1863 0.0024 0.00049 0.20049 2045.931 4.988 33

34 492.2235 0.0020 0.00041 0.20041 2456.118 4.990 34

35 590.6682 0.0017 0.00034 0.20034 2948.341 4.992 35

40 1469.7716 0.0007 0.00014 0.20014 7343.858 4.997 40

45 3657.2620 0.0003 0.00005 0.20005 18281.310 4.999 45

50 9100.4382 0.0001 0.00002 0.20002 45497. 191 4.999 50

00 — — — 0.20002 — 5.000 00

32
Table A-7 8% UPW* Factors Modified for Energy Price Escalation

Rate of Energy Price Escalation

Year 1% 2% 3 % 4% 5% 6% 7% 8% 9% 10%

1 .9352 .9444 .9537 .9630 .9722 .9815 .9907 1 1.0093 1.0185

2 1.8098 1.8364 1.8633 1.8903 1.9174 1.9448 1.9723 2 2.0279 2.0559

3 2.6276 2.6788 2.7307 2.7832 2.8364 2.8903 2.9448 3 3.0559 3.1125

4 3.3925 3.4745 3.5580 3.6431 3.7298 3.8182 3.9083 4 4.0935 4.1887

5 4.1078 4.2259 4.3470 4.4711 4.5985 4.7290 4.8628 5 5.1406 5.2847

6 4.7768 4.9356 5.0994 5.2685 5.4429 5.6229 5.8085 6 6.1975 6.4011

7 5.4023 5.6058 5.8170 6.0363 6.2640 6.5003 6.7455 7 7.2641 7.5382

8 5.9874 6.2388 6.5014 6.7757 7.0622 7.3614 7.6738 8 8.3406 8.6983

9 6.5345 6.8367 7.1541 7.4877 7.8382 8.2065 8.5935 9 9.4271 9.8759

10 7.0461 7.4013 7.7766 8.1734 8.5923 9.0360 9.5046 10 10.5237 11.0773

11 7.5246 7.9346 8.3703 8.8336 9.3263 9.8502 10.4074 11 11.6304 12.3009

12 7.9726 8.4382 8.9365 9.4694 10.0394 10.6492 11.3017 12 12.7473 13.5472

13 8.3906 8.9138 9.4765 10.0817 10.7328 11.4335 12.1878 13 13.8746 14.8166

14 8.7819 9.3631 9.9915 10.6712 11.4069 12.2033 13.0657 14 15.0123 16.1095

15 9.1479 9.7873 10.4826 11.2390 12.0622 12.9588 13.9355 15 16.1606 17.4264

16 9.4902 10.1880 10.9510 11.7857 12.6994 13.7003 14.7972 16 17.3195 18.7676

17 9.8103 10.5665 11.3977 12.3121 13.3189 14.4280 15.6509 17 18.4891 20.1337

18 10.1096 10.9239 11.8237 12.8191 13.9211 15.1423 16.4967 18 19.6696 21.5250

19 10.3895 11.2615 12.2300 13.3073 14.5066 15.8434 17.3347 19 20.8610 22.9421

20 10.6513 11.5803 12.6175 13.7774 15.0759 16.5315 18.1650 20 22.0634 24.3855

21 10.8961 11.8814 12.9871 14.2301 15.6293 17.2068 18.9875 21 23.2769 25.8556

22 11.1251 12.1657 13.3395 14.6660 16.1674 17.8695 19.8025 22 24.5017 27.3529

23 11.3992 12.4343 13.6757 15.0858 16.6905 18.5202 20.6098 23 25.7378 28.8780

24 11.5894 12.6880 13.9963 15.4900 17.1991 19.1587 21.4097 24 26.9854 30.4313

25 11.7287 12.9275 14.3020 15.8792 17.6936 19.7884 22.2022 25 28.2445 32.0134

33
Table A-8 10% UPW* Factors Modified for Energy Price Escalation

Rate of Energy Price Escalation

Year 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%

1 0.9182 0.9273 0.9364 0.9455 0.9546 0.9636 0.9727 0.9818 0.9909 1.0000

2 1.7612 1.7871 1.8131 1.8393 1.9657 1.8921 1.9188 1.9457 1.9727 2.0000

3 2.5353 2.5844 2.6340 2.6844 2.7354 2.7869 2.8391 2.8921 2.9456 3.0000

4 3.2460 3.4027 3.4027 3.4834 3.5656 3.6492 3.7344 3.8213 3.9097 4.0000

5 3.8986 4.0092 4.1225 4.2388 4.3581 4.4801 4.6053 4.7336 4.8650 5.0000

6 4.4978 4.6449 4.7966 4.9531 5.1146 5.2808 5.4524 5.6294 5.8117 6.0000

7 5.0480 5.2344 5.4278 5.6284 5.8367 6.0524 6.2765 6.5089 6.7498 7.0000

8 5.5521 5.7810 6.0188 6.2669 6.5260 6.7959 7.0780 7.3723 7.6793 8.0000

9 6.0159 6.2878 6.5722 6.8705 7.1839 7.5124 7.8577 8.2201 8.6004 9.0000

10 6.4417 6.7577 7.0903 7.4411 7.8118 8.2028 8.6161 9.0524 9.5130 10.0000

11 6.8328 7.1935 7.5755 7.9807 8.4113 8.8682 9.3539 9.8696 10.4174 11.0000

12 7.1919 7.5977 8.0299 8.4909 8.9837 9.5095 10.0717 10.6722 11.3138 12.0000

13 7.5216 7.9725 8.4553 8.9733 9.5300 10.1274 10.7698 11.4601 12.2020 13.0000

14 7.8243 8.3199 8.8536 9.4293 10.0513 10.7227 11.4487 12.2335 13.0819 14.0000

15 8.1022 8.6421 9.2266 9.8604 10.5490 11.2964 12.1092 12.9929 13.9539 15.0000

16 8.3574 8.9408 9.5758 10.2680 11.0240 11.8492 12.7516 13.7384 14.8178 16.0000

17 8.5918 9.2179 9.9029 10.6535 11.4776 12.3821 13.3767 14.4706 15.6742 17.0000

18 8.8069 9.4747 10.2090 11.0177 11.9103 12.8953 13.9844 15.1891 16.5223 18.0000

19 9.0044 9.7129 10.4957 11.3622 12.3235 13.3900 14.5757 15.8947 17.3630 19.0000

20 9.1857 9.9337 10.7641 11.6878 12.7178 13.8666 15.1507 16.5873 18.1958 20.0000

21 9.3512 10.1385 11.0154 11.9957 13.0942 14.3259 15.7101 17.2674 19.0211 21.0000

22 9.5042 10.3285 11.2509 12.2870 13.4537 14.7688 16.2546 17.9355 19.8394 22.0000

23 9.6446 10.5046 11.4714 12.5623 13.7968 15.1955 16.7841 18.5913 20.6501 23.0000

24 9.7735 10.6679 11.6777 12.8225 14.1241 15.6065 17.2989 19.2349 21.4531 24.0000

25 9.8919 10.8193 11.8710 13.0686 14.4367 16.0026 17.7998 19.8670 22.2490 25.0000

34
Table A-9 122 UFW* Factors Modified for Energy Price Escalation

Rate of Energy Price Escalation

Year 1% 2% 32 4Z 52 62 7% 8% 9% 10%

1 .9018 .9107 .9196 .9286 .9375 .9464 .9554 .9643 .9732 .9822

2 1.7150 1.7401 1.7654 1.7908 1.8164 1.8422 1.8681 1.8941 1.9204 1.9468

3 2.4484 2.4955 2.5432 2.5915 2.6404 2.6899 2.7400 2.7908 2.8421 2.8941

4 3.1097 3.1834 3.2565 3.3349 3,4129 3.4922 3.5731 3.6554 3.7392 3.8246

1 5 3.7061 3.8099 3.9163 4.0253 4.1371 4.2516 4.3690 4.4891 4.6123 4.7384

6 4.2438 4.3804 4.5212 4.6664 4.8160 4.9702 5.1292 5.2931 5.4620 5.6360

7 4.7288 4.9000 5.0775 5.2616 5.4525 5.6504 5.8556 6.0683 6.2889 6.5175

8 5.1662 5.3732 5.8292 5.8144 6.0492 6.2941 6.5495 6.8159 7.0936 7.3832

9 5.5606 5.8042 6.0597 6.3276 6.6086 6.9034 7.2125 7.5368 7.8768 8.2335

10 5.9162 6.1967 6.4924 6.6042 7.1331 7.4800 7.8459 8.2319 8.6391 9.0686

11 6.2370 6.5541 6.8903 7.2468 7.6248 8.0257 8.4510 8.9022 9.3809 9.8888

12 6.5262 6.8796 7.2563 7.6577 8.0857 8.5422 9.0291 9.5485 10.1028 10.6944

13 6.7870 7.1761 7.5928 8.0393 8.5179 9.0310 9.5813 10.1718 10.8054 11.4856

14 7.0222 7.4461 7.9023 8.3936 8.9230 9.4936 10.1089 10.7728 11.4892 12.2626

15 7.2343 7.6920 8. 1870 8.7227 9.3028 9.9315 10.6130 11.3523 12.1547 13.0258

16 7.4256 7.9159 8.4487 9.0282 9.6589 10.3458 11.0946 11.9112 12.8023 13.7753

17 7.5981 8.1198 8.6895 9.3119 9.9927 10.7380 11.5546 12.4501 13.4326 14.5115

18 7.7536 8.3056 8.9108 9.5753 10.3057 11.1092 11.9942 12.9697 14.0460 15.2345

19 7.8939 8.4747 9.1144 9.8200 10.5991 11.4605 12.4141 13.4708 14.6430 15.9446

20 8.0204 8.6288 9.3017 10.0471 10.8741 11.7930 12.8152 13.9540 15.2240 16,6420

21 8.1345 8.7691 9.4739 10.2580 11.1320 12.1076 13.1985 14.4199 15.7894 17.3270

22 8.2373 8.8968 9.6322 10.4539 11.3737 12.4054 13.5646 14.8692 16.3397 17.9997

23 8.3301 9.0132 9.7778 10.6357 11.6004 12.6873 13.9144 15,3024 16.8752 18.6604

24 8.4137 9.1191 9.9118 10.8046 11.8129 12.9540 14.2486 15.7202 17.3964 19.3093

25 8.4892 9.2156 10.0349 10.9614 12.0121 13.2065 14.5678 16.1231 17.9037 19.9467

35
APPENDIX B

COMPUTER PROGRAM TO CALCULATE TOTAL LIFE-CYCLE COSTS

This section provides a comprehensive computer program, called TLCC, written in BASIC,

which can calculate total life-cycle costs, in present-value and in annual-value form,

associated with a building-related project. TLCC uses the algorithms described in section

6 of this report. The building-related project can be divided into a number of capital

investment categories (e.g., land, building, equipment), in order to reflect differences

in cost inflation rates, depreciation schedules, and/or tax treatments. Up to 10 capital

investment categories can be defined and analyzed if such differentiation is warranted.

An example of the output generated by TLCC is shown in table B-l, corresponding to the

input data file shown in table B-2.

While the TLCC program is quite flexible in its ability to treat inflation and tax adjustments, it can also be used to solve simple problems where taxes and inflation are not

considered. One of three tax status alternatives can be specified for the analysis:

profit-making enterprise, tax-exempt status, and private residential (homeowner). Tax

savings due to depreciation; operating, maintenance and repair (OM&R) costs; and fuel costs

are not considered for the latter two categories. In addition, investment tax credits,

property taxes, tax savings from interest, and capital gains taxes are not considered for

the tax-exempt category, but they are included in the evaluation of homeowner investments.

Up to three separate financing arrangements can be analyzed, each with separate loan

amounts, lengths, and terms. The present value of all finance payments (interest and

principal) over the study period is calculated, together with the present value of any

remaining principal at the end of the study period. If the loan is to be fully amortized

over its life, the loan type (F(I,6)) is designated as 1. If interest, but no principal,

is paid on the loan, with the entire principal paid at the end of the loan life, the

loan type is designated as 2.

Up to 5 replacements to capital can be specified for each capital investment category.

Each replacement can have its own depreciation schedule and resale value if specified.

This does not affect the depreciation schedule for the capital investment category to

which it is assigned.

All investments (including replacements) and operating-related costs are entered in baseperiod dollars, rather than in future-year dollars. Separate cost inflation factors can be

entered for each cost category. (Replacement costs are inflated at the same rate as the

capital investment category to which they are assigned.) In addition, for energy cost

36
projections, different cost inflation factors can be used during different time intervals

over the study period.

Table B-3 provides a list of input variables needed to run the program. Table B-4 gives

some of the intermediate calculation variables used in the program. Table B-5 provides

the correct format for entering the data into the program. Data is typically entered

starting with line 9000.

In its simplest form, only one capital investment category with an investment cost and one operating cost need be entered, together with a study period length and discount rate. In

such a case, all other data entries are made with zeroes (0). Specification of one or more capital investment categories (C2), one or more replacements (C(I,12)), one or more

mortgage loans (Fl), one or more non-annually recurring OM&R costs (M4), or one or more inflation-rate intervals (E(2,I)) requires that the corresponding number of entries be

made in full for each.

Three methods of depreciation can be specified: (1) straight line, (2) declining balance,

and (3) sum of digits. If depreciation is not used, the method is specified as 0 and no further depreciation data is needed. Specification of a depreciation rate must be made

for the declining balance method. For example, specify 2 for a double (200%) declining

balance method. For the straight-line or sum-of-digits methods enter 0 for the depreciation rate. Basic Internal Revenue Service (IRS) rules are used in computing annual depreciation. For the straight-line and sum-of-digits methods, salvage value in base-period

dollars is deducted from the investment cost before setting up a depreciation schedule.

Additional first year depreciation (as allowed by law) can be specified. The accelerated

depreciation method automatically switches over to the straight-line method when the latter

allows greater deductions than the former. The salvage value and life for depreciation

purposes are specified separately from the actual expected resale value and useful life

of a capital investment. Depreciation tax savings, like other tax credits, are discounted

from the end of the year to which they apply.

Property taxes (other than for land) are estimated yearly using a constant rate of decline

in asset value to reflect physical deterioration and technical obsolescence until the

expected resale value is reached. These remaining asset values are in turn adjusted

upwards to reflect inflation. Land value is adjusted only for inflation. The adjusted

value is then multiplied by an assessment factor to arrive at an assessed value for tax

computation purposes. A different assessment factor can be specified for each capital

investment category; the assessment factor specified is also used for any capital replacement costs associated with a capital investment category. Property taxes are assumed to

be paid at the beginning of the year.

37
Resale value (as a percentage of first cost, unadjusted for inflation) is specified for

each capital investment and replacement as of the end of the study period (or at the

time of disposal if less than the study period). A negative resale value can be used

if disposal costs are expected to outweigh asset value. The resale value is adjusted for

inflation using the inflation rate specified for the appropriate capital investment

category. The resale value is meant to reflect a projection of actual asset value at the

end of the study period (or useful life) rather than "salvage" value for depreciation

computational purposes.

Capital gains tax liabilities are calculated on the resale value of the capital investments

-A and replacements, adjusted for inflation. Taxes are computed at capital gains rates for

the difference between the inflation-adjusted resale value and the basis (the original

cost less accumulated depreciation) calculated by the straight-line depreciation method,

regardless of the depreciation method used. If an alternative depreciation method is used

(e.g., declining balance or sum of digits), the difference between the basis calculated

using the straight-line method and the basis calculated using the alternative method is

taxed as ordinary income. The program calculates no capital loss tax credit if the

adjusted resale value is less than the basis. In general, good accounting practice would

increase the depreciation rate in order to preclude such an anticipated capital loss.

38
LISTING OF TLCC COMPUTER PROGRAM

TLCC

10 PEM:

20 REM:

30 REM:

40 REM:

50 REM:

100 DIM

105 DIM

106 DIM

110 DIM

120 DIM

130 DIM

180 READ A$

185 READ Il,Nl,Tl,T2,T3,T4

190 READ C2

230 FOR 1=1 TO C2

205 READ C$(I)

210 READ C ( I ,1) ,C (I ,3)

214 IF C ( I , 3

) =0 THEN 218

216 READ C (I ,2) ,C (I ,4) ,C (I , 5) ,C (I ,6)

218 FOR J=7 TO 12

220 READ C(I,J)

225 NEXT J

228 IF C(I,10)<999 THEN 233

229 IF C ( I , 1 2

) =0 THEN 233

230 PRINT "WARNING: LAND CANNOT HAVE REPLACEMENTS. RUN TERMINATED"

231 STOP

233 IF C(I ,10)

= C(I ,2) THEN 235

234 PRINT "WARNING DEPRECIATION LIFE OF "C$(I)" EXCEEDS ACTUAL LIFE."

235 IF C (I ,10) >0 THEN 240

236 PRINT "EXPECTED LIFE OF "CS(I)" MUST > 0. RUN TERMINATED."

237 STOP

240 IF C ( 1 , 1 2

) =0 THEN 290

250 FOR K=1 TO C(I,12)

260 READ Y(I,K) ,R(I,K) ,L(I,K) ,S(I,K) ,A(I,K) ,E(I,K)

263 IF A ( I , K )

= L (

, K

)

THEN 266

264 PRINT " WARNING : DEPRECIATION LIFE OF REPLACEMENT " K

" 10 "C$(l)

265 PRINT " EXCEEDS ACTUAL EXPECTED LIFE"

266 IF A ( I , K

)

> O THEN 270

267 PRINT "EXPECTED LIFE OF REPLACEMENT" K

" TO "C$(I)" MUST >0. RUN TERMINATED.

270 NEXT K 290 NEXT I 295 READ FI

300 FOR 1 = 1 TO FI

310 FOR J=1 TO 6

320 READ F ( I , J

)

330 NEXT J

340 NEXT I 350 READ ml, M2

360 READ M4,M5

370 FOR J=1 TO M4

THIS PROGRAM PROVIDES A TOTAL LIFE-CYCLE COST ANALYSIS OF A

BUILDING-RELATED PROJECT, CONSISTENT WITH THE PROPOSED ASTM

STANDARD FOR LIFE-CYCLE COST ANALYSIS. IT WAS DEVELOPED AT

THE NATIONAL BUREAU OF STANDARDS BY STEVE PETERSEN IN 1980,

AND LAST MODIFIED ON JUNE 11, 1980.

C (10 , 13 )

, F ( 3 , 9 ) , X ( 4 , 40 ) ,U(10,5)

D(?,40) ,E(4 ,5) ,Z (2,40)

V (10,5)

Y ( 1 0 , 5 )

, R ( 1 0 , 5 ) ,L(10,5) ,S(10,5)

A ( 1 0 , 5 ) , B ( 1 0 , 5 ) ,1(4,5) , P ( 4 , 5

)

W ( 2 5

)

39
TLCC CONTINUED

3 80 READ M ( 1 , J ) ,M(2,J)

382 IF M ( 1 , J ) <=N1 THEN 390

384 PRINT "WARNING: NON-RECURRING O&M OCCURS IN YEAR (S) BEYOND STUDY PERIOD390 NEXT J

395 READ N2

396 FOR 1=1 TO N2

397 READ E(1 ,1) ,E(2,I+1)

400 FOR J = 1 TO E ( 2 , 1+1

410 READ I (1+1 ,J) , P ( I ,J)

420 NEXT J

430 FOR J=1 TO E ( 2 , 1+1 ) -1

435 IF I (1+1 , J+l) <N1+1 THEN 455

440 I (I,J)=Nl+l-I (1+1 , J)

445 E { 2 , I

) =J

450 GOTO 480

455 I (I ,J)=I (1+1 ,J+1)-I (1+1 ,J)

460 NEXT J

465 I (I ,J+l)=Nl+l-I (1+1 ,J + 1)

470 E ( 2 , I

) =J+1

480 NEXT I 490 REM: ESTABLISH VARI ABLESS FOR TAX PAYING STATUS AND LOAN TYP

500 T$ ( 1

) =

" PROFIT MAKING ENTERPRISE"

513 T$ ( 2 ) = "TAX EXEMPT"

520 T$ ( 3

)

"PRIVATE RESIDENTIAL (TAX PAYING)"

530 L$ (1 ) = "AMORT I ZED"

540 L$ (2) =" INTEREST ONLY"

1000 MAT W=ZER

1010 REM: COMPUTE INITIAL COST , W(l), AND INITIAL DOvvN PAYMENT, W(2)

1015 F2=0

1020 FOR 1=1 TO FI

1025 REM: COMPUTE TOTAL AMOUNT BORROWED LESS "POINTS" COST, F2

1030 F2 = F2 + F (I ,1) * ( 1 — F ( I ,5)

1040 NEXT I 1060 FOR 1=1 TO C2

1070 W(1)=W(1)+C(I ,1)

1060 NEXT I 1090 W ( 2

) =W ( 1

) -F2

1100 REM: COMPUTE LOAN PAYMENT PER TIME PERIOD FOR ITH LOAN, F(I,7)

1105 FOR 1=1 TO FI

1110 IF F ( I , 6

) =1 THEN 1120

1115 F(I,7)=F(I,3)/F(I,4)

1116 GOTO 1170

1120 IF F (I , 3) <>0 THEN 1150

1130 F(I,7)=1/(F(I,2)*F(I,4))

3140 GOTO 1170

1150 F(I,7) = (F(I,3)/F(I,4) ) * ( 3 +F ( I , 3 ) /F ( I , 4 )

)

' ( F ( I , 2) *F (, 4 )

1160 F(I,7)=F(I,7)/ ( (1+F(I,3)/F(I,4) )

( F ( I ,2)*F(I,4) ) — 1

1170 NEXT I 1180 REM: COMPUTE UPW FACTOR FOR ITH LOAN PAYMENT SCHEDULE, F(l,9)

1190 FOR 1=1 TO FI

40
TLCC CONTINUED

1200 REM: COMPUTE MIN: (STUDY PERIOD, LOAN LIFE) FOR ITH LOAN, F(I,8)

1210 F ( I , 8

) =N

1220 IF Nl <=F ( I , 2 ) THEN 1240

1230 F(I , 8)=F(I ,2)

1240 IF 11=0 THEN 1280

1250 F(I,9)=(((1+I1/F(I,4))~(F(I,8)*F(I,4)))-1)

1260 F(I,9)=F(I,9)/(I1/F(I,4)*(1+I1/F(I,4) ) " ( F ( I , 8

) * F ( I , 4 ) )

)

1270 GOTO 1290

1280 F(I,9)=F(I,8)*F(I,4).

1290 REM: COMPUTE P.V. OF ALL LOAN PAYMENTS MADE DURING STUDY PERIOD, W(3)

1320 W(3)=w(3)+F(I,1)*F(I,7)*F(I,9)

1330 NEXT I 1400 REM: COMPUTE INTEREST PAID IN EACH YEAR X(2,J), CUMM INTEREST PAID AT

1401 REM: YEAR J X ( 4 , J ), REMAINING PRINCIPAL AT END OF EACH YEAR X ( 1 , J ) AND

1402 REM: ANY REMAINING PRINCIPAL W(4)

1404 FOR 1=1 TO FI

1406 IF F ( I , 6

) =1 THEN 1420

1408 W(4)=W(4)+F(I ,1)/ ( 1 + I 1 ) F(I ,8)

1410 FOR J=1 TO F ( I , 8

)

1412 X(4,J)=F(I,1)*F(I,3)

1414 W(6)=W(6)+X(4,J)/(1+I1)~J

1416 NEXT J 1418 GOTO 1560

1420 REM

1430 X ( 1 ,0)=F(I,1)

1440 FOR J=1 TO F ( I , 2

)

1450 X ( 2 , J

) =0

1460 X (3 , 0) =X (1 , J-l

)

1465 REM: X ( 3 , K

) =REMA1NING PRINCIPAL AFTER EACH LOAN PAYMENT K IN YEAR J

1470 FOR K=1 TO F(I,4)

1480 X(3,K)=X(3,K-1)*(1+F(I,3)/F(I,4) ) -F (I , 7

) *F(I , 1

)

1490 X (2, J) =X (2 ,J)+X (3 ,K-1) *F(I ,3)/F(I ,4)

1500 NEXT K 1510 X(1,J)=X(3,F(I,4)

)

1530 X ( 4 , J

) =X ( 4 , J ) +X ( 2 , J

)

1535 W (6 ) =W (6 ) +X (4 , J ) / ( 1+1 1

)

’

1540 NEXT J

1550 W ( 4

) = W ( 4 ) +X (1 , N 1 ) / ( 1 + I 1

) ~ N

1560 NEXT I 1570 W ( 5

) =W ( 2 ) +W (3 ) +W (4

)

1600 REM: COMPUTE ANNUAL DEPRECIATION ALLOWANCE FOR EACH FACTOR Z(2,J),

1601 REM: CUMM S.L. DEPRECIATION D(1,J) AND CUMM ACTUAL DEPRECIATION (D(2,J))

1610 MAT D=ZER

1620 FOR 1=1 TO C2

1625 IF C ( I , 3

) =0 THEN 1698

1630 Dl=C (I ,1)

1640 D2=C ( I , 2

)

1659 D3=C ( I , 3

)

1660 D4=C ( I , 4

)

1670 D5=C ( I , 5

)

41
TLCC

1680

1690

1692

1693

1694

1695

1696

1697

1698

1700

1710

1720

1730

1740

1741

1750

1760

1770

1780

1790

1800

1810

1820

1P40

1850

1860

1865

1870

1 p 7 S

1 8P3

1890

1895

1900

2200

2210

2220

2222

2224

2226

2230

2240

2300

2310

2320

2330

2340

2350

2360

2370

2372

CONTINUED

D6=C(I ,6)

GOSUB 4600

FOR J = 1 TO D2

IF J >N 1 THEN 1697

W(7)=W(7)+Z(2,J)/(1+I1) "J

D(2,I)=D(2,I)+Z(2,J)

D(1,I)=D(1,I)+Z(1,J)

NEXT J

NEXT I FOR 1=1 TO C2

FOR K=1 TO C ( 1 , 12

W(10)*W(10)+R(I,K) *( (1+C(I,7) )/(l + Il) )" (Y(I,K)-1)

IF L ( I , K ) >0 THEN 1760

PRINT "REPLACEMENT fK" FOR FACTOR **C$ ( I )*' SHOULD BE TREATED AS"

PRINT " REPAIR SINCE DEPRECIATION LIFE = 0"

STOP

D1=R ( I , K

) *(1+C(I,7))~(Y(I,K)-1)

D2=L (I ,K)

D3=C (1,3)

D4=C (1 ,4)

D5 = S (I ,K)

D6=C(I ,6)

GOSUB 4600

FOR J=Y(I,K) TO Y ( I , K ) +L (I , K) -1

IF J >N 1 THEN 1890

W (8 ) =W ( 8 ) +Z ( 2 , J) / (1+1 1

) " J

REM: U ( I , K

) =CUMM DEPRECIATION FOR KTH REPLACEMNT OF ITH FACTOR

U(I,K)=U(I,K)+Z(2,J)

V (I,K)=V(I,K)+Z(1 ,3)

NEXT J NEXT K NEXT I W ( 9) =K ( 7 ) +W ( 8

REM: COMPUTE P.V. OF INVESTMENT TAX CREDIT FOR FACTORS , W ( 1 1

FOR 1=1 TO C2

W(11)=W(11)+C(I ,9) *C(I , 1 ) / (1+11)

FOR K = 1 TO C (I , 12)

W(12)=W(12)+R(I,K)*C(I,9)*( <1+C(I,7) )/(l+Il) )"Y(I,K)

NEXT K NEXT I W (13 ) =W (11 ) +W (12)

REM

FOR 1=1 TO C2

REM: COMPUTE MIN (STUDY PERIOD, USEFUL LIFE)

C (I ,13) =N1

IF C(I ,10) > = N1 THEN 2360

C(I ,13)=C(I,10)

w(14)=W(14)+C(I,l)*C(I,ll)*( ( 1+C ( I , 7 ) )/ (1 + 11)

)

* C ( I , 1 3

D7=C(I ,1) *C(I,11) * (1+ C (I , 7)

) "C(I ,13)

IF D7>=C (I ,1) -D (1 ,1) THEN 2380

42
TLCC

2373

2374

2375

2376

2377

2380

2381

2385

2390

2400

2410

2420

2430

2440

2450

2460

2462

2463

2464

2465

2466

2467

2468

2469

2475

2480

2490

2500

2510

2520

3000

3010

3020

3030

3050

3060

3100

3120

3130

3140

3200

3201

3210

3215

3216

3217

3220

3230

3231

3232

CONTINUED

IF D7>=C ( I , 1

) -D ( 2 , 1 ) THEN 2385

PRINT "WARNING: RESALE PRICE OF "C$(I)‘* IS LESS THAN " PRINT M REMAINING BASIS. DEPRECIATION RATE SHOULD BE INCREASED.

PRINT “ CAPITAL LOSS NOT COMPUTED."

GOTO 2400

D6=(D7-(C(I,1)-D(1,I) )

) *T3+(D(2,I)-D(1,I) ) *Tl

GOTO 2390

D6=(D7-(C(I,1)-D(2,I) )

) *T1

W(17)=W(17)+D6/(1+I1) "C ( I , 13

REM

FOR K=1 TO C (I ,12)

C { I , 13 ) =N1

IF A ( I , K ) +Y ( I , K ) -1 >=N 1 THEN 2450

C(I,13)=A(I,K) +Y ( I , K

) -1

W(15)=W(15)+R(I,K)*B(I,K)*( ( 1 +C ( I , 7 ) )/ (1+11) ) C ( I , 1 3 ) D7=R (I,K)*E(1,K) * (1+C (I ,7)

) “C(I ,13)

IF D7>=R(I,K)-V(I,K) THEN 2468

IF D7>=R (I ,K) -U (I ,K) THEN 2475

PRINT "WARNING: RESALE PRICE OF REPLACEMENT "K" TO “C$(I)

PRINT " IS LESS THAN THE REMAINING BASIS. DEPRECIATION RATE SHOULD"

PRINT " BE INCREASED. CAPITAL LOSS IS NOT COMPUTED."

GOTO 2490

D6= (D7- (R ( I ,K)-V (I ,K) )

) *T3+ (U ( I , K

) -V (I , K )

) *T1

GOTO 2480

D6= ( D7- (R (I ,K) -U (I ,K) ) ) *T1

W ( 1 8

) =W ( 1 8 ) +D6/ (1+11) "C ( I ,13)

NEXT K NEXT I W ( 1 6

) = W ( 1 4 ) +W (15)

W(19)=W(17)+W(18)

REM: COMPUTE P.V. OF RECURRING O&M

IF M2=I 1 THEN 3350

M3=( ( 1 +M2 ) / ( 1 1-M2 )

) * ( 1- (

( 1 +M2 ) / ( 1 + 1 1 )

) "Nl)

GOTO 3060

M 3 = N

W ( 20 ) =M1 *M3

REM: COMPUTE P.V. OF NON RECUPRING O&M

FOR J=1 TO M4

W(21)=W(21)+M(2,J) * ( ( 1 +M5 ) / ( 1 +1 1 ) )"M(1,J)

NEXT J

REM: COMPUTE P.F. OF PROPERTY TAXES FOP FACTORS, W(22), AND

REM: REPLACEMENTS, W(23)

FOR 1=1 TO C2

C (I ,13) =N1

IF C(I,10)>= Nl THEN 3220

C (I , 13 ) =C ( I , 10

FOR J = 1 TO C (I ,10)

IF J>N1 THEN 3260

IF C ( I , 10 ) <999 THEN 3235

REM: COMPUTE PROPERTY TAX FOR LAND (NON-DECLINING REAL VALUE)

43
TLCC CONTINUED

3233 W(22)«W(22)+C(I f l)*C(I,8)*T2*( (1+C(I,7) )/(l+Il) )~ (J-l)

3234 GOTO 3250

3235 REM D8=CUMM S.L. DEPRECIATION BASED ON ACTUAL LIFE AND ACTUAL RESALE VALUE

3240 D8=((C(I,1)-C(I,1)*C(I,11))/C(I,13))*(J-1)

3245 W(22)=W(22)+(C(I,1)-D8)*C(I,8)*T2*( (1+C(I,7) )/(l+Il)

) " (J-l)

3250 NEXT J

3260 REM

3270 FOR K=1 TO C(I,12)

3271 C(I ,13)=A(I ,K)

3272 IF Y ( I , K ) +A ( I , K

) -1 <Nl THEN 3280

3273 C(I,13)=N1-Y(I,K)+1

3280 FOR J=Y(I,K) TO Y ( I , K ) +A ( I , K

) -1

3290 IF J >Nl THEN 3320

3300 D8= ( (R(I ,K)-R(I,K) *B(I ,K) )/C(l ,13) ) * (J-l)

3305 W(23)=W(23)+(R(I,K)-D8)*C(I ,8) *T2*( (1+C(I,7) )/(l+Il)

) ~ (J-l)

3310 NEXT J

3320 NEXT K 3330 NEXT I 3340 W ( 24 ) =W ( 22 ) +W ( 23

)

3400 REM: E(3,I)=UPW* FOR ITH ENERGY TYPE

3410 FOR 1=1 TO N2

3420 E ( 3 , I

) =0

3430 FOR K=1 TO E(2,I)

3440 D9=l

3450 FOR J=0 TO K-l

3460 D9=( ( ( 1 +P ( I , J ) ) / ( 1+1 1 ) ) I (I ,J) ) *D9

3470 NEXT J

3480 IF I1 = P ( I , K ) THEN 3530

3490 D8=(1+P(I,K) )/(Il-P(I,K)

)

3500 D7=l-( (1+P (I ,K) ) / ( 1 +1 1 )

)

' I ( I , K

)

3510 E(3,I)=D9*D8*D7+E(3,I)

3520 GOTO 3540

3530 E(3,I)=L(3,I) +D9* I ( I , K

)

3540 NEXT K

3550 NEXT I 3600 REM :E(4,I)=P.V. OF ENERGY TYPE I 3610 REM: W(25)=P.V. OF ALL ENERGY EXPENDITURES

3620 FOR 1=1 TO N2

3630 E(4,I)=E(1,I)*E(3,I)

3640 W ( 2 5

) =W ( 2 5 ) +E ( 4 , 1

)

3650 NEXT I 4590 GOTO 8000

4600 REM: SUBROUTINE TO CALCULATE DEPRECIATION ALLOWANCE

4630 IF D3<4 THEN 4660

4640 PRINT "DEPRECIATION TYPE FOR "C$(I)" IS MI SSPEC I I F IED

4650 STOP

4660 IF D3=0 THEN 5050

4665 D7=Dl * ( 1 -D6

)

4680 REM: STRAIGHT LINE METHOD

4690 FOR J=1 TO D2

44
TLCC CONTINUED

4700 Z(1,J)=Z(2,J)=D7*(1-D5)/D2

4710 NEXT J

4720 ON D3 GOTO 5040,4730,4960

4730 REM: DECLINING BALANCE METHOD

4740 D9=0

4750 FOR J=1 TO D2

4760 Z (2,J)=D4/D2* (D7-D9)

4765 REM : Z ( 2 , J

) = DEPRECIATION ALLOWNACE FOR YEAR J

4770 IF D7-D9-Z (2 , J) <=D7*D5 THEN 4910

4780 IF (D7* (1-D5) -D9) / (D2-J+1 ) >Z ( 2 ,J) THEN 4820

4790 D9=D9+Z ( 2 , J

)

4795 REM: D9=CUMM DEPRECIATION

4800 NEXT J

4810 GOTO 5040

4820 REM: SWITCH FROM DECLINING BALANCE TO STRAIGHT LINE

4830 Jl=J

4840 D8= (D7* ( 1-D5 ) -D9 ) / ( D2-J+1

)

4850 FOR J=J1 TO D2

4860 Z ( 2 , J ) =D8

4890 NEXT J

4900 GOTO 5040

4910 REM: BASIS CANNOT FALL BELOW SALVAGE VALUE

4915 J1=J

4920 Z(2,J)=D7*(1-D5)-D9

4925 REM: D7*(l-D5) = MAX AMOUNT THAT CAN LEGALLY BE DEPRECIATED

4930 FOR J=J1 +1 TO D2

4940 Z ( 2 , J ) =0

4950 NEXT J

4955 GOTO 5040

4960 REM : SUM OF DIGITS METHOD

4970 D8=0

4980 FOR J=1 TO D2

4990 D8=D8+J

5000 NEXT J

5010 FOR J=1 TO D2

5020 Z (2,J) = (D7* (1-D5) ) * (D2-J+l)/D8

5030 NEXT J

5040 Z (2,1)=Z (2,1 )+Dl*D6

5050 RETURN

5000 REM

8000 FOR 1=1 TO 5 8010 PRINT

8020 NEXT I 8030 PRINT USING 8600,

8040 PRINT

8050 PRINT USING 8610,

8055 PRINT

8060 PRINT USING 8620, A?

8070 B$=DAT$

8089 PRINT USING 8630, B$

45
TLCC CONTINUED

8090

8100

8110

8120

8130

8140

8150

8160

8170

8180

8190

8200

8210

8220

8230

8240

8250

8260

8270

8275

8276

8280

8290

8300

8305

8310

8320

8330

8340

8350

8360

8370

8380

8390

8395

8400

8410

8420

8422

8423

8424

8425

8426

8427

8429

8430

8440

8450

8460

8470

PRINT USING 8640 , Nl

PRINT USING 8650 , 11*100

PRINT USING 8660 , T$ (T4

PRINT USING 8670 , Tl *1 00

PRINT USING 8680 , T3*100

PRINT

PRINT

USING 8690 , T2*100

PRINT USING 8700 , FOR 1=1 TO C2

PRINT USING 8710 ,C$ (I) ,C (I ,1)

NEXT I PRINT

PRINT USING 8720,

FOR 1=1 TO FI

PRINT USING 8730,I,F(I,1),F(I,2),F(I,3)*100,F(I,5)*100,L$(F(I,6))

NEXT I PRINT

PRINT USING 8600

PRINT

PRINT USING 8735,

PRINT

PRINT USING 8740

PRINT USING 8750, W(2)

PRINT USING 8760, W(3)

IF W(4) <5 THEN 8320

PRINT USING 8770, W(4)

PRINT USING 8780, W(10)

PRINT USING 8790, W(16)

T9=W ( 2 ) +W ( 3 ) +W ( 4 ) +W ( 1 0

) -ft ( 1 6

IF T4=3 THEN 8430

PRINT USING 8800, T9

PRINT USING 8810

IF T4=2 THEN 8400

PRINT USING 8820 ,W( 9) *T1

T9=T9-W ( 9

) *T1

PRINT USING 883 0 , W ( 6

) *T1

PRINT USING 8840, W ( 1 3

T9=T9-W (13) -W ( 6

) *T1

IF T4=2 THEN 8430

IF W (19) >=0 THEN 8427

W9=ABS ( W ( 1 9 )

PRINT USING 8846, W9

GOTO 8429

PRINT USING 8845, W ( 1 9

T9=T9+W (19)

PRINT USING

PRINT

PRINT USING

PRINT USING

PRINT USING

8850 , T9

8860

8870 , W ( 20

8880, W(21)
TLCC CONTINUED

8480

8482

8485

8490

8495

8500

8510

8520

8530

8540

8550

8560

8562

8565

8568

8569

8570

8571

8573

8575

8576

8579

8580

8585

8590

8592

8595

8597

8598

8600

8610

8620

8630

8640

8650

8660

8670

8680

8690

8700

PRINT USING 8890, W(25)

T8=W ( 20 ) +W ( 21 ) +W ( 25)

IF T4 = 3 THEN 8560

PRINT USING 8900, W(24)

T8=T8+W ( 24

)

PRINT USING 8800, T8

ON T4 GOTO 8520,8540

T7=T1*T8

GOTO 8550

T7=T1 *W ( 24

)

PRINT USING 8905, T7

PRINTUSING 8910 , T8-T7

PRINT

PRINT USING 8920 ,T9+T8-T7

PRINT

PRINT

PRINT USING 8930

PRINT

IF 11=0 THEN 8579

A=(I1*(1+I1) ~Nl)/( { (1+11) ~N1)-1)

GOTO 8580

A=1/N1

T6=A*T9

T5=A* (T8-T7)

PRINT USING 8940, T6

PRINT USING 8950, T5

PRINT USING 8960, T6+T5

PRINT

PRINT USING 8600 *********************************

TOTAL LIFE-CYCLE COST ANALYSIS

PROJECT NAME: ' LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL

DATE OF ANALYSIS: ' LLLLLLLLLLLLLLLLLLL

STUDY PERIOD: ## YEARS

DISCOUNT RATE: ##.#%

TAX STATUS: ' LLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL

INCOME TAX RATE: ##.#%

CAPITAL GAINS TAX RATE: ##.#%

PROPERTY TAX RATE: ##.*%

INVESTMENT CATEGORY PURCHASE COST

*

8710

8720

8730

8735

8740

8745

8750

8760

8770

e780

'LLLLLLLLLLLLLLLLLLL $#########

FINANCING AMOUNT LIFE INTEREST RATE POINTS TYPE

LOAN # $######### ## YEARS ##.##% ##.##% 'CCCCCCCCCCCCC

I. PRESENT-VALUE LIFE-CYCLE COST ANALYSIS

A. PRESENT-VALUE INVESTMENT COSTS

$#######

INITIAL DOWN PAYMENT

MORTGAGE PAYMENTS

REMAINING PRINCIPAL

REPLACEMENTS TO CAPITAL

$########

########

########

########

47
TLCC

8790

8800

8810

8820

8830

8840

8845

8846

8850

8860

8870

8880

8890

8900

8905

8910

8920

8930

8940

8950

8960

9000

9010

9020

9030

9040

9050

9060

9070

9080

9090

9095

9100

9110

9120

9130

9140

9150

9160

9170

9180

9190

9200

9210

9300

9310

9320

9400

9410

9420

CONTINUED

B.

RESALE VALUE AT END OF STUDY

SUBTOTAL

INCOME TAX ADJUSTMENTS

TAX SAVINGS FROM DEPRECIATION

(########)

$########

(########)

TAX SAVINGS FROM INTEREST PAYMENTS

INVESTMENT TAX CREDITS

CAPITAL GAINS ON INVESTMENT RESALE

CAPITAL LOSS ON INVESTMENT RESALE

(########)

(########)

########

(########)

NET PRESENT-VALUE INVESTMENT COST $########

PRESENT-VALUE OPERATING, MAINTENANCE AND REPAIR COSTS

ANNUAL RECURRING COSTS (NON-FUEL)

NON-ANNUAL RECURRING COSTS

FUEL COSTS

PROPERTY TAXES

TAX SAVINGS FROM OM&R

NET PRESENT-VALUE OM&R COSTS

C. TOTAL PRESENT-VALUE LIFE-CYCLE COSTS

II. ANNUAL-VALUE LIFE-CYCLE COSTS

A. ANNUAL-VALUE INVESTMENT COSTS

B. ANNUAL-VALUE OM&R COSTS

C. TOTAL ANNUAL-VALUE LIFE-CYCLE COSTS

DATA "TEST PROBLEM"

DATA .12,30

DATA .46, .025, .28,1

DATA 3

DATA "BUILDING", 1000000

DATA 1,25,0,0,0

DATA . 1 , . 75 ,

0

DATA 50 , .

5

DATA 1 DATA 20,25000,10,0

DATA 20,0

DATA "EQUIPMENT" ,100000

DATA 1,10,0,0, .1

DATA . 1 , . 5 , .

1

DATA 1 5 , . 1 DATA 1 DATA 16,100000,10,0

DATA 1 5 , . 1 DATA "LAND" ,100000

DATA 0 DATA . 1 , . 8 ,

0

DATA 999,1.0

DATA 0 DATA 2 DATA 900000,20, .12,12,0,1

DATA 50000,5, .15,1,0,2

DATA 50000 ,.

1

DATA 5 ,

. 1 DATA 5,20000

$########

########

########

########

(########)

$########

$########

$########

########

$########

48
TLCC CONTINUED

9430 DATA 10,10000

9440 DATA 15,20000

9450 DATA 20,10000

9460 DATA 25,20000

9500 DATA 2

9510 DATA 10000,3

9520 DATA 1, .12

5530 DATA 11 , .10

9540 DATA 21,. 08

9550 DATA 20000,2

9560 DATA 1,.12

9570 DATA 16, .08

9999 END
TABLE B-l SAMPLE TLCC COMPUTER PROGRAM OUTPUT

*************************************

TOTAL LIFE-CYCLE COST ANALYSIS

PROJECT NAME: TEST PROBLEM

DATE OF ANALYSIS: WED 06/18/80

STUDY PERIOD: 30 YEARS

DISCOUNT RATE: 12.0%

TAX STATUS: PROFIT MAKING ENTERPRISE

INCOME TAX RATE: 46.0%

CAPITAL GAINS TAX RATE: 28.0%

PROPERTY TAX RATE: 2.5%

INVESTMENT CATEGORY PURCHASE COST

BUILDING $1000000

EQUIPMENT $100000

LAND $100000

FINANCING AMOUNT LIFE INTEREST RATE POINTS TYPE

LOAN 1 $900000 20 YEARS 12.00% 0.00% AMORTIZED

LOAN 2 $50000 5 YEARS 15.00% 0.00% INTEREST ONLY

* * * * ****** ***** ********* * * * *******

I. PRESENT-VALUE LIFE-CYCLE COST ANALYSIS

A. PRESENT-VALUE INVESTMENT COSTS

INITIAL DOWN PAYMENT

MORTGAGE PAYMENTS

REMAINING PRINCIPAL

REPLACEMENTS TO CAPITAL

RESALE VALUE AT END OF STUDY

SUBTOTAL

INCOME TAX ADJUSTMENTS

TAX SAVINGS FROM DEPRECIATION

TAX SAVINGS FROM INTEREST PAYMENTS

INVESTMENT TAX CREDITS

CAPITAL GAINS ON INVESTMENT RESALE

$250300

S27036

28371

94069

( 362911)

$936566

( 199593)

( 320559)

( 16424)

105822

NET PRESENT-VALUE INVESTMENT COST $505815

B. PRESENT-VALUE OPERATING, MAINTENANCE

ANNUAL RECURRING COSTS (NON-FUEL)

NON-ANNUAL RECURRING COSTS

FUEL COSTS

PROPERTY TAXES

SUBTOTAL

TAX SAVINGS FROM OM&R

NET PRESENT-VALUE OM&R COSTS

AND REPAIR COSTS

$1148332

61612

786479

391329

$2387752

( 1098366)

$1289386

C. TOTAL PRESENT-VALUE LIFE-CYCLE COSTS $1795201

II. ANNUAL-VALUE LIFE-CYCLE COSTS

A. ANNUAL-VALUE INVESTMENT COSTS

B. ANNUAL-VALUE OM&R COSTS

C. TOTAL ANNUAL-VALUE LIFE-CYCLE COSTS

$62794

160069

$222863

*************************************

5D
TABLE B-2 SAMPLE INPUT DATA FILE FOR TLCC COMPUTER PROGRAM

9000 DATA "TEST PROBLEM"

9010 DATA .12,30

9020 DATA .46 , .025, .28,1

9030 DATA 3

9040 DATA "BUILDING", 1000000

9050 DATA 1,25,0,0,0

9060 DATA .1, .75,0

9070 DATA 50 , .5

9080 DATA 1 9090 DATA 20,25000,10,0

9095 DATA 20,0

9100 DATA “EQUIPMENT" ,100000

9110 DATA 1,10,0,0, .1

9120 DATA . 1 , . 5 , . 1 9130 DATA 15, .1

9140 DATA 1 9150 DATA 16,100000,10,0

9160 DATA 15, .1

9170 DATA "LAND" ,100000

9180 DATA 0

9190 DATA . 1 , . 8 ,

9200 DATA 999,1.0

9210 DATA 0

9300 DATA 2

9310 DATA 900000,20 , .12,12,0 , 9320 DATA 50000 ,5, .15,1 ,0 ,2

9400 DATA 50000,.

9410 DATA 5 , . 1

9420 DATA 5,20000

9430 DATA 10,10000

9440 DATA 15,20000

9450 DATA 20,10000

9460 DATA 25,20000

9500 DATA 2

9510 DATA 10000,3

9520 DATA 1, .12

9530 DATA 11, .10

9540 DATA 21 , .08

9550 DATA 20000,2

9560 DATA 1 , .12

9570 DATA 16 , .08

9999 END

51
TABLE B-3 INPUT VARIABLES TO TLCC COMPUTER PROGRAM

VARIABLE DESCRIPTION

A$ PROJECT TITLE

11 DISCOUNT RATE

N1 STUDY PERIOD

T1 INCOME TAX RATE

T2 PROPERTY TAX RATE

T3 CAPITAL GAINS TAX RATE

T4 TAX STATUS

T4 = 1 PROFIT-MAKING ENTERPRISE

T4 = 2 TAX EXEMPT

T4 = 3 PRIVATE RESIDENTIAL

C2 TOTAL NUMBER OF INVESTMENT CATEGORIES

FOR EACH INVESTMENT CATEGORY (1=1,

C$(I)

C(I,1)

C(I ,2)

C(I ,3)

C(I,3) = 0

C(I ,3) = 1 C(I,3) = 2 C(I ,3) = 3

C(I,4)

C(I ,5)

C(1 ,6)

C(I,7)

C(I,8)

C(I ,9)

C(I,10)

C(I,11)

C(I , 12)

C2)

NAME OF I th INVESTMENT CATEGORY

NOMINAL PURCHASE COST

DEPRECIATION LIFE

DEPRECIATION METHOD

NO DEPRECIATION

STRAIGHT LINE

ACCELERATED

SUM OF DIGITS

ACCELERATION RATE (0 if C(I,3)^2)

SALVAGE VALUE (FOR TAX PURPOSES)

ADDITIONAL FIRST YEAR DEPRECIATION

(% of C(I,1))

COST INFLATION RATE

FIRST YEAR ASSESSED VALUE FOR PROPERTY

TAX PURPOSES (% of C(I,1))

INVESTMENT TAX CREDIT (% of C(I,1))

ACTUAL EXPECTED USEFUL LIFE (use 999 for land)

ESTIMATED RESALE VALUE AT END OF USEFUL LIFE

OR END OF STUDY PERIOD, WHICHEVER COMES FIRST

(% of C(I,1), in Base Year Dollars)

NUMBER OF REPLACEMENTS DURING STUDY PERIOD

FOR EACH CAPITAL REPLACEMENT (K = 1, 2, ...

Y(I,K)

R(I,K)

L(I,K)

S(I,K)

A(I,K)

B(I,K)

FI

C(I,12))

YEAR OF REPLACEMENT

COST OF REPLACEMENT (Base Year Dollars)

DEPRECIATION LIFE OF REPLACEMENT

SALVAGE VALUE (% of R(I,K)) FOR TAX PURPOSES

ACTUAL EXPECTED USEFUL LIFE

ESTIMATED RESALE VALUE AT MIN (END OF USEFUL

LIFE, END OF STUDY PERIOD)

NUMBER OF MORTGAGE LOANS

FOR EACH LOAN (I = 1, 2, ...» FI)

F(I.l)

F(I,2)

F(I,3)

F(I,4)

F(I,5)

F(I ,6)

F(I ,6) = 1 F(1 ,6) = 2 Ml

M2

M4

M5

AMOUNT BORROWED

LIFE OF LOAN (YEARS)

INTEREST RATE (ANNUAL)

NUMBER OF PAYMENTS PER YEAR

"POINTS" (in % of Loan Amount)

LOAN TYPE

FULLY AMORTIZED

INTERST ONLY, PRINCIPAL PAID AT END OF LOAN LIFE

ANNUAL RECURRING OM&R COST (Base Year Dollars)

INFLATION RATE FOR Ml (ANNUAL)

NUMBER OF NON-ANNUALLY RECURRING OM&R COSTS

INFLATION RATE FOR NON-ANNUALLY RECURRING OM&R

COSTS

52
TABLE B-3 (Continued)

FOR EACH NON-ANNUALLY RECURRING OM&R COST

M( 1 » J)

M(2,J)

N2

(i - 1, 2, M4)

YEAR OF OCCURRENCE

AMOUNT (Base Year Dollars)

NUMBER OF ENERGY TYPES USED

FOR EACH FUEL TYPE USED (I = 1, 2, N2)

E(1 ,1) ANNUAL FUEL COST (Base Year Dollars)

E(2 , I) NUMBER OF DISCRETE FUEL INFLATION RATES

FOR EACH DISCRETE FUEL INFLATION RATE (I = 1, 2, ...» E(2,I)

1(1, J) YEAR IN WHICH P(I,J) BEGINS

P(I,J) FUEL INFLATION RATE IN J th TIME PERIOD

TABLE B-4 INTERMEDIATE CALCULATION

W (1)

W (2)

W (3)

W (4)

W (5)

W (6)

W (7)

W (8)

W (9)

W(10)

W(ll)

W(12)

W(13)

W(14)

W(15)

W(16)

W(17)

W(18)

W(19)

W(20)

W(21)

W(22)

W(23)

W(24)

W(25)

VARIABLES USED IN TLCC COMPUTER PROGRAM

INITIAL COST OF ALL FACTORS

INITIAL DOWN PAYMENT

P.V. OF LOAN PAYMENTS

P.V. OF PRINCIPAL REMAINING AT END OF

STUDY PERIOD

W(2) + W(3) + W(4)

P.V. OF INTEREST PAID ON LOANS DURING

STUDY PERIOD

P.V. OF DEPRECIATION FOR INITIAL INVESTMENTS

P.V. OF DEPRECIATION FOR REPLACEMENTS

W(7) + W(8)

P.V. OF ALL REPLACEMENT COSTS

P.V. OF INVESTMENT TAX CREDITS FOR INITIAL

INVESTMENTS

P.V. OF INVESTMENT TAX CREDITS FOR

REPLACEMENTS

W(ll) + W(12)

P.V. OF RESALE VALUE OF INITIAL INVESTMENT

P.V. OF RESALE VALUE OF REPLACEMENTS

W(14) + W(15)

P.V. OF CAPITAL GAINS TAX ON INITIAL INVESTMENTS

P.V. OF CAPITAL GAINS TAX ON REPLACEMENTS

W( 17) + W(18)

P.V. OF ANNUALLY RECURRING MAINTENANCE

P.V. OF NON-ANNUALLY RECURRING MAINTENANCE

P.V. OF PROPERTY TAXES PAID ON INITIAL

INVESTMENT

P.V. OF PROPERTY TAXES PAID ON REPLACEMENT

W(22) + W(23)

P.V. OF ENERGY COSTS

53
TABLE B-5 DATA FORMAT FOR TLCC COMPUTER PROGRAM

DATA

A$

DATA

REPEAT

(C2)

TIMES

REPEAT (FI) TIMES

REPEAT (M4) TIMES

REPEAT

(N2)

TIMES

DATA

Repeat (E(2,I))

Times

11 N1

DATA

T1 T2 T3 T4

DATA

C2

DATA

DATA

c$(D C(I,1)

DATA

C(1 ,3)

DATA

C(I,2) C(I,4) C(I,5) C(I ,6)

DATA

C(I,7) C(I,8) C(I,9)

DATA

C(I,10) C(I,11)

DATA

C(I,12)

DATA

Y(I,K) R(I,K) L(I,K) S(I,K)

DATA

A(I,K) B(I,K)

FI

DATA

F(I,1) F(I ,2) F(I ,3) F(I,4) F(I,5) 1

Ml M2 M4 M5

M(1,J) (M2 , J)

N2

E(1,I) E(2,I)

1(1, J) P(I,J)

use this line only if C(1 ,3) * 0

use only if

C(1 ,12) * 0

use only

F(1 ,6) if FI ^ 0

54
APPENDIX C

TLCC EVALUATION FOR A SAMPLE INVESTMENT PROBLEM

Investor: Corporate Owner of an Existing Industrial Plant

Objective: To provide space heating for the plant at lowest cost.

Alternatives

Considered: (1) Continue use of existing oil-fired furnace using No. 2 fuel oil without

modification of the system,

(2) Purchase and install a waste heat recovery system to the jacket of the

plant exhaust stack to supplement the existing space heating furnace

and reduce its consumption of fuel oil by 90%.

Level of TLCC Analysis: After Taxes, After Inflation

TABLE C-l SAMPLE INVESTMENT PROBLEM: DATA AND ASSUMPTIONS

Time Horizon (Investor's Holding Period)

3

Discount Rate

Inflation Rate Investment Cost Data

Purchase and Installation Price

Down Payment

Loan Interest Rate Loan Life

Yearly Loan Payment

Asset Life

Depreciation (Straight-Line)

Loan Interest Payments

Resale Value at End of 7 Years c Recurring 0&M (Non-fuel) Costs

Existing Furnace^

Waste Heat Recovery System

O&M Costs

Energy Costs

Fuel Consumption for Space Heating

without Waste Heat Recovery

Fuel Consumption for Space Heating

with Waste Heat Recovery

Base Year Fuel Price

Fuel Price Escalation Rate, Compounded Annually

Federal Corporate Tax Rates

State Tax Rates

7 years

15%

8%

$35,000

$3,500

12.5%

7 years

$7,012

20 years

$1 ,750/yearb Deductible from Taxable

Income $22,750 (1 + .08) 7

$500

$200

Deductible form Taxable

Income

1,000 MBtu/year (1,055 GJ/year)

100 MBtu/year (106 GJ/year)

$5. 69/MBtu ($5 .39/GJ)

12 .% 46% income tax rate

28% capital gains rate

Not considered

3 A relatively short time horizon was selected for this example to facilitate a year-byyear display of costs; however, short time horizons are not atypical of many business

investment analyses.

b Based on straight-line depreciation, 20 year life, and a book value of $35,000.

c Salvage value is based on the remaining book value after seven years, adjusted for

inflation over the seven year holding period.

^ Non-fuel 0&M costs for the existing furnace are assumed to be unchanged by addition

of the waste heat recovery system.

55
The TLCC of each of the two alternatives over the seven year holding period is calculated

and displayed in the series of tables that follow. Tables C-2 through C-4 give the year—byyear results for alternative 1; that is, continuing to use the existing oil-fired furnace

without modification. Tables C-5 through C-10 give the results for alternative 2; that is,

supplementing the existing system with a waste heat recovery system. (The TLCC's of the

alternatives are then compared to determine the lowest cost option.)

By comparing tables C-4 and C-10, we can see that the fuel cost reductions from the waste

heat recovery system more then offset its after-tax investment and other costs. Therefore,

the waste heat recovery system has the lowest TLCC and is the preferred investment alternative on economic grounds.

56
TABLE

C-2.

ALTERNATIVE

1:

FUEL

COSTS

WITHOUT

ADDITION

OF

THE

WASTE

HEAT

RECOVERY

SYSTEM

<J> tH0 Li •> 3 0 0 ^ fa fa O Ov

fa fa fl *H

w

O

H <j CO 4J

X

(0 *0 fa* > 3 fa X fa 00

fa 0 CO (0 (0

w 0 O H O

<J

O co fa

</> fa03 0) 0 fa

fa fa TJ

O

N

fa 0 fa

w fa < 0 fa | 0 0 fa\ 3 fa X fa in 0 (0 0 0 w 0 O H o < CJ 0

fa 0o

fa

X fa 0 O H 3

T> 0

fa 0 0 O ^ O O fa vO

fa CJ fa

w

O

X 0 fa 3 fa>

O 3 U T3 in 0 0 3 0 ^"

fa fa

O 0 0 t-< U O 0 0 a

fa 0 fa 0 a fa 3 0 3

fa fa s 0

fa 0 0 fa B 3 3 0 0 fa G 3 fa CQ 0 fa fa X < 3

cr0

fa

*a - o 0

fa o

fa fa 3 0 fa fa fa fa fa 0 0 <J> 0 3

fa fa

CM

ON

ON

00CO

00

m

vO

CM

O'vO

in

VO

Ov

SJCM

CMV0

CO

CM

CO

Ov

fa

coin

in

oo co oo<*

m

fam

m

vOo

vO 0O 0

fa ** 0 0

fa

B * o o X 0 vO vO vO vO VO vO vO

fa

a 0 fa 'd- <r <r <r

fa 0 Eh 0 O fa fa o

fa fa 0 /*“

0 0 O *3- 3 fa fa 'w' co 00 <r co 00 fa Ov

fa fa fa

X CO ov

m CM CO < 0 fa. co fa ON Ov o CM in

fa fa CO 0 fa 0 vO 00 o fa CM 3 0 o X H fa fa 0 O 0 ^\ 0 U fa CM <

CM CM CM CM CM CM CM + + + + + OOo ooo

57
TABLE

C-3.

ALTERNATIVE

1:

OPERATION

AND

MAINTENANCE

COSTS

WITHOUT

ADDITION

OF

THE

WASTE

HEAT

RECOVERY

SYSTEM

</>

x

n

a) • O 4J T3 C 00

IM

BO

w

«m »H X»J CO •H

X si- 00 •a- o m <r CM o 03 4-1 '-v m CO CM 1—

Ov 00 00 ov 3 4-1 X cO rs. CM CM CM CM r—i V—i rH si- s-/ > C CO cO rH W 44 eu a o H CM M

<3 c_>

B <J> M MO VO r-4 in 00 CM CO Ov 4-1 3 4J CTv vO rs H CM in m

00 CL,

O VO

mm rs. Ov CO o

V/ CO CO OO vOm co o

pL, • • • • • • • Xlao

</>

X

M >

lO 03

— Cl, o 4-1 43 C B O vO iH

•H CO •H

w to /N 4) 4-> 1 CM m o rs 00 CO 4-1 n* 3 4-1 X CO Ov »—

Mi- vO Ov CM vO o

'w' 3 (0 cO iH sr CM CO en co CO <•

H

B o H «M S-' <! o BM

</>

C • o 4-1 CO /^N •H o CO B in /N X

4-1 4J o Ow 00 00 o CO 00

m <r

vO

u o •M

X Mf vO ov i CO vO Ov

w « 3 0) 4J CM CM CM CO CO CO CO H T) 3 X O

01

Q l3 3 04 O T3

03 Q

03

4-1

K (0 0)

>4 e X « m O o CO 03 VO vO vO vO vO vO vO

s-/

au

H 4J Sf sf si- <r

i-i

B cO o w pci u M

•CO4-1 0) —

fH CO 4-1

B ‘N « O >44 O CO 3 u < H w

O CO

OO

m CO E M X «a- 00 CO 00 CO ov

m s-/ g X 4-1 c0 m m vO vO 00 < -a oo •H CM o o <M W u B • MB M i—i CM CO si- m vO r- O 03 /> rv

•H *H 00 00 00 oo 00 00 00

/-s 4J rH o O o O o O o co CO a • • • • • 'w' r—i *H

<M 4-3 + + + + + + + B »H W 2 H H H H r—

rH

H

X

w v-/ V> v-/ V-/ v-/ -

43 <J> O

•H « M 4-1 03 CO a, o o CM 1 u o 'w' 03

CO SC

m

CO <« « oM

r-< CO

O r-l CM CO <* uo VO

w 4) >4

58
TABLE C-4 ALTERNATIVE Is TLCC OF CONTINUING USE OF THE EXISTING

FURNACE WITHOUT ADDITION OF THE WASTE HEAT RECOVERY SYSTEM

(1) (2) (3)

PV OF Fuel PV of TLCC, after taxes and inflation $

Costs, $ O&M, $ (1) + (2)

19,377 1,482 20,859

59
TABLE

C-5

.

ALTERNATIVE

2

:

FUEL

COSTS

WITH

THE

WASTE

HEAT

RECOVERY

SYSTEM

03 u

3 Q3 h W T3 ^

<4-4 C O H < « O 03 > 2 u *

n-' CLi C 00 03 coh <5 o

CO ON

•H w4J X

03 ^ M 00

0)

'—«' o

(0 w

1-1 ^ o

iM 4J CO u

03 CM

<o- M

0J T3 C ^ rH*JdOr^

(d « >H V

§ < *J I K aJ-^ C w cd h in

<2 co H cq w o o v oo W

C 4J CO O CO C

•H O O vO x 4J s a *h w {QUO 4J X

E-4 3 M M O

*T3 <4-4 0) 3 in

0) 3 X3 W 0C2 <U Q

a>

4-» o

oj e M o X 0) O U 0) u a C EH 03 MM ft5 oo

</> MM y-s

a> <u * sr 3 iJ C V C*« U-i O X

<J *H /-s 4J cn H AJ 01 V 03 CO M x

3 O (d A C U CJ M

C BJ V

< w

o> a

o o

M 4J a. 0)

fl

a) ^ 0

o3 m a> 3 03 M . J.S3! <5 a*

a>

*3 0k O 0) •H o

M •H 3

a> M 4J

/-N CM CM PQ CM 2 0) M ^ oo 0) </>

<0 3

PQ (M

M

^-N CO

*—

03 >4

ON

ON

CM

CM

ON

CM

cn

oo

CM

vO

r^- CM

on

NO

CM

CMvO

CM m

m

CM

NO

cn

On

NO

On

vO00

ON m

CM

cn

>3

-

VO M

oo cn cn -3" oo

vOo

vO

cn oo

ON CM

cm cn

oo cm m

VO M vO M

cn <r <3- m

ONm

vO<1

- VO vO VO

<r

vO

<r

VO

<r

vO

o

o

o

o

o

o

o o

o o

o

o

o

o

ON

NOm

OMCMcnstmvor60
TABLE

C-6.

ALTERNATIVE

2:

PURCHASE

AND

INSTALLATION

COST

OF

THE

WASTE

HEAT

RECOVERY

SYSTEM

fl

u *

vi a>

a

*M Vl

O

<3 <M -H

fl

flB

<;

U 4J J

00fl> ss a o

00 »—

fl *H I O

flm

fl N—

fl +

Oj

H

M

M C*4 CM

<J>

X *

fl CO Eh fl ON o

<VH -H

X o O ao > fl w Ot *fl0) aS

coVi 3 O

04 VI co cj

fl &H

CO Vl CO O CO fl ^ h a n o n

X viO Vi *H

w

fl

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X

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73 fl fl v£> fl I—ITl v

o4 fl O

fl vi

fl <u Vi a

xa

O

O fl vi

aOH fl

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CJ

M

CO fl fl CO Vi vi

fl

C

vl fl

fl

a

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</> . fl

floJ VI

x

fl CM fl CN o a »-h Sn o > a * & & N

COCOVi

fl

Vi fl O So 3 vi Hi cj s 3 fl

C*4 * **m

fl fl fl

fl fl fl flop

fl .J < fl Dm

fl Vi g g ° l

fl

fl4

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vD

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vO

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cO st

CM Os

vOon

st

CM

rHO

co r* co in

on on co

no >f cm »-h

CMm

00 CM co ON H CM m | ON CO 1 II m St -S’ CO • • • • CM

Vl

fl

flSoc

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Vl

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fl M• A

00CO

Os

vO vO vO NO 1 CO

st St 1 </>R/sm

CMH•

'd- r>» CM ON

CO oo r-«. 1 "N

vfl

O >3* r>» 1 o a a A o CM CM I—

m

COo o o rH oA • 73 m o fl

O CO Vl fl </> a 1 1 1 pH V-/ 1 1 1 j A • A m ON CO CM .. m A

<J> vi

m CM c *

fl co CO a </> fl 5k a

fl it

a

a rH -S O c m O

fl CM O rH mh

iH • o 1 1 1 1 1 1 1 1 1 1 >\ CO rH /^s fl

Vl 00 fl

fl CO *H

fl ON fl SO r >

CO

fl VI 1 fl

fl fl O CM CO CM CM CM CM rH fl H rH H iM 73 O Vi o o o o 1 fl • a

co r>. n* rs. r-v rv fl s/ rH £* fl 1 VIo

rH “N VI Ou © fl

fl

m jC

fl ••Oa * VI

CO fl o >sCO 1 1 fl o m

a 1 j j j JC -H A fl 1 o

CJ VJ CO •H Vi

Vi fl </>

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A fl > VI Vi m >

On CO fl CO •H

fl VI

w Vi iH M fl <J> fl

fl

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m fs VI 73 o c H fl fl X)

61
TABLE C-7 . ALTERNATIVE 2: DEPRECIATION ALLOWANCES FOR THE WASTE HEAT RECOVERY SYSTEM

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

Annual

Depreciation3

, $

Corporate

Income

Tax

Rate, $

Annual Tax

Reduction

Due to

Depreciation

Allowance, $

(l)x(2)

UPW

Factor,

15%, 7 years

PV of

Depreciation

Allowance, $

(3) x (4)

1,750 46 805 4.160 3,349

a Based on straight-line depreciation method, 20 year life, and book value of $35,000.

I

62
TABLE

C-8.

ALTERNATIVE

2:

RESALE

VALUE,

NET

OF

CAPITAL

GAINS

TAX,

FOR

THE

WASTE

HEAT

RECOVERY

SYSTEM

oo >

Cm Z MI r-N

<U Cd oo

f-l

ti) </> 4J r-s Ml •H - 00 (0 * CM 03 w on 3 C X c O -H /-n CM o

tO l-*.H •H Mm O n_/ Ml O to •HO

0)

MiCM

Mi CM O ON (0 • 3 4J m Ml PM U 3 3 W <0 co C 3

(Mi • CO

-'?« Mi

CO 3

Ml

a 33 o iH -c/3- /“n tn in

CO v£> CO i-n Ml « w <r O a

•H CO | CNI rH

CM

C 'v •CO- to -h eg Mi O tO w CO 3 MM o > o O p

tn o

rH •H 8 Ml E 3 o •H

co -co- in mm

O

C

w <r •H 3

•H « x

m c Mi 3 X r-v s a O tflsf <r 3 H s_/ "3 •3 3

Ml 3 3 P

Mi •H O rH

Mi 1 a Ml 6^ .C

co

p 00

C

X « o •H

•H tO 0) 00 •H 3 (OHM CM Ml Mi O to 3 Ml Pd Ml CO O

nM 3

Mi Mi 3 3

rH Ml 3

Ctf •» CO

O 3 fn

4J CO

w *3

•H

C | eg IN. *H s

cd cd eg vO 3 •3 u o ^ H Ml P

CO 3 3 O

</>

©

a

O

©

A

X o m

•O co o co C Mi o •co- W CO m in • -X 03 cn C mm O 03 >1 </> o o O 3 CM •H M H N CM Mm mi 3

tO

O 3 3 > Mm rH rH O Ml Mm 3

CO

C

O *H > O 3 O

</> 8 o O 3 -H .O * Ml Ml

(0 3 a rH

•3 CO >N 3 C Mi o 3 iH C

03

W CO ON 3 •H rH 03 ON rH Ml OO

CO 03 >M

A 3 3 •H

CO 3 00 P C Mi

5)H In CO •H 3 O

Pd to 00 00 > MM •H 3 o Mi Mm X O O Ml e 3 e O Ml o 3

*3 Mi •3 3 3

Mi 3 3 3

tO 3 X 3

03

m mj CQ 3 X

63
TABLE

C-9.

ALTERNATIVE

2:

NON-FUEL

OPERATION

AND

MAINTENANCE

COSTS

WITH

ADDITION

OF

THE

WASTE

HEAT

RECOVERY

SYSTEM

</> s >- bO 01 o 4J T3 C c-v

4-. 4-1

CO CO

m CO cn <! vO ON -3 o rH <J (0 *H 4-^ m CO rH Ov n- m

ON 3) 4-1

X co CO CO CM CM CM CM o

'w' > 3 4i

X <0

ft.

C

W (C rH I" CM

C

O

H 4-1

w

<5 0 c

</> C/3-

M

4-1 <0

>4 vO rH

m 00 CM CO ON

O

/N

O ON vO »H CM in C_> 00 3 4-1 SO in in ON CO

v-/ ft. o 00 vO in CO

X C/3 (0 • • • • • • • vS

ft. o>

</> ft.

X

u

bO 01 rH O 4-1 T3 c td 44 C O vO 4-1 /-s iH <J CO *H '—/

00 i—vO <r vO o 00 o

0) 4-1 | o <r rH

m o H 3 4J x m ^ C (0 U H C O H 4-1 w < U C

Mf (

-3

mm VO vO

M

C </> O

•rl •> 4J 4-1 CO O O M C <-v 3 4-i o o m V O Tt V 00

m VO 00 co rH CM sO # # 41 X •3- O co r- »H m

pi 3 x o

<5 <«

a <r

ro co -3 <*mm

x o •o

w <d ai H Q

6^

ai

4-1 «

<d

v ai

4.

a 4-i o o «j VO vO vO vO vO vO vO

m

a o pi <3 <*- -3- <f <r

w

u c O M

x

u id H

C/3-

4-1 -

co

C o o U *rl

4-1 ^-s S id n v« rH w vO vO CM CM ON rH o

<r

O 44

x

m rH 00 in CM fH o C /-^ 00 00 ON o fH CM

rH

H CM 0k 0> 0k CQ v 3 4. e ai

rH fH fH

a 4-i <C 4H<

44

C 01 fH CM cn <rm vO

O -H -s /-V “N

•H rH 00 00 oo 00 00 00 00

4-1 O. o o o o o O

O

<d *rl • • • • • • • CO rH 4J

v-x 4-1 fH a + + + + + + + M £ rH rH rH rH rH rH rH

s-/ NH SH V—

V-^ VH '•w'

T3O «

•H cd 44 4-1 ai co

ft. o o CM 1 c_> o ai

CO £ cd 3

CQ o

44

H cd s-* a)

O rH CM CO

m vO

>•

64

Includes

base

year

O&M

cost

for

existing

system

($500)

and

waste

heat

recovery

system

($200).
TABLE C-10. ALTERNATIVE 2: TLCC WITH ADDITION OF THE WASTE HEAT RECOVERY SYSTEM

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

PV of Fuel

Costs, $

PV of

O&M, $

PV of

Investment

Costs, $

PV of

Tax Reductions

Due to Depreciation

Allowance, $

PV of

Resale, $

TLCC, After

Taxes and

Inflation, $

(1) + (2) + (3) - (4) - (5)

1,936 2,074 27,318 3,349 12,947 15,032

65
APPENDIX D

SELECTED LCC REFERENCES

1. Smith, Gerald W. Engineering Economy (Ames, Iowa: Iowa State University Press, 1973).

2. Grant, E. L. and Ireson, W. G. Principles of Engineering Economy , 5th ed.

(New York, New York: The Ronald Press Co., 1970).

3. Mishan, E. J. Cost-Benefit Analysis , Expanded ed. (New York, New York: Praeger

Publishers, Inc., 1976).

4. Dasqupta, A. K. and Pearce, D. W. Cost-Benefit Analysis (New York, New York:

Barnes and Noble, 1972).

5. Sassone, Peter G. and Schaffer, William A. Cost-Benefit Analysis; A Handbook

(New York, New York: Academic Press, 1978).

6. American Telephone and Telegraph Company. Engineering Economy , 3rd ed. (New York,

New York: McGraw Hill Book Company, 1977).

7. Ruegg, Rosalie T. Life-Cycle Costing Manual for the Federal Energy Management and

Planning Programs , National Bureau of Standards Special Publication (In Press) 1980.

8. Kirk, Stephen J. "Life Cycle Costing: Increasingly Popular Route to Design Value,”

and "Life Cycle Costing, Taken Step by Step," Architectural Record (A two part article),

December 1979 and January 1980.

9. Hausman, Jerry A. "Individual Discount Rates and the Purchase and Utilization of

Energy-Using Durables," Bell Journal of Economics , Vol. 10, No. 1, Spring 1979.

10. Fisher, Gene H. Cost Considerations in Systems Analysi s, R-490-ASD, The Rand Corporation (New York, New York: American Elsevier Publishing Co., 1971).

11. Park, William R. Cost Engineering Analysis (New York, New York: John Wiley and Sons,

1973).

12. Ruegg, Rosalie T., McConnaughey , John S., et. al. Life-Cycle Costing; A Guide for

Selecting Energy Conservation Projc .ts for Public Buildings , National Bureau of Standards Report BSS 113 (Washington, D.C.: U.S. Government Printing Office, SD Cat. No.

003-003-01980-1, 1978).

66
13 . Marshall, Harold E. and Ruegg, Rosalie T. "Life-Cycle Costing Guide for Energy

Conservation in Buildings, Energy Conservation through Building Design , ed.

Donald Watson (New York, New York: Architectural Record Book, McGraw-Hill, 1979).

14. Simplified Energy Design Economics , ed. Forrest Wilson, National Bureau of Standards

Special Publications 544 (Washington, D.C.: U.S. Government Printing Office, SD

Cat. No. 003-003-02156-3, 1980).

67
NBS-114A (REV. 0-7 8 )

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBSIR 80-20402. Gov't Accession No. 3. Recipient's "fM

4. TITLE AND SUBTITLE

RECOMMENDED PRACTICE FOR MEASURING LIFE-CYCLE COSTS OF

BUILDINGS AND BUILDING SYSTEMS

5. Publication Date June 1980

Perfwmlnfi Organisation

7. AUTHOR(S) Rosalie T. Ruegg, Stephen R. Petersen, and

Harold E. Marshall

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, DC 20234

P»i0ct/Task/Wortt Unit No. 8M..1 fj

11. Contract/Grant No.

12. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street, City, state, zip)

Same as item 9

13. Type of Report & Period Covered

Final

: 15. SUPPLEMENTARY NOTES

[~] Document describes a computer program; SF-185, FIPS Software Summary, is attached.

16. ABSTRACT (A 200-word or leas factual summary of most significant information. If document includes a significant bibliography or

literature survey, mention it here.) Rising prices of labor, material, and particularly energy have forced builders,

architects, engineers, building owners and operators, and code writers to identify

building designs and building systems that will be cost effective in the long run. This report describes how to measure the life-cycle costs of buildings and building

systems. Life-cycle cost analysis, when applied to building decisions, provides

an economic evaluation of the net dollar effect, over time, of purchasing, constructing/installing, maintaining, operating, repairing, and replacing buildings

or building systems. This recommended practice for making life-cycle cost

evaluations will assist the private and public building communities in making

cost-effective decisions.

17. KEY WORDS (a ix to twelve entries ; alphabetical order; capitalize only me first letter of the first key word unless a proper name;

separated by semicolons)

Benefit-cost analysis; buildings; building economics; building systems standard;

cost; discounting; economic analysis; inflation; life-cycle cost; present worth

analysis; recommended practice.

18. AVAILABILITY [X) Unlimited

| | For Official Distribution. Do Not Release to NTIS

Order From Sup. of Doc., U.S. Government Printing Office, Washington, DC

20402, SD Stock No. SN003-003-

fXI Order From National Technical Information Service (NTIS), Springfield, VA. 22161

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