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U.S. DEPARTMENT OF COMMERCE/National Bureau of Standards

A Benefit-Cost Model

of Residential Fire

Sprinkler Systems
Tm he National Bureau of Standards' was established by an act of Congress on March 3, 1901. The ^ Bureau's overall goal is to strengthen and advance the nation's science and technology and facilitate their effective application for public benefit. To this end, the Bureau conducts research and provides: (1) a

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

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'Hcadquarlers and Laboratories at Gailhersburg, MD, unless otherwise noted; mailing address Gaithcrsburg, MD 20899. ^Somc divisions within the center are located at Boulder, CO 80303. 'Located at Boulder, CO, with some elements at Gaithcrsburg, MD.
A Benefit-Cost Model of

Residential Fire Sprinkler Systems

Rosalie T. Ruegg

Sieglinde K. Fuller

Operations Research Division

Center for Applied Matiiematics

National Engineering Laboratory

National Bureau of Standards

Gaithersburg, MD 20899

VATIONAI BUHZAa OF STANDARDS

UBRART ' ^ • - - CiC/00

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Prepared for: Fire Safety Technology Division

Center for Fire Research

National Engineering Laboratory

National Bureau of Standards

Gaithersburg, MD 20899

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

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Issued November 1984
National Bureau of Standards Technical Note 1203

Natl. Bur. Stand. (U.S.), Tech. Note 1203, 149 pages (Nov. 1984)

CODEN: NBTNAE

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1984

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

This study was conducted at the National Bureau of Standards (NBS) , by the

Operations Research Division of the Center for Applied Mathematics for the

Fire Safety Technology Division of the Center for Fire Research.

The purpose of the study is to develop decision models for evaluating the cost

effectiveness of providing fire loss protection in houses through the use of

automatic sprinkler systems. The focus is on modeling the investment decision

as it affects the individual homeowner. The model of the homeowner's

investment decision is illustrated in selected hypothetical cases, an appendix

to the report develops parallel decision models from the standpoint of

developers and local governments. The intended audiences of the report are

principally managers of government agencies and private organizations

concerned with the research, development, and commercialization of residential

sprinkler technology. It may also be of interest to developers, city planners

and managers, building owners and users, and other members of the building

community who are interested in the economics of sprinklers in home fire

protection.

iii
ACKNOWLEDGMENTS

Special appreciation is extended to members of the Center for Fire Research

who provided advice on technical aspects of sprinkler systems: Jack Snell,

Center Director; Andrew Fowell, Chief of the Fire Safety Technology Division;

Alan Gomberg, former Acting Leader of the Fire Hazard Analysis Group; and John

Hall and Wayne Stiefel, members of that group.

The authors also wish to thank Harold Marshall and Robert Chapman, both of the

NBS Center for Applied Mathematics, and Joseph Greenberg of the Center for

Building Technology, for their helpful reviews of the report. Special credit

is due Barbara Llppiatt, of the Center for Applied Mathematics, for her

excellent assistance in compiling cost data.

Finally, the authors wish to acknowledge the invaluable assistance and

cooperation they received from people in private industry, nonprofit

organizations, and local government in estimating the costs and benefits of

sprinkler systems.

iv
ABSTRACT

This paper develops and applies decision models for evaluating the economic

efficiency of providing fire loss mitigation in houses through the use of a

new technology: fast-response sprinkler systems. A model is developed for

calculating present value net benefits as they would accrue to an owneroccupant or an owner of a rental house who installs a sprinkler system.

Costs and benefits of owning a system are estimated for selected hypothetical

cases pertaining to a new, single-family dwelling in the United States. The

estimates are then used to illustrate the model. Minimum or maximum values

that key decision variables must take in order for sprinkler systems to be

cost effective in the selected applications are calculated through break-even

analysis. Related models are developed for evaluating the economic merits of

sprinkler systems from the standpoint of developers and local governments.

Implications for the research and building communities are discussed.

Keywords: Building economics; economic analysis; fire protection; life-cycle

costing; net benefit analysis; residential fire safety; riskbenefit analysis; sprinkler systems.
TABLE OF CONTENTS

Page

PREFACE ill

ACKNOWLEDO^ENTS iv

ABSTRACT v

LIST OF FIGURES viii

LIST OF TABLES ix

EXECUTIVE SUMMARY xi

1

.

INTRODUCTION 1

1.1 Background 1

1.2 Purpose, Approach, Scope and Organization 7

2

.

METHODOLOGY 10

2.1 The Decision Process 10

2.2 Model of the Homeowner's Investment Decision 11

2 .

3

Evaluation Techniques Used in the Model 24

2.4 Economic Parameters and Assumptions 29

3

.

SELECTED APPLICATIONS 33

3.1 Costs 33

3.1.1 Purchase and Installation Cost Estimates 33

3.1.1.1 Component Cost Estimates 34

3.1.1.2 Financing and Tax Effects 48

3.1.1.3 Other Potential Costs of Purchase and

Installation 53

3.1.2 Operating, Maintenance, Repair and Replacement

Costs 54

3.1.2.1 Operating Costs 54

3.1.2.2 Maintenance, Repair, and Replacement Costs 58

vi
TABLE OF CONTENTS (continued)

Page

3.1.3 Increased Property Taxes 64

3.1.4 Cost Summary 65

3.2 Benefits 65

3.2.1 Reduced Risk of Death and Injury 67

3.2.2 Reduced Risk of Direct Loss 75

3.2.3 Reduced Risk of Indirect Costs 78

3.2.4 Insurance Cost Savings 82

3.2.5 Municipal Cost Savings in Fire Protection Services

(Potential Property Tax Savings to the Homeowner)... 91

3.2.6 Governmental Incentives 97

3.2.7 Other Potential Benefits 99

3.2.8 Summary of Benefits Estimates 100

3.3 Case Study Results 102

3.3.1 Base-Case Results 102

3.3.2 Additional Case Results 109

4. SUMMARY AND CONCLUSIONS 115

SELECTED REFERENCES 118

APPENDIX. Related Decision Models for the Builder/Developer and

the Municipal Government A-1

vii
LIST OF FIGURES

Page

1. Residential Sprinkler Systems 3

2. System Design Used to Develop Component Cost Estimates 35

3. Assumed Annual Rate of Replacement of Sprinkler Heads During

System Life 60

4. Determining the Area of the "New Development" for Vfliich

Fire Station Costs Will Be Avoided 93

viii
LIST OF TABLES

Page

1. Automatic Fire Sprinkler System with Copper Piping for a New, Two-Story, 2175 Square Foot Urban Dwelling: Cost

Summary 38

2. Automatic Fire Sprinkler System with Polybutylene Piping

for a New, Two-Story, 2175 Square Foot Urban Dwelling:

Cost Summary 40

3. Cost Estimates for Residential Sprinkler Systems Based on System Costs as a Stated Percentage of House Construction

Costs 43

4. Cost Estimates for Residential Sprinkler Systems Based on Estimate Costs per Square Foot of Floor Area 46

5. Summary of "Base Case" Costs for Residential Sprinkler

Systems 66

6. Estimated Impact of Sprinklers on Fire Deaths and Injuries

in One- and Two-Family Houses 71

7. Estimated Percentage Reductions in Fire Deaths and Injuries

Attributable to Residential Sprinkler Systems 72

8. Estimated Impact of Sprinklers on Direct Fire Loss in Oneand Two-Family Houses 76

9. Estimated Indirect Costs of Residential Fires 79

10. Estimated Impact of Sprinklers on Indirect Fire Costs in

One- and Two-Family Houses 80

11. Estimated Property Insurance Rates in the U.S. for One- or Two-Family Dwelling and Contents 87

12. Summary of Benefits Estimates 101

13. Summary of Data and Assumptions for Estimating Benefits for

the Base-Case Illustration 103

14. Summary of Data and Assumptions for Estimating Costs for the

Base-Case Illustration 104

15. Summary of Data and Assumptions for Other Illustrations 105

16. Summary of Economic Assumptions Used in Case Studies 106

ix
LIST OF TABLES (CONTINUED)

17. Base-Case: Net Benefits Calculation 107

18. Base-Case: Break-Even Analysis 108

19. Summary of Net Benefits for Additional Hypothetical Case Studies... 110

20. Case II: Break-Even Values 114

X
EXECUTIVE SUMMARY

Fire is the second most frequent cause of accidental death in U.S. homes.

Well over a billion dollars of residential property loss results each year

from residential fires. A potential for large savings exists in measures to

reduce residential fire losses. In the face of budgetary pressures, a growing

number of towns, cities, and individuals are seeking new approaches to fire

mitigation which would offer effective protection at lower cost.

The purpose of this report is to develop and illustrate a methodology for

assessing the economic feasibility of one new strategy for preventing

residential fire losses: fast-response sprinkler systems. The focus is on

modeling the investment decision as it affects an individual homeowner, but

the interrelationship of this decision with that of builders and municipal

governments is also discussed.

The report provides background on recent changes in residential sprinkler

technology, the decision process by which sprinklers are installed in houses,

and the role of economic analysis in addressing key issues related to

diffusion of the technology. It develops a benefit-cost model for determining

the expected value of net benefits as they would accrue to a homeowner who

invests in a fast-response sprinkler system.

The benefit-cost model encompasses the future benefits to a homeowner of

purchasing and installing a residential sprinkler system, as well as the

life-cycle costs of owning the system over its expected life. Potential

benefits consist primarily of reduced risk of death and injury from fire;

xi
reductions in risk of direct property losses and indirect losses such as

medical and legal expenses, missed work, and cost of temporary shelter;

possible savings in fire insurance costs; and possible reductions in local

property taxes if the comiminity collectively adopts sprinklers. Potential

costs consist primarily of purchase and installation costs, adjusted for future

resale value; operating, repair, replacement, and maintenance costs; and

property taxes based on the value of the system. The model also takes into

account financing costs and applicable income tax adjustments.

The model expresses the benefits of reduced fire losses in expected value

dollars, reflecting the probability of fire occurring and of deaths. Injuries,

and direct and Indirect losses resulting under alternative conditions of fire

protection. Various components of system operating costs are also modeled

as expected values, reflecting their functional relationship to the

probability of fire occurring. All dollars of benefits and costs are taken

over the entire period during which the homeowner is expected to have home

sprinkler protection, and are adjusted to present value dollars so that they

can be compared on a time-equivalent basis. Present value costs are subtracted

from present value benefits to yield net present value benefits or losses.

The model assumes that the homeowner is risk neutral and seeks to maximize the

net benefits obtainable from available funds. Hence, from an economic analysis

point of view, positive net benefits from applying the model are interpreted to

mean the homeowner will generally wish to purchase a system, while net losses

xii
indicate the contrary, apart from possible constraints such as income

availability and the size of the initial cash outlay requirements.

These assumptions constitute limitations of the model in that homeowners in

actuality exhibit varying degrees of risk preference, have imperfect

information, and in any case do not always behave as rational economic

decisionmakers. Despite these limitations, correct application of the model

can be expected to suggest tendencies of the homeowner to wish to buy or not

to buy the system.

Parallel decision models for builders/developers and for local governments

are also developed and presented in Appendix A of the report.

The report applies the decision model in a series of nine case illustrations,

all of which are hypothetical in nature. The cases both demonstrate how the

model is used and allow inferences to be drawn about the potential economic

feasibility of sprinkler systems under the specified conditions.

All of the cases are based on (1) a system for a new, two-story, 2,175 square

feet urban dwelling, that meets the requirements of NFPA 13D-1980 Standard;

(2) an "average" probability of fire derived from aggregate U.S. fire

statistics; (3) sprinkler system performance based on the results of recent

laboratory and field tests of system effectiveness; (4) long-run average

opportunity cost to the homeowner of 11.3 percent, including inflation and

xiii
6% excluding inflatiou, on alternative investments of equal risk; (5) a value

per life of $0.50 million and per injury of $0.02 million; (6) a 40 percent

marginal composite income tax bracket for the homeowner; (7) a system life of

30 years; (8) direct and indirect losses per fire corresponding to averages of

sample loss data for the U.S. and (9) insurance rates and property tax rates

and property tax rates corresponding to averages of sample data for the U.S.

The distinguishing features of each case and its "bottom line" estimate of net

benefits or losses are suumiarized briefly and may be compared in the following

matrix. Break-even analysis is conducted to indicate the minimum or maximum

changes in the values of key variables which would be necessary to equate

benefits and costs under various conditions. For example, the results of the

break-even analysis indicate that for Case I, any one of the following values

would be sufficient to yield a break-even outcome, all other factors remaining

the same: (1) a value of life of $2.6 million (not discounted); (2) a

probability of incurring a fire about 7 times the U.S. average rate; (3) a

percentage reduction in the insurance rate about 5 times that assumed; and (4)

an annual property tax reduction to the homeowner of about $100. For Case II,

examples of computed break-even values are the following: (1) a reduction in

system costs of about 6 percent; (2) a probability of incurring a fire only

slightly greater than that assumed; and (3) an average value of uninsured

property loss per fire without sprinklers about 3 times larger than the

estimated U.S. average dollar loss for houses without sprinklers.

xiv
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The results of the case studies are based on many assumptions, and it should

be recognized that under different conditions, actual net benefits may be

significantly different from those found in these illustrations. However, the

cases provide some insight into the cost effectiveness of residential

sprinkler systems in particular applications.

Some inferences that may be drawn from the case studies are the following:

(1) The cost effectiveness of residential sprinkler systems is improved by

code changes which allow the use of approved plastic pipe. (2) Sprinkler

systems may be uneconomical for homeowners who independently purchase systems

and who are subject to low-to-average probabilities of fire and risks of

death, injury, and property loss; but they may be cost effective for homeowners subject to higher risk of fire and in greater peril of injury if fire

occurs. (3) Sprinkler systems are more likely to be cost effective, other

factors being the same, for homeowners who are part of a community of

sprinkler users and who receive the benefit of attributed cost avoidance by

local government or by the home builder. (4) Homeowners who live in

localities with "water standby fees" or who use the commercial sprinkler

systems are unlikely to have a cost-effective sprinkler system under average

probabilities of fire and related death, injury, and property loss. (5)

Sprinkler systems are more likely to be cost effective when used in situations

where additional protection is needed, such as a situation where the benefits

of smoke detectors alone may not be attainable, for instance when occupants

are hearing-impaired or otherwise incapacitated and cannot respond to a

detector warning signal.

XVI
The findings, though based on hypothetical cases, are helpful in identifying

the following areas for further investigation: (1) the potential of municipal

cost savings from sprinklered houses and the feasibility of corresponding

local tax reductions, (2) the feasibility of cost/performance tradeoffs

between sprinklers and housing density and between sprinklers and fireresistant construction methods and materials, (3) the availability of

discounts on insurance premiums, (4) the practice of levying water demand

charges on sprinklered houses, (5) approaches to lowering the costs of

purchasing and installing sprinklers, (6) retrofit capability, (7) partial

systems for fatality-prone areas of the house, and (8) benefits accruing to

households with different behavioral and demographic characteristics and

living in houses of different construction and age. The usefulness of the

model as a decision tool for the homeowner can be increased by incorporating

utility analysis. The models for builders/developers and for local government

(Appendix) can be refined, tested, and used as aids to decision making.

xvii

1. INTRODUCTION

1.1 Background

Residential fires cause more deaths, injuries, and property losses than any

other kind of fire. Over 4,000 people were killed and another 14,000 injured

in the approximately 522,000 reported fires that occurred in one- and two-family

dwellings in the United States during 1981. More than 20,000 fire fighters were

injured trying to extinguish these fires and rescue the occupants. Many of the

injured suffered emotional damage. Over one and a half billion dollars of

direct property loss resulted. ^ Indirect costs, such as the costs of temporary

shelter, missed work, and legal, medical and funeral expenses, added nearly half

a billion dollars of additional loss.^

There is a potential for large savings through measures to reduce residential

fire losses. This report is one step in the search for cost-effective

solutions.

There are a number of strategies available for substantially reducing

residential fire losses. These include enlarging the number and size of

fire stations, carrying out public education programs to change human

behavior in the built environment, increasing the fire resistance of building

construction materials and furnishings through research and development and

code and standards requirements, and installing protective systems within

^ Fire in the United States, Fourth Edition , Federal Emergency Management

Agency, Washington, D.C. 20472, September 1982.

^Michael J. Munson and James C. Ohls, Indirect Costs of Residential Fires , Federal Emergency Management Agency, U.S. Fire Administration, Washington, D.C.

20421, July 1979.
houses. However, these loss avoidance strategies can also be costly, and

their costs add to the direct and indirect costs of fire losses to constitute

the total cost of fires to the nation. As public resources for fire

protection become increasingly limited, it becomes urgent for public

officials, building designers, builders, and building ovmers to examine

performance/ cost tradeoffs among the alternative strategies for fire

protection and to identify ways to minimize the overall cost of fires to

individuals, communities, and to the nation.

The focus of this study is the development of a methodology appropriate for

determining the potential cost effectiveness of one strategy for preventing

residential fire losses: an automatic sprinkler system for installation in

one- and two-family housing. An automatic sprinkler system consists of a

configuration of water piping to which are connected automatic sprinkler

heads, devices which open individually and automatically by operation of a

heat-responsive releasing mechanism to discharge water in a specific pattern

and density over a designated area. Sprinkler systems reduce losses to people

and property by suppressing fire spread and either extinguishing the fire

altogether or containing it to a smaller size. Thus sprinkler systems

generally increase the time and available routes for occupants to escape

fires, and they limit the amount of property damage.

To illustrate the sprinkler system being discussed, figure 1 shows in part A

the diagram of a sample configuration of piping for a residential sprinkler

system; part B illustrates a fast-response sprinkler head; and part C depicts

a sample design schematic for a residential system.
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sprinklers are a relatively new technology for residential use. A recent

news report indicates that there are only about 2,000 houses in the United

States which have sprinkler systems,^ In contrast, sprinkler systems have

long been widely used in commercial and institutional buildings, where their

effectiveness in saving lives and protecting property has been well

documented,

2

A major impediment until recently to the use of sprinkler systems in

residences was the absence in the marketplace of systems specially engineered

for home use. Faster sensing and activating devices are generally required

for residential use than for commercial use because temperatures and gases

rise to lethal levels faster in smaller rooms with lower ceilings. Moreover,

differences in the typical distributions and nature of room contents cause the

commercial sprinkler heads not to be well suited for residential use. Another

problem has been system appearance. ^ in a survey, a significant proportion of

homeowners voiced apprehension about the possible deleterious appearance in

their homes of commercial-type systems. Fear of accidental discharge

accounted for further reluctance of homeowners to install the systems.^ The

1 "Dousing Home Fires," The Washington Post , Saturday, July 10, 1982, p. E-1.

^Federal Emergency Management Agency, Report to Congress on Fire Protection

Systems: Detectors, Remote Alarm Systems, and Sprinklers , Washington, D.C.:

U.S. Government Printing Office, June 1981).

3 John J. Carlin III and Allen Stephens, "New Residential Sprinkler Standards

Adopted," The International Fire Chief , February 1981, p. 23.

^Rolf Jensen & Associates, Inc., Study to Establish the Existing Automatic

Fire Suppression Technology for Use in Residential Occupancies , prepared for

U.S. Department of Commerce, National Fire Prevention and Control

Administration (Washington, D.C., August 1977), pp. 2-6.
high cost of commercial-type systems, as well as the lack of an active

distribution and service network for residential users, further discouraged

their adoption for residential use. These impediments, together with a low

level of public awareness of the fire problem—and, hence, low value assigned

to fire protection systems —resulted in little activity in the residential

sprinkler market.

Recent developments, however, suggest the need for a closer look at the

potential for sprinkler systems in houses. Engineering developments include

the production and marketing of a residential fast-response sprinkler head

that activates 5 to 15 times faster than previously available commercial-type

heads. 1 It also has an improved water distribution pattern better suited to

residential use. The likelihood of unnecessary activation of sprinkler heads

beyond those in the immediate vicinity of a fire is reduced. ^ The threat of

accidental discharge also has been reduced to extremely low levels: less than

one-in-one million sprinkler heads per year compared to the roughly one-in-one

hundred per year chance of having a home fire big enough to be reported to the

fire department.-^

^Ad Hoc Insurance Committee on Residential Sprinklers, Report on 1980 Property

Loss Comparison Fires (Reprinted by Federal Emergency Management Agency, U.S.

Fire Administration, National Fire Data Center, Washington, D.C.), November

1980, p. 22.

2"New Residential Sprinkler Standards Adopted," The International Fire

Chief , February 1981, p. 23.

^Federal Emergency Management Agency, Report to Congress .
Design developments include the production of specially designed residential

sprinkler systems which are less obtrusive and may meet aesthetic requirements

for most houses. Design changes embodied in the revised 1980 National Fire

Protection Association (NFPA) 13D Standard for residential sprinklers offer

the potential of lower cost systems. The allowance of a combined piping

system serving both sprinkler and domestic needs offers the potential of lower

piping costs, and the allowance of a small-orifice sprinkler head reduces

water flow requirements. Furthermore, although not explicitly listed as

acceptable piping material, plastic piping—with its considerable potential

for further cost reductions—is not precluded by the 13D Standard provided it

be approved by a testing and inspection agency laboratory.

Additional cost improvements are provided by the reductions in fire insurance

that some companies are offering to homeowners with sprinklered houses. And,

perhaps most importantly, communities that use residential sprinkler systems

on a large scale may be able to reduce the costs of centralized fire

protection.

Assessment of the technical performance and impact potential of the improved

residential sprinkler system is underway, ^ as are research efforts to improve

^National Fire Protection Association, Inc. , Sprinkler Systems —One- and

Two-Family Dwellings, 1980 , ANSI/NFPA 13D (November 20, 1980).

^Edward K. Budnick, Estimating Effectiveness of State-of-the-Art Detectors and

Automatic Sprinklers on Life Safety in Residential Occupancies , National

Bureau of Standards, NBSIR 84-2819, January 1984.
further the engineering and design of the system. 1 Benefit-cost studies are

needed to estimate its current and potential economic feasibility.

1,2 Purpose, Approach, Scope and Organization

The purpose of this study is to develop a benefit-cost model for evaluating

the economic efficiency of providing fire loss protection in one- and twofamily houses through the use of automatic sprinkler systems, and to

demonstrate the use of the model through selected hypothetical case studies.

The homeovmer's perspective is taken in the model, because the homeowner is

the ultimate decisionmaker and the elements of this model are fundamental to

formulating other decision models. It is recognized, however, that

builders/developers and municipal governments also play critical roles in the

decision process; and those roles in relationship to the homeowner are

discussed and requirements for additional decision models are treated.

The results of a benefit-cost study have a number of potential applications.

Managers of government fire research programs, charged with reducing the total

cost to the nation of residential fires, can use benefit-cost studies to

identify fire research efforts with large potential payoffs, needed changes in

building codes and standards, promising areas for coordinated decisionmaking,

and information which can improve decisions of homeowners, developers, and

communities regarding residential fire protection. City planners and managers

seek information that will assist them in formulating economically efficient

strategies for protecting the lives and property of citizens from destruction

^Battelle Columbus Laboratory, Development of an Experimental Prototype LowCost Electronic Sensor/ Actuator for a Residential Automatic Sprinkler Head , Report prepared for the Federal Emergency Management Agency, Undated.

7
by fire. Architects, engineers, builders, and developers look, for ways to

deliver safe housing at affordable prices. And consumers seek information

regarding the cost effectiveness and performance of new methods of fire

protection.

The approach is, first, to outline the decision process, pointing out the

interactions of homeowner decisions with those of builders/developers and

government. Then a model of the individual homeowner's investment decision is

developed. (Parallel models of builder/developer and local government

decisions are also developed and presented in the appendix of the report.)

Estimates of life-cycle benefits and costs to a hypothetical homeowner of

installing and operating a sprinkler system are then made, based on U.S.

average statistics and stated assumptions. Inferences are drawn from the

results, and recommendations for further research are given.

The benefit-cost model employs conventional techniques of discounted cash flow

analysis over an extended period of time, taking into account probabilistic

estimates of sprinkler impact on fire losses. Break-even analysis is used to

estimate maximum/minimum values of selected parameters to test conditions

under which sprinkler systems are cost effective. Sensitivity analysis is

performed by varying the data and assumptions in 9 case studies.

The benefit-cost model is generally applicable to the evaluation of

sprinkler systems in all kinds of buildings. The illustration of the model in

this study, however, is limited to new, one- and two-family dwellings.

Retrofit applications to existing housing and applications to apartment buildings are not considered. The economic assessment is based on a level of

sprinklers conforming to the ANSI/NFPA 13D-1980 Standard.

8
The remainder of the report is organized in four major parts. In part 2, the

decision process is discussed and the homeowner's decision model is developed.

Part 3 contains the case studies. Part 4 contains a discussion of the findings, their implications, and suggestions for further research. An appendix

concludes the report. The appendix develops models of system cost

effectiveness from the prospective of the builder/developer and the municipal

government, incorporating elements of the model of the homeowner's decision.
2 . METHODOLOGY

2.1 The Decision Process

The decision to include fire sprinkler systems in houses may be made by

individual homeowners, by builders/developers who, responding to market

demand, may offer them as a standard feature in speculative housing, or by

municipal governments who may mandate their use through the code process. The

investment decisions of individual homeowners and builders/developers may be

influenced by costs and benefits, as well as related tax, code, and zoning

provisions of local. State, and national governments. Some municipal

governments may offer builders/developers and homeowners financial inducements

to install sprinkler systems, predicated on a substitutability of

self -protection strategies, such as sprinklers, for collectively provided fire

protection strategies, such as fire stations. For instance, builders/

developers who agree to install sprinklers in speculative housing may be

offered cost-reducing concessions by the local government in the form of

zoning approvals for higher density housing, reduced code requirements for

fire resistant construction, and lessened land set-aside requirements for fire

lanes and stations. These cost reductions may increase the builder's profit,

and/or lower housing costs to consumers. Hence, while public officials do not

directly purchase and install residential sprinkler systems, their decisions

can critically affect the investment decisions of those who do.

The ability of a community to reduce collectively provided protection services

in exchange for self protection is dependent on the proportion of residents

who invest in sprinklers. For example, the decision of only a few homeowners

to install sprinklers affords little opportunity for changing housing

densities or scaling down the size of fire stations.

10
2.2 Model of the Homeowner's Investment Decision

For the purpose of this study, the homeowner's decision criterion for

investing in fire protection will be defined as maximizing the expected value

of net benefits from the available budget. Thus, the evaluation model

captures both the expected value of benefits to be derived from a residential

sprinkler system and the total life-cycle costs of owning, operating,

maintaining, and repairing a system. Total present value benefits

N /eVBj \ V] I

1 consist of expected reductions in risk of death and injury,

3=1 l(i+d)jy

reductions in expected direct and indirect losses, and reductions in certain

N / EVC-j \

homeownership costs. Total present value costs ^ | j are the sum of

j = l\(l+d)^/

purchase and installation costs, operating, repair and maintenance costs, and

other increased costs of homeownership attributable to the sprinkler system.

Net present value benefits are the excess of benefits over costs, and net

present value losses are the excess of costs over benefits.

The model can be represented as follows:

N / EVBj - EVCj

j = l\ (1 + d)J

11
where.

ENB = expected present value dollars of net benefits (or loss) to a homeowner from owning a fire sprinkler system,

EVB-j = expected value of homeowner's benefits in year j,

EVCj = expected value of homeowner's costs in year j,

N = the number of years over which benefits and costs of the system

are evaluated, beginning with j = 1, and

d = the homeowner's discount rate.

Dividing total benefits and total costs of the sprinkler system into major

components, the model may be restated as follows:

N / EVBj

J=U (1+d)^

N / EVCj

= DI + PL + C + IN + MTS + OB (2)

j=l\ (1+d)^

= PI - S + OP + M + P + OC (3)

and ENB = [DI + PL + C + IN + MTS + OB] - [PI - S + OP + M + P + OC] (4)

where.

The "bar" denotes present value, and

DI = present value of reduced risk of death and injury,

PL = present value of reduced risk of uninsured and non-reimbursable

direct losses,

C = present value of reduced risk of out-of-pocket indirect costs,

IN = present value of insurance premium discounts (Note that total

insurance costs need not be taken into account if it is assumed

that insurance will be purchased whether or not the homeowner buys

sprinklers, i.e. only the differential cost attributable to

sprinklers need be included.).

12
MTS = present value of local tax savings due to municipal cost

reductions,

OB = present value of other sprinkler benefits, such as lower

construction costs due to lower requirements for fire resistant

construction,

PI = present value of purchase and installation costs taking into

account financing, deductions of interest costs from taxable

income, and other applicable tax effects,

S = present value of resale proceeds of the sprinkler system if the

house is sold prior to the end of its useful life,

OP = expected present value of total life-cycle operating costs,

M = present value of maintenance, repair, and replacement costs,

P = present value of property tax,

OC = present value of other costs resulting from sprinkler use.

The formulas for calculating each of the above present value benefit and cost

items are described below. The present value benefits of reduced risk of

death and injury to the homeowner (DI) are modeled as follows:

DI = [(p(s,f).p(F&D)pc'DV) + (i(s,f)«P(F&I)pc«IV)]*(UPW* ) , (5)

d,n,e

where.

p(s,f) = predicted fractional reduction in the probability of death

given a fire, attributable to a sprinkler system, i.e.^

P(D|F)pc - P(d|F)s

p(s,f)

p(d|f) pc

where P(d|f) denotes the probability of death given a fire and

subscripts pc and s denote risk conditions prior to and after

sprinkler installation, respectively,

P(F&D)p(. = joint probability of fire (F) and death (D) given a condition

of prior protection, pc, i.e., P(F&D)pc = P(F) P(D|F)pc,

DV = estimated dollar value of a death averted.

13
i(s,f) = predicted fractional reduction In the probability of an Injury

given a fire, P(i|f), attributable to a sprinkler system,

where i(s,f) is analogous to p(s,f) above.

P(F&I)pj, = joint probability of fire (F) and injury (I) given a condition

of prior protection, pc, i.e., P(F&I)pc = P(F) P(l|F)pc,

IV = estimated dollar value of an injury averted.

UPW = a modified uniform present worth discount formula for finding

d>n,e ^)^Q present value to the homeowner of a series of amounts

escalating at a compound rate of e over n periods, where

,n"

UPW* = ( 1+e) . d,n,e (d-e)

1 -/1+e , if e ^ d, and

l+d;

UPW*d,n,e = ^» if e = d.

This expression of the formula does not include the number of occupants of the

house because it is developed for intended use with fire, death, and injury

frequency data which implicitly reflect some average occupancy rate. To apply

the model to cases with specific occupancy levels, it would be necessary to

add an adjustment factor to account for occupancy levels smaller or larger

than implied in national data averages.

The present value benefits of reduced risk of uninsured and non-reimbursable

direct losses to the homeowner (PL) can be modeled as follows:

PL = Ji(s,f) .P(F) 'LDpc'UPW* (6)

d,n,e

where.

Jl(s,f) = predicted fractional reduction in direct uninsured and non- reimbursable fire loss attributable to a sprinkler system.

P(F) = probability of fire occurring,

estimated dollar value of dire

loss per fire under prior protection state, pc, and

LDp(, = estimated dollar value of direct uninsured and non-reimbursable

UPW as defined previously for equation 5.

d,n,e

14
The present value benefits of reduced risk of out-of-pocket indirect costs

(C), such as legal expenses, temporary shelter, and transportation, can be

modeled as follows:

"C = c(s,f) • P(F) • CVpc • UPW* , (7)

d,n,e

where,

c(s,f) = predicted fractional reduction in indirect fire costs,

CVpc ~ estimated average value of out-of-pocket indirect costs per

fire under the prior protection state, pc, and

P(F) and

r

d,n,e

UPW as defined previously.

The present value benefit of a discount in insurance premiums due to

sprinklers (IN) can be modeled as follows:

Tn = id(in . IS) • UPW* , (8)

d,n,e

where,

id = the fractional discount in premiums for homeowner's insurance for a sprinklered house,

in = the insurance rate per $1,000 of homeowner's coverage,

IS = the amount of insurance coverage, in $1,000' s, and

UPW as defined previously.

d,n,e

(Equation 8 is elaborated upon in section 3.2.4 to take into account the

presence or absence of discounts related to smoke detectors and to distinguish

owner-occupied and rental housing.)

15
The present value benefits accruing to the homeowner from a passthrough of municipal reductions in costs of collective fire protection

services (MTS) can be modeled as follows:

MTS = n AS+AL + I AO.+AM. + AN. + AOS.

J J J J • UCR^,n • UIWd,n

H

(1-tf)

(9)

where,

MTS is modeled mainly for fire station cost reductions or cost

avoidance, and

A denotes reduction in costs attributable to sprinklered houses,

AS = reduction in fire station structure costs,

AL = reduction in fire station land costs,

UCR^ n

~ uniform capital recovery formula for amortizing the structure

land, operating, maintenance, staffing, and other costs at the

estimated municipal discount rate, d, over n years,

UPW^j jj = uniform present worth fornaila for finding the total present

value over n years of the amortized cost at the homeowner's

discount rate, d,

0^ = operating cost of the fire station in year j,

M-j = maintenance cost of the fire station in year j,

N-j = staffing costs to provide fire protection services in year j,

OSa = costs in year j of other collective fire protection services,

H = number of households sharing the cost reductions or cost

avoidances for collectively provided fire protection services

and

tf = homeowner's marginal federal income tax rate.

16
Other present value benefits to the homeowner of having a sprinkler system

(OB) might include lower construction and materials costs due to lessened code

requirements for fire resistance, and lower land costs due to increased

density allowances or smaller land set-aside requirements. These other

potential benefits are neither modeled in detail nor included in the benefits

estimates of this paper. As mentioned before, benefits represented by MTS and

OB are likely to arise only if the individual homeowner buying a sprinkler

system is part of a large, geographically significant bloc of sprinkler

owners.

Purchase and installation costs can be adjusted to a present value basis (PI),

taking into account financing of the system as part of the house mortgage^, as

well as related tax effects, as follows:

n

PI = (PI- DP) +[PI.(l-DP)'(UCRi^ji)'(UPWd,;i/n)] " I [ (t) .(RPj) -(i) '(SPWd, j ) ] - j=l

TC - DTS, (10)

where,

PI = contract cost of system purchase and installation,

DP = fraction of PI placed as a downpayment,

UCRj^ £ = uniform capital recovery discount formula for amortizing the

amount borrowed at mortgage loan interest rate, i, over i loan

payment periods,

UPW(j ^/n = uniform present worth discount formula for finding the

present value of the mortgage payments over the study period,

where the UPW is based on i periods if Ji<n and on n periods

if i>n (if Ji>n, such that the UPW is based on n, the estimate

of resale value should deduct any remaining loan costs owed at

the time of resale)

,

^The system is considered to be financed as part of the mortgage, since it is

assumed to be installed in a newly constructed house.

17
t = marginal composite (Federal, State, and local) income tax rate

of the homeowner,

RPj = remaining principal outstanding on the loan in year j, where,

for j = 1, RPi=PI • (1-DP), and for j>l, RPj-i - [(PI) •(1-DP) • (UCRi^£) - (RPj_i).(i)],

i = interest rate on the mortgage loan,

SPWd -j = single present worth discount formula for finding the present

value of the mortgage interest tax deduction in year j

,

TC = present value of any available governmental tax credits to

purchasers of home sprinkler systems.

DTS = present value of income tax savings due to depreciation of

system acquisition costs if applicable (generally applicable

only to rental housing)

.

The present value of resale proceeds realizable from selling the house prior

to the end of the system's useful life (S) are deducted from other costs, and

can be modeled as follows:

"S = Sn • SPW* , (11)

d,n,e

where,

Sjj = selling price of system at the end of the study period, where

Sn is adjusted for any outstanding balance on the mortgage loan, as well as applicable capital gains tax and, for a rental house,

depreciation recapture tax, and

SPW = single present worth formula, modified to include a constant

d,n,e rate of escalation over n years, for use in finding the present

value of resale at the end of year n.

The expected present value of life-cycle operating costs (OP), consisting of

water costs, water damage costs, and, for systems with pumps, electricity

costs, can be modeled as follows:

OP = WC + WD + ¥ , (12)

•As sprinkler systems become more widely used, it may be possible to refine

the estimation of resale price by incorporating a sprinkler variable into

residential hedonic price indices to reflect sprinklers as one of the

attributes which may influence housing prices. See, for example, Michael G.

Ferrl, "An Application of Hedonic Indexing Methods to Monthly Changes in

Housing Prices, 1965-1975," AREUER Journal , Vol. 5, 1977, pp. 455-465.

18
where.

WC = present value of water costs with the sprinkler system versus without it,

WD = present value of water damage costs with the sprinkler system

versus without it, including costs from accidental discharge,

E = present value of electricity costs, for operating the system, if

applicable.

Water consumption costs and water damage costs will be incurred only if the

system is activated. There are two main types of activation that may be

considered: (1) intended activation induced by fire and (2) inadvertent, or

accidental, activation. The latter is likely the only significant type to

evaluate, because water consumption and water damage that would result from

having the fire department extinguish a fire are likely to far outweigh that

resulting from sprinkler activation.

The present value water consumption costs (WC^) for accidental discharge,

though likely to be trivial in most cases, can be estimated using the

following equation:

wcad = p(ds|nf) • (W . Uad) • UPW* . [1 - (t .A)] (13)

d,n,e

where.

W^AD ~ present value of life-cycle water consumption cost for

accidental discharge.

P(DS|nF) = conditional probability of discharge (DS) given no fire (NF)

P(DS|nF) = P(NF&DS)

P(NF)

19
W = cost per unit of water,

^AD ~ units of water consumed during accidental discharge,

t = marginal income tax rate of the homeowner, and

A = 1 if rental unit,

if owner-occupied.

The water damage costs from accidental discharge (WD^) can be modeled in a

comparable way as follows:

wdad = p(ds|nf) • (Dad) * upw* • [i - (t • a)] (i4)

d,n,e

where.

D^D = cost of repairing water damage in case of accidental discharge,

and all other variables are as in equation (13).

The remaining element of operating costs is the present value of electricity

costs, E, for a system requiring a pump. This cost would be modeled similarly

to WC^D, except that electricity price and quantity would be substituted for the

price and quantity of water, W • U.

The present value of maintenance, repair, and replacement costs (M) over the

life cycle can be modeled as follows:

n M =|(wni . hm . UPW* ) + I [(wrri * ^rvO + ^rri] • SPW*

d,n,e j = i

-J

-^ " d,j,,

. [l-(t.A)], (15)

20
where,

Wm = wage rate per hour for routine maintenance,

h^ = length of time in hours required for annual routine

maintenance,

UPW*

d>ii»e = uniform present worth discount formula modified to allow for

escalation of the wage rate at rate e,

^rri ~ wage rate per hour for repair and replacements in year j

,

'^rri ~ average length of time in hours required for repair and

replacement in year j

,

mj-j-A = materials cost for repair and replacement in year j,

SPW = single present worth discount formula modified to allow for

<i»j»6 escalation of prices at rate e,

t = marginal composite income tax rate of the homeowner, and

A = 1 if a rental unit,

if owner-occupied.

The present value of increased property taxes (P) over the life cycle can be

modeled as follows, based on a straight-line obsolescence rate: _ n

P = 5; [PI . (1 - j/n) . tp . SPW* . (1 - t)], (16)

j = l d>j,e

where.

PI = contract purchase and installation cost of the sprinkler

system.

1-j/n = obsolescence factor, designed to result in a zero remaining

tax base at the end of the system life, and

tp = effective property tax rate.

SPW* = single present worth formula, modified to include a constant rate

d,j,e of escalation over j years, for use in finding the present value

of increased property taxes, and

t = marginal composite income tax rate of the homeowner.

21
The investment in the sprinkler system is estimated to be economically

efficient if the present value of expected net benefits is positive, i.e. if

NB>0. The assumptions are that the investor is risk-neutral and other

things remain equal. Other factors which may in fact not remain equal and

which are not incorporated in the model include such things as valuation of

aesthetic effects, consumer willingness to use new technologies, availability

of system sales and system maintenance service in the marketplace, and local

codes governing the use of sprinklers.

It should also be noted that an estimate of positive net benefits for

sprinklers does not necessarily mean that homeowners will purchase them, even

disregarding noneconomic considerations. Previous studies have shown, for

instance, that a homeowner's decision to purchase analogous kinds of new

housing technologies have depended critically on other economic factors such

as the relative size of the initial cash outlay, the particular pattern of

cash flows, or the perceived value of the investment as a status symbol.

Further complicating the prediction of a homeowner's investment decision based

on expected value results is variable risk preference. Homeowners may be

risk-seeking, risk-indifferent, or risk-averse, as reflected in the shape of

their utility functions. The criterion described above of maximizing the

expected value of net benefits is relevant only if the decisionmaker's

^See, for example, Arthur J. Reiger, Marketplace Realities and Solar

Economics . (U.S. Department of Housing and Urban Development Report,

distributed by the National Solar Heating and Cooling Information Center)

,

June 1978.

22
utility function is linear, which it may or may not be. If it is not linear

(i.e., the decisionmaker is not risk neutral), then preferred acts of

investments can only be identified by converting expected values to expected

utilities. This is possible for individuals, but there is no well-founded

procedure for combining individual utility functions to obtain a group utility

function, and, in fact, it may even be impossible to do so.^

A further limitation is the static nature of the model. It fails to capture

fully the dynamic interactions of community, developer, and homeowner

decisions. For example, community cost avoidance, which is modeled as a lower

property tax to the homeowner, may simultaneously affect the conditional

probabilities of fire loss and changes in insurance rates. Developer cost

reductions from building more densely may alter the incidence of fire, and

affect the homeowner in ways not captured by the model.

Some limitations are imposed not by the model itself but by the unavailability

of data. It is difficult or impossible to obtain for all components of the

model reliable and consistent data.

Despite these limitations, the above model can be helpful in predicting the

market potential of residential sprinkler systems. The cost effectiveness of

a new technology is an important determinant of its market rate of diffusion.

^See Arrow's impossibility theorem in K.J. Arrow, Social Choice and Individual

Values , second ed.. New Haven, Connecticut: Yale University Press, 1963.

23
[Decision models for the builder/developer and of the municipal government are

developed and presented in the appendix. These show how the elements of the

models are interrelated.]

2.3 Evaluation Techniques Used in the Model

This section gives a brief reference to some of the techniques employed in the

benefit-cost model for the convenience of the reader who is unfamiliar with

the techniques.! The reader who does not require this background may wish to

go directly to section 3.

Life-Cycle Approach . When first costs are relatively high and related

benefits accrue over time, an economic evaluation method that employs a lifecycle approach, accounting for benefits and costs over the investor's time

horizon, is generally appropriate. "Life-cycle costing" is a method for

summing the stream of an investment's costs over time, where these costs are

adjusted to a time-equivalent basis by a technique called discounting. ^ The

same type of approach can be applied to benefits, whereby the stream of

benefits over time is also discounted and summed. By subtracting discounted

•'•For a general reference to benefit-cost analysis, see E. J. Mishan, CostBenefit Analysis , New York: Praeger, 1982.

^For a further description of life-cycle costing, see Rosalie Ruegg and Harold

Marshall, "Economics of Building Design," Solar Age , July 1981, pp. 22-27;

Rosalie T. Ruegg, Stephen R. Petersen, and Harold E. Marshall, Recommended

Practice for Measuring Life-Cycle Costs of Buildings and Building Systems , National Bureau of Standards, NBSIR 80-2040, June 1980; Rosalie T. Ruegg,

Harold E. Marshall, and Porter Driscoll, "Life-Cycle Costing," Architectural

Graphics Standards , 7th Edition, February 1981; Rosalie T. Ruegg, LifeCycle Cost Manual for the Federal Energy Management Program , National Bureau

of Standards, Handbook 135 (Revised), May 1982; and Louis P. Clark, A LifeCycle Cost Analysis Methodology for Fire Protection Systems in New Health

Care Facilities , National Bureau of Standards, NBSIR 82-2558, July 1982.

24
costs from discounted benefits, the net benefits (or net losses) measured in

either present value or annual value dollars can be determined. By dividing

discounted benefits by discounted costs, a benefit-cost ratio can be

calculated. By accumulating future discounted benefits (less future

discounted costs) on a year-by-year basis and comparing the result to the

initial investment cost, the time to payback can be found. And, by solving

for the interest rate that, when used in the appropriate discounting foinnulas,

will equate benefits and costs, the internal rate-of-return on the investment

can be determined.

Discounting-*^

To an individual the value of a specific sum of money depends on precisely

when it is to be received. Given the existence of interest rates and the

opportunity of borrowing and lending, benefits in hand afford reinvestment

opportunities, and it is generally preferable to receive benefits earlier than

later. Costs deferred afford opportunities for interim uses of funds for

other purposes, or the avoidance of borrowing costs; hence, it is generally

preferable to defer costs. The "investment opportunity cost" can be accounted

for by charging an interest rate for using resources over the relevant period

of time. This procedure is usually called "discounting," and is accomplished

through the use of compound interest formulas, or factors computed from the

formulas, which can be used to convert differently timed cash flows to a

time-equivalent basis, e.g., the present value, or annual value. The formulas

and factors incorporate the investor's opportunity cost in terms of an

^A more detailed treatment of the discounting process may be found in Harold

E. Marshall and Rosalie T. Ruegg, Simplified Energy Design Economics , National

Bureau of Standards, NBS Special Publication 544, 1980, pp. 16-20.

25
interest rate, usually referred to as the "discount rate." Discount rates may

be expressed in either "nominal" or "real" terms. Nominal rates include both

the opportunity cost of postponed receipts of money and the effects of

inflation. Real rates reflect only the opportunity cost, not inflation.

Annual values and present values are equally valid ways of adjusting amounts

to a common time basis for comparison and either can be used to compute

measures of net benefits. Annual values express all costs and benefits as

though they occurred in uniform yearly amounts over the study period, whereas

present values express all costs and benefits as though they occurred in a

lump sum at the beginning of the study period. Annual values and present

values are time equivalents. This analysis expresses final dollar amounts as

present values, but uses annual values in certain intermediate calculation

steps.

Treatment of Inflation . A valid economic analysis requires that a common unit

of measure be used for evaluating benefits and costs. This means that dollars

of equal purchasing power (constant dollars) be used to indicate the various

benefits and costs occurring over time, rather than dollars of changing

purchasing power (current dollars) . If benefits and costs are stated in

current dollars, that is, in terms of the particular values of the dollar that

are expected to hold in the years the benefits or costs occur, their value

must be converted to constant dollars in a benefit-cost analysis. Current

dollars may be converted to constant dollars prior to the discounting

26
operation through the application of a price deflator index, followed by discounting with a real discount rate, that is, one that does not include purely

inflationary or deflationary change. Alternatively, current dollars may be

converted to constant dollars in the discounting operation through the use of

a nominal discount rate, that is, one that does include a projection of the

inflationary or deflationary rate of change. As a variation of the first

approach, most prices and values used at the beginning of the study period may

be assumed to remain the same over the study period when measured in constant

dollars, and only those prices estimated to change at a rate faster or slower

than the rate of general price inflation need be adjusted through the use of

differential price escalation rates. Since benefits and costs are already in

constant dollars when this approach is used, a real discount rate should be

used.

The discounting factors used in the models are the Single Present Worth Factor

(SPW), the Uniform Present Worth Factor (UPW) , the Uniform Capital Recovery

Factor (UCR); the Uniform Present Worth Factor modified to incorporate a

constant rate of escalation (UPW*) , and the Single Present Worth Factor also

modified to incorporate a constant rate of escalation (SPW*). The SPW and

SPW* factors are used to convert a single future amount to an equivalent

present value. The UPW and UPW* factors are used to convert amounts recurring

over some specific number of periods to present values. The UCR factor is

used to convert a present value to a series of uniformly recurring amounts.

27
The incorporation of SPW* and UPW* factors in the model developed in section

2.2 allows for differential price escalation rates if the analyst chooses.

However, in the case illustrations in this report all values are assumed to

escalate at the general rate of inflation, i.e., a zero differential rate is

used.

Expected Value Analysis . Even though the occurrence of future fires is not

known with certainty, there is a known probability distribution based on fire

statistics which can be used to calculate expected values of related benefits

and costs.

In this study, sprinkler benefits in terms of reduced property losses,

indirect costs, and fewer deaths and injuries are calculated as expected

values by multiplying percentage loss reductions (based on sprinkler

effectiveness test data) by estimated values of loss associated with a fire

in the absence of sprinklers, and multiplying the result by the

probability of fire occurrence. The expected value of benefits in future

years can be discounted to a present value equivalent by multiplying each

year's expected value by the appropriate single-amount discount factor and

summing across years or, if annual benefits are uniform or change at a

constant rate, simply by multiplying the initial year's expected value by the

appropriate UPW or UPW* factor.

28
Sensitivity Analysis * By testing the responsiveness of benefit-cost results

to variations In values assigned to different parameters, sensitivity analysis

allows the Identification of those parameters that are most Important to the

economic success of residential sprinklers. Additionally, sensitivity

analysis is useful in assessing the consequences of uncertainty in data and in

assumptions. It does not tell the decision maker the values that should be

used, but it shows the Impact of using different values.

Break-Even Analysis . Another approach that can provide useful information to

decisionmakers in the face of uncertainty is break-even analysis. By setting

benefits equal to costs, and leaving the value of one of the parameters

unspecified, it is possible to solve for the minimum or maximum value which it

must take in order for the system to be minimally cost effective.

2.4 Economic Parameters and Assumptions

This section discusses establishing values for the discount rate, inflation

rate, real price changes, system life, study period, and tax rates.

The discount rate, a compound rate of interest used to convert benefits and

costs occurring at different times to a common time, should reflect the

investor's opportunity cost of capital. The higher the rate, the lower will

be the present value of future costs and benefits.

29
There is no single rate that is appropriate for all investors, but in a

"generic type" of study such as this, it is desirable to choose a rate that

will be representative "on the average" for the subject group of investors.

There is a wide disparity among homeowners as to their discount rate, since at

any given time some will be in net debt positions at interest rates ranging

from low to high, and some will be in credit positions at yields also ranging

from low (in some cases yields may be negative after taxes and inflation) to

high.

As background to selecting a discount rate for the case studies, the average

of real, after-tax rates of return to investors in all grades of nonfinancial

common stock and long-term corporate bonds over the 1947-1975 period was

examined, and was found to be 7 percent. ^ Additionally, discount rates by

income class, as derived by Hausman for individuals purchasing energy-using

durable goods, were considered. In the late 1970' s, the implicit discount

rates for homeowners with incomes between $35,000 and $50,000 ranged from 5.1

percent to 8.9 percent. ^ With this general guidance, a rate of 6 percent was

selected for use in the case studies. The 6 percent rate is defined as a real

rate, after taxes.

^See description of approach and data analysis in Rosalie T. Ruegg, et. al. , Economic Evaluation of Solar Energy Systems in Commercial Buildings ; Methodology and Case Studies , National Bureau of Standards NBSIR 82-2540, pp.

87-89, as based on historical trends in rates of return to investors published

by Daniel M. Holland and Steward C. Meyers, Trends in Corporate Profitability

and Capital Costs , WP 937-77, Alfred P. Sloan School of Management (Cambridge,

Mass: Massachusetts Institute of Technology), 1977.

2 Jerry A. Hausman, "Individual Discount Rates and the Purchase and Utilization

of Energy-Using Durables," Bell Journal of Economics, Vol. 10, No. 1, 1979.

30
Because there is little basis for projecting differential rates of inflation

for most of the categories of costs and benefits of sprinkler systems, most of

them are assumed to inflate at the rate of general price inflation. The rate

of general price inflation is set at 5 percent per annum. In the case of

interest expense and depreciation expense—both items which are based on

historical costs and are not variable with inflation (variable rate mortgages

are not treated) —it is necessary to convert the costs to their constant

dollar equivalents. This is done by discounting the nominal cash flows with a

nominal discount rate which is adjusted to reflect the assumed 5 percent

inflation rate. The inflation-adjusted, market rate is 11.3 percent; i.e.,

0.06 + 0.05 + (.06) (.05) = 0.113 or 11.3 percent.!

The study period is the length of time over which costs and benefits from the

sprinkler system are calculated. The length of the study period need not

coincide with the length of the system life. The model allows for system

replacements and resale or disposal values to reconcile the two. However, for

the purpose of the case studies, the study period is selected to coincide with

the assumed system life.

There is no empirically validated life for fast-response residential sprinkler

systems. However, system components are similar to components for which there

is some experience with durability. Plumbing systems in houses generally have

long lives; sprinkler apparatus in commercial buildings appear to have

relatively long lives. A study period and system life of 30 years are

assumed.

^The market rate is equal to the real rate plus the inflation rate plus the

product of the two rates.

31
Marginal Federal income tax rates range among homeowners from a low of about

10 percent to a high of about 50 percent. To the Federal income tax rate can

be added any applicable State and local income tax rates, taking into account

the deductibility of one from the other. For the case studies, a composite

marginal income tax rate of 40 percent is used to evaluate tax effects.

Effective property tax rates in the U.S. range from about 0.82 percent to 7.46

percent.^ The national average effective rate in U.S. cities of 2.15 percent

is used in the case studies to evaluate property tax effects.

lu.S. Bureau of the Census, Statistical Abstract of the United States 1980 , Washington, D.C.

32
3. SELECTED APPLICATIONS

The purpose of this section is to demonstrate the use of the model in selected

applications. The model serves as a framework for data collection and

estimation. The data are then applied to a series of hypothetical case

studies pertaining to new single-family houses in the U.S. under specified

conditions of fire risk, property values, loss rates and construction and

system costs.

3.1 Costs

This section discusses approaches for estimating values of the various cost

components, develops sample costs for the selected applications, and shows the

conversion of estimates to present value dollars. Emphasis is placed on

estimating purchase and installation costs, and three approaches are taken to

developing those estimates. (Research and code enforcement costs are not

considered.)

3.1.1 Purchase and Installation Cost Estimates

The principal approach taken to estimating purchase and installation costs is

the component method of construction cost estimating, whereby itemized

estimates are developed for the costs of piping, valves, fittings, sprinkler

heads, and other elements of sprinkler systems for new one- and two-family

houses.

The results are compared with estimates derived by expert opinion, application

of "rule-of-thumb" guidelines, and by update of a previous cost study.

33
3.1.1.1 Component Cost Estimates

To employ the component cost estimating method, which is in effect a "custom"

approach, it is necessary to have a description of the main physical

characteristics of the system. Figure 2 illustrates the physical basis used

to develop the component cost estimates. The figure shows the floor plan and

schematic of a sprinkler system for a two-story, colonial-style house with

basement. The house has a total floor area of 2,175 square feet, with 1,975

square feet of the area protected by sprinklers. The level of protection

corresponds to the minimum requirements of the NFPA 13D-1980 Standard,

Exceptions to required coverage allowed by the Standard are employed. These

exceptions include: bathrooms not exceeding 55 square feet with

noncombustible plumbing fixtures; small closets of which the least dimension

does not exceed 3 feet, the area does not exceed 24 square feet, and the walls

and ceilings are surfaced with noncombustible materials; open attached

porches; and entrance foyers which are not the only means of egress. As

required by the Standard, maximum coverage for the individual sprinkler heads

is 144 square feet, the sprinklers are no more than 6 feet distant from walls

and partitions and no more than 12 feet distant between one another on or

between pipe lines; and the distance between sprinklers within a compartment

is not less than 8 feet. The sprinkler system is assumed to be a wet system

and areas with piping are assumed to be not subject to freezing.

Houses vary considerably in size and layout; water pressure conditions vary;

local building code requirements differ; and the NFPA 13D-1980 Standard

allows leeway in pipe configuration and materials. Therefore, it is

34
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35
impossible to specify in detail a "universal" residential sprinkler system.

The system depicted in figure 2 is intended only as a basis for developing

approximate reference costs. It is in no way offered as a recommended design.

It should be noted that costs of actual systems may differ substantially

from those developed here, reflecting not only differences in system size and

design but also in regional costs.

Reflecting the potential variation in requirements for pipe size, low- and

high-cost estimates are developed for the sample system depicted in figure 2,

based on the smallest (1/2 inch) and the largest (1 1/2 inch) diameter pipe

which would ever likely be used in a system (1 1/2 inch would generally be

used only for supply pipe diameters). In practice, a combination of pipe sizes

might be used, the choice depending on design configuration, local water

pressure factors and code requirements. Pipe 3/4" or 1 inch in diameter would

be more typical than the boundary estimates used in the study. Estimates

based on 1 1/4 inch pipe are also included for comparison with a previous

s tudy . 1

The sample cost estimates are developed for both copper M and polybutylene

piping. The copper provides a high end estimate and the polybutylene, the low

end of the range for piping costs. Copper pipe is currently most widely used

for plumbing systems, but polybutylene pipe offers the potential of

•••A comparison is made with cost estimates (updated by this Study) developed by

Rolf Jensen and Associates, Inc., Study to Establish the Existing Automatic

Fire Suppression Technology for Use in Residential Occupancies , A Summary

Report, August 1977.

36
substantial cost reductions and is currently being used in residential

sprinkler systems. Comparative tests for plumbing systems found total

installed labor and materials costs to be about 44 percent less for

polybutylene than for copper pipe.^

Estimated costs for a two-family dwelling are developed by applying a

multiplier to the single-family estimates. The procedure treats a duplex as

two end-unit town houses and uses an adjustment multiplier from the MEANS

Building Construction Cost Guide 1982 .

Costs reflect assumptions of average construction quality, and are based on

average materials prices and labor rates for 30 major U.S. cities. The labor

rates include overhead and profit.

Table 1 gives component cost estimates based on copper piping. The estimated

total system cost for a single-family dwelling ranges from a low of $2,466 for

a system with 1/2 inch diameter pipe to a high of $3,935 for 1 1/2 inch

diameter pipe. The total cost of a system using 1 1/4 inch pipe is estimated

at $3,724.

^Interview with Kathy Vernot, Director, Life-Safety Division, Central

Sprinkler Corporation, November 1981.

^Results of a study performed by the National Association of Home Builders, as cited in Shell Chemical Company Performance Report , SC: 550-81, September

1981.

3r. S. Means Co., Inc., MEANS Building Systems Cost Guide 1982 , 118 Construction Plaza, Duxburg, MA.

37
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$1.13 and the high $1,81. Expressed as cost per square foot of protected

area, the low end is $1.25 and the high $1.99. The estimated average cost per

sprinkler head ranges between $117 and $187. The fire sprinkler kit comprises

from 28 to 45 percent of estimated total system cost, depending on pipe

diameter.

For one unit of a two-family dwelling, where each unit is equal in size to the

single-family dwelling the estimated total cost of a copper-pipe system ranges

from $2,327 to $3,741.

The top part of table 2 gives component cost estimates based on the use of

polybutylene pipe. The lower part of the table gives estimates based on

polybutylene pipe derived by applying a fixed 44 percentage cost reduction to

the estimates for copper piping.

The total cost of a single-dwelling sprinkler system using plastic pipe is

estimated to range from a low of $1,718 (installed cost based on individual

components computation) for 1/2 inch pipe to a high of $2,697 (installed cost

based on percentage computation) for 1 1/2 inch pipe. The estimated cost per

unit of living area for the single-family dwelling ranges from a low of

$0.79/sq.ft. for 1/2 inch pipe to a high of $1.25/sq.ft. for 1 1/2 inch pipe.

The unit cost of protected area ranges from a low of $0.87/sq.ft. for 1/2

inch pipe to a high of $1.37/sq.f t,. for 1 1/2 inch pipe. The cost per

sprinkler head for the single-family dwelling ranges from $82 to $129. Cost

of the system for one unit of a two-family dwelling equal in size to the

single-family dwelling is estimated to be 5 percent less.

39
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It should be noted that the cost differential between copper and plastic pipe

is sensitive to the cost of copper. Prior to 1981-1982, plastic pipe would

have offered a larger margin of savings over the cost of copper pipe than at

the time of this study.

Let us now compare the above component cost estimates with estimates developed

by the two other approaches, beginning with cost estimates suggested by people

knowledgeable in the field. Fire protection consultants interviewed for a

recent newspaper article suggested a cost range of $1,700 to $2,000 for a

sprinkler system for a "typical" 2,000 square-foot dwelling. ^ This estimate

brackets the component cost estimate of table 2 based on 1/2" polybutylene

piping.

In 1979, the president of the National Automatic Sprinkler and Fire Control

Association estimated that a sprinkler system could be installed in a one-or

two-family dwelling unit of between two-to-three thousand square feet for less

than $1,200, of which about $500 would be for materials and about $600 for

labor. He further estimated that about $100 of the total materials cost would

be for sprinkler heads and related components supplied by sprinkler manufacturers. ^ Updated to 1982 dollars, these figures become $1,500 for the

^"Dousing Home Fires," The Washington Post , July 10, 1982, p. E-1.

^Edward J. Reilly, "Residential Sprinkler Systems —Where Do We Go From Here?"

(Paper presented at the Fourth Annual Conference on Low Cost Residential

Sprinkler Systems, sponsored by the U.S. Fire Administration, September 25-26,

1979), p. 3.

41
total system cost, and $600 and $700 for materials and labor, respectively.

This estimate is about $200 less than the component cost estimate for 1/2"

polybutylene piping developed here.

Estimates as to how much it should cost to purchase and install a sprinkler

system, expressed as a percentage of the construction cost of the house in

which it is installed, range from about 1 percent to 2 percent of the cost of

the house. 2 For "typical" commercial, industrial, storage, and institutional

buildings, sprinkler system costs have been reported to represent about 1.5

percent of total construction costs.

Table 3 shows cost estimates for residential sprinkler systems based on

sprinkler costs as 1.0, 1.5, and 2.0 percentages, respectively, of estimated

house construction costs. The cost estimates are derived by applying the

stated percentages to 1980 and 1981 sales prices of new, private, one-family

houses, multiplied by a factor of 0.8 to adjust for estimated average land

cost. The first two columns of the top portion of the table give the 1980 and

1981 median and mean sales prices. The last three columns of the table give

the estimated costs.

^1979 cost data are updated to 1982 prices by multiplying them by a factor of

1.228 developed from the Department of Commerce Composite Construction Cost

Indexes for 1979 and April 1982, as reported in U.S. Department of Commerce,

Bureau of Industrial Economics, Construction Review, Vol. 28, No. 3, May/June

1982.

^See, for example, "Dousing Home Fires," The Washington Post , and John J.

Carlin, III and Allen Stephens, "New Residential Sprinkler Standards Adopted,'

The International Fire Chief , February 1981, p. 23.

^Reilly, "Residential Sprinkler Systems", p. 10.

42
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43
Inspection of these sprinkler system cost estimates, derived as specified percentages of house construction costs, reveals the obvious limitation of this

estimation method: it fails to account for a fixed element of system costs

and for variations in system costs not adequately predicted by house

construction costs. For example, a house that sells for $35,000 can have a

number of rooms comparable to an $80,000 house, although the rooms will likely

be smaller and/or less well constructed. A similar number of sprinkler heads

may be required in both cases to meet code requirements. Although the linear

footage of piping required may be less for the less expensive house, it is not

likely to be proportionately less in relation to construction cost

differences, other things being equal. In short, the cost of a sprinkler

system will likely be lower, the lower the cost of the house, but the

relationship between system cost and house cost is unlikely to be linear.

Hence, estimating sprinkler costs as 1 to 2 percent of construction costs is

likely to hold reasonably well only when applied to houses within a limited

price range.

The cost estimate in table 3 closest in amount to that produced by the

component cost estimate of table 2 for 1/2" polybutylene piping is provided

by taking 2.0 percent of a house sales price of $100,000.

Cost estimates for sprinkler systems are also often quoted in terms of an

average cost per square foot of total housing floor area or of protected floor

area. For example, the cost of systems installed in compliance with the San

Clemente, California, residential sprinkler system ordinance was reported in

1981 to average about $0.50 per square foot, unspecified as to total area or

44
protected area.^ A 1977 study estimated costs at $0.65 per square foot of

protected area for new houses in urban areas and $0.85 per square foot of

protected area for new houses in rural areas. ^ This translates into $0.80

and $1.04, respectively, in 1982 dollars.

For conunercial buildings, a typical industrial-type sprinkler system was

estimated in 1979 to cost approximately $0.80 per square foot of building

space, -^ which equals about $0.98 per square foot in 1982 dollars. A study of

alternative methods of achieving fire safety in health care facilities, a

specialized application of sprinklers, estimated the cost of installing

sprinklers in nonhazardous areas at $2.00 per square foot of protected area in

1978 dollars.^ This cost, which could be expected to be higher than that for

either commercial or residential applications, translates into $2.80 per

square foot of protected area in 1982 dollars.

Table 4 shows the results of applying the above estimated sample costs per

square foot of house area to the range of house sizes reported in 1980.

This estimation approach has limitations akin to the preceding approach, due

to the assumption of a linear relationship between sprinkler system costs and

house size. The cost per square foot estimates of $0.50 and $0.80 result in

l"San Clemente Protects New Residences With Automatic Sprinklers," Fire Chief

Magazine , August 1981, p. 100.

^Rolf Jensen and Associates, Fire Suppression Technology , p. 11.

^Federal Emergency Management Agency, Report to Congress , p. 52.

^Robert E. Chapman, Phillip T. Chen and William G. Hall, Economic Aspects of

Fire Safety in Health Care Facilities: Guidelines for Cost-Ef f ective

Retrofits , National Bureau of Standards Interagency Report 79-1902, November

1979.

45
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46
total cost estimates similar to those produced in table 3 by the 1.5 and 2.0

percentage figures. The total cost estimates resulting from the use of $0.98

per square foot for houses in the 1,600-2,399 size range are closely in line

with the estimates of $1,700 to $2,000 for a 2,000 square foot house suggested

recently by fire protection consultants, and also bracket the component cost

estimate for 1/2" polybutylene piping. Tlie use of the health care cost per

square foot produces total cost estimates substantially higher than any

suggested by experts for residential systems,

A comparison of the component cost estimates of table 1 for a 1 1/4" copper

pipe system with updated estimates of an earlier study (Rolf Jensen and

Associates, Inc. , 1977) based on 1 1/4" copper pipe, showed the component cost

estimates to be somewhat higher: $1.89/ft^ of protected area versus $1.00/ft^

for the updated Jensen Study; and $1,77 per sprinkler head versus $141 for the

updated Jensen Study.

To provide for sensitivity testing of the outcome to piping material and size,

cases are Included in section 3,3 based on 1/2 inch polybutylene pipe and on 1

1/4 inch copper pipe, the former representing the low end of the pipe cost

range and the latter the high end. The cost of a system using 1/2 inch

polybutylene pipe as estimated by the component cost method of table 2 is the

cost estimate selected for performing the selected base-case example in

section 3,3,1 (after adjustments for financing and tax effects). The estimated

cost of a system using 1 1/4 inch copper pipe is used in the sensitivity

analysis of section 3,3,2,

47
3.1.1.2 Financing and Tax Effects

The preceding cost estimates reflect neither the effects of financing nor

related taxes. This section evaluates financing and tax effects and

incorporates them into the analysis.

Financing. If a purchase is financed at the same rate as the purchaser's

opportunity cost, i.e., the purchaser's borrowing rate equals the discount

rate, financing a purchase has no effect on its present value acquisition cost

before taxes . But if the borrowing rate is lower than the purchaser's

discount rate, present value acquisition costs will be reduced by financing

the purchase, and it will be economically advantageous for the purchaser to

finance the purchase rather than to pay cash.

Based on a fixed-rate/uniform payment loan, the present value purchase and

installation cost of a sprinkler system is calculated by amortizing the loan

over the life of the loan at the specified borrowing rate, bringing the stream

of loan payments back to present value at the specified discount rate, and

adding the result to any downpayment amount. Although the sprinkler system

costs will probably be included as part of the total house price and financed

with the rest of the house, it is possible to treat it separately for the

purpose of analysis.

Mortgage Interest Tax Deductions . For both an owner/occupant and an owner of

a rental unit, the interest payments on a loan to finance the purchase of the

system are deductible from taxable income, effectively reducing the

acquisition cost of the system. With a fixed rate/uniform payment loan, the

interest and principal components of each loan payment change over time.

48
Because only the Interest component is tax deductible, it must be separately

estimated. This can be done period-by-period by calculating interest on the

remaining principal balance, subtracting the interest from the payment

amount—therein determining the contribution of that payment to reducing the

principal—and then reapplying the interest rate to the new loan balance. The

resulting cash flow is then multiplied by the marginal income tax rate, each

value is discounted to present value, and the results summed to find the

present value savings of interest expense deductions.

Combined Financing and Interest Tax Deductions. The present value of purchase

and installation costs with financing and after interest deductions from

taxable income can be calculated by equation 10 of section 2.2, omitting

the last two terms for tax credit (TC) and depreciation (DTS).

Using the component cost estimates for purchasing and installing polybutylene

piping of 1/2 inch diameter and assuming financing of the entire amount over

30 years at a market rate of interest of 15.5 percent compounded annually, an

inflation-adjusted, after-tax discount rate of 11.30 percent, ^ and a marginal

income tax rate of 40 percent, the present value of purchase and installation

to either an owner/occupant or an owner of a rental unit is $1,445, comprised

of total present value payments of $2,292 and an income tax savings of $847,

and calculated by equation 10 as follows:

•'As was noted previously, purely inflationary effects must be removed from the

analysis. Since the market rate of interest of 15.5 includes inflation, it

is not appropriate to use the 6 percent real discount rate without adjusting

it to include inflation. Applying the assumed inflation rate of 5 percent to

the assumed after-tax real discount rate of 6 percent, yields 11.3 percent

(i.e., .06 + .05 + (.06) (.05) = .113).

49
30

PI=[($1,718)(0)+[($1,718)(1-0)(0.157)(8.5)] - I [(0.4)(RP.)(0.155)(SPW ,,3 .)]

j=l

= $1,444.66. (17)

This is the amount of purchase and installation cost used for the base-case

analysis in section 3.3.1.^

Depreciation and Other Tax Effects . Several other tax effects may alter the

effective ownership cost of a system to the owner of a rental house. The most

important of these is depreciation of system acquisition costs, which reduces

the after-tax costs of owning a system. Less important in most cases are

capital gains tax and the depreciation recapture tax which are imposed upon

sale. For residential real property, the gain from the resale of the property

is taxed as ordinary income to the extent that accelerated cost recovery

deductions exceed the depreciation that would have been allowed if the

straight-line method had been used over a 15-year period. If the straight-line

method is elected, all gain is taxed as capital gain. (Code Sec. 1250, Economic

Recovery Tax Act of 1981.)

The impact of depreciation depends on the depreciation method and period, as

well as the owner's tax rate. For new rental houses, a sprinkler system would

usually be depreciated according to the same method and period used for the

house. Residential property is currently depreciated according to either the

accelerated cost recovery system or the straight-line method, usually over 15

years.

^The calculation was performed by use of a computer program.

50
Based on the accelerated cost recovery system and a depreciation period of 15

years, the present value of Income tax savings Is modeled as follows:

15

DTS^CR = I UDBj • ACRFj • t • SPW^j (18)

where ,

DTS^Cg^ = present value of income tax savings due to deductions from

taxable income of depreciation expense based on the

accelerated cost recovery system method,

UDBj = undepreciated balance of the depreciation cost basis remaining

in year j , normally equal initially to the full cost of system

purchase and installation, and thereafter to the undepreciated

balance at the beginning of the prior year less depreciation

taken that year,

ACRF-j = accelerated cost recovery factor which may be calculated as (100/15)(1.75),

t = homeowner's marginal income tax rate, and

SPW^ A = single present worth discount factor.

[Note that depreciation is based on historical costs

and its nominal amount does not change in response to

inflation or deflation; therefore, its value falls in terms

of constant dollars if there is inflation. This can be taken

into account by discounting the yearly nominal depreciation

amount, UDB-; • ACRF-; , with a discount rate which includes the

inflation rate or by adjusting the yearly depreciation amount

to constant dollars prior to the discounting operation.]

Based on the straight-line depreciation method, the present value of income

tax savings is modeled as follows:

De

DTSsL = I (Pl/De) • t • SPW^ a , (19)

3=1

51
where

,

DTSgL = present value of tax savings due to deductions from taxable

income of depreciation expense based on the straight-line

depreciation method,

PI = depreciation cost basis, normally equal to the full cost of

system purchase and installation,

De = depreciation period,

t = homeowner's marginal income tax rate, and

SPW^ j is as defined for eq. (18).

Using the straight-line method over 15 years, a marginal composite income tax

rate of 40 percent, and an inflation-inclusive discount rate of 11,3 percent,

the present value of the depreciation tax savings to the owner of a rental

house is $358; i.e.,

15

DTSgL = I 1718

j=l 15 (0.4)(SPWj .113) = $357.74. (20)

This is the depreciation value used in the feasibility analysis for a rental

house in section 3.3.2. Since the resale value of the system at the end of

the thirty-year study period is assumed to be zero, there are no capital gains

and no depreciation recapture tax to consider.

At the present there are no tax credits available to homeowners who purchase

and install sprinkler systems. If available, tax credits provide a powerful

stimulus to demand, because they reduce ownership cost by nearly a dollarfor-dollar of credit. The present value of cost reductions due to tax credits

can be calculated as follows:

52
TC = tc • PI • (SPWi^d) , (21)

where

,

TC = present value of tax credit cost reductions,

tc = percentage tax credit,

PI = purchase and Installation cost of the system, and

SPWj (J = single present worth factor for year 1 , assuming a one time

credit at the end of the tax year in which the system is

purchased,

(Tax credits are discussed further in section 3.2.6.)

3.1.1.3 Other Potential Costs of Purchase and Installation

Some localities have requirements, restrictions, and/or charges which raise

the cost of purchasing and installing a residential sprinkler system. There

may be, for example, special requirements for meters or backflow prevention

valves, which are not technically necessary in most cases. 1 Localities may

also impose large monthly "water standby charges" or considerable permit fees

in conjunction with a requirement that larger pipe size be used if sprinklers

are installed. For instance, this study identified a policy of one public

works commission of levying a $1,400 permit fee for a 1 inch lead-in pipe and

a $3,400 permit fee for all/2 inch lead-in, and of requiring all/2 inch

lead-in when a sprinkler system is used. This extra permit charge is in

addition to the differential labor and materials cost of laying the larger

pipe. Such a p«>rmit fee would add $2,000 to the cost of a sprinkler system,

raising the estimated total contract cost of a sprinkler system to between

$3,718 and $5,935 (tables 1 and 2) depending on the choice of plastic or

copper and the size of the pipe.

1 Federal Emergency Management Agency, Report to Congress , p. 53.

53
The rationality of this type of water demand charge is questionable because

community water usage will likely be lowered, not raised, by sprinklers, since

less water is required to control small fires than to fight large fires.

This type of charge, where it is imposed, constitutes a significant cost

impediment to sprinkler use, and its validity and impact appear to warrant

further exploration.

This potential cost is omitted from the base-case analysis, but is taken

into account in the sensitivity analysis.

3.1.2 Operating, Maintenance, Repair and Replacement Costs

3.1.2.1 Operating Costs

The expected value of life-cycle operating costs to the owner/ occupant (OP) is

found as the present value sum of water costs (WC) , water damage costs (WD),

and, for systems with pumps, electricity costs (E). Although the expected

value of OP is estimated to be a trivial amount that can be omitted from the

analysis, each of the cost components is treated in turn below to demonstrate

why the amount is estimated to be trivial.

Water costs would be incurred only if a system were activated. If the water

line to the sprinkler system were metered, the homeowner or occupant would

incur the cost; if the line were unmetered, the community would bear the cost.

The fast-response time and the limit of activation to sprinklers in the

immediate vicinity of a fire could be expected in most cases to limit the

llbid, p. 53.

54
quantity of water released to a small fraction of the quantity of water that

would be required if the local fire department combated the fire after an

elapsed response time.

At a flow rate of 9 gallons per minute (the design flow rate of a recent test

sprinkler system) , an activated sprinkler head would release 270 gallons of

water over a period of 30 minutes. This is about the same as a typical day's

domestic water consumption for a household of four, and the marginal cost

would generally be only a few cents.

The costs of water consumption and water damage can be evaluated as expected

values, taking into account the probability of system activation in case of

fire or accidentally.

The probability of fire occurring during a year in a one- or two-family

dwelling is slightly less than 1 in 100 (it is 0.00856 based on 1981 data).

The probability that a system is properly maintained and will operate

effectively in response to a fire is estimated at 92 percent.^

^The mean value for water consumption in the U.S. is 6,552 gallons per month

for a household of 4 and the corresponding mean marginal price for water is

$.78/1,000 gal, as developed in S. F. Weber, B. E. Thompson and B. C. Lippiatt

in Economic Framework for Cost-Ef fective Residential Water Conservation

Decisions , NBSIR 81-2304, prepared by the National Bureau of Standards for the

U.S, Department of Housing and Urban Development, Washington, D.C. , August

1981.

^Gomberg jet al .

, A Decision Model for Evaluating Residential Fire-Risk Reduction Alternatives , NBSIR, in preparation 1984. See also section 3.2.1 for

further explanation.

^Gomberg , et^ al . , Evaluating Alternative Strategies For Reducing Residential

Fire Loss, NBSIR 82-2551, August 1982, p. 15.

55
Using the above estimated probability of a properly functioning system (.92),

the probability of fire (.00856), a water charge of $.00078/gal, the

assumption that at most three sprinkler heads will be activated for no more

than 30 minutes if a fire occurs—probably more heads activated and for a

longer time than would generally occur—a real discount rate of 6 percent, a

study period of 30 years, and level constant dollar prices (i.e., real price

escalation rate e = 0), one calculates the following life-cycle water

consumption cost to the owner/occupant for activation induced by fire:

WCj. = (0.92) (.00856) ($.00078) (810 gal) (13.765) (22)

= $0,068.

As expected, this cost is found to be trivial and can be omitted from the

analysis.

The other water-related costs of a fire-induced sprinkler activation are the

life-cycle costs of any water damage. It seems reasonable to assume that in

absence of the sprinklers a much larger water damage would result from

conventional fire fighting approaches. Because of the difficulty of

estimating comparative costs, the differential value of water damage incurred

by the homeowner is set equal to zero in the case studies, i.e. WDp = 0.

Now consider water consumption costs and water damage costs associated with

accidental activation, i.e. discharge of water when there is no fire.

Although we do not know what the frequency of this type of failure for

residential systems will be, we know that it is very rare in commercial and

industrial applications.^ According to one study, "the leakage rate of

^Federal Emergency Management Agency, Report to Congress .

56
sprinklers has been approximately one per year for each 3,000,000 sprinklers,"

and when leakage occurs it is generally limited to a single sprinkler head.^

The present value of the water consumption cost in case of fire-induced

activation was shown to be trivial, and since the probability of accidental

discharge for a residential application is low and uncertain, a specific

calculation of this cost is not included in these examples.

The water damage costs from accidental discharge would be specific to the

circumstances. For a library of rare books or a gallery of paintings, the

water damage of actually incurred accidential discharge might be incalculable.

But under more typical conditions, the damage would likely be confined to a

single room or portion of a conventially furnished room and the discharge, if

prolonged, might entail costs of suctioning water from carpets, carpet

cleaning and other floor refurbishing, possibly dry wall repair, repainting,

and furniture cleaning and repair. A part of these costs might be covered by

insurance.

Again, because there are no statistics on the frequency of accidental

discharge for residential applications but there is reason to believe that it

will be quite small, water damage costs are not included in the sample

calculations. In the model of section 2.3 provisions are, however, made for

calculating water consumption costs and water damage from accidental

discharge.

^Rolf Jensen and Associates, Inc., Fire Sprinkler Technology , p. 5-3.

57
The other element of operating costs included in the initial listing is

electricity cost, E, for a system requiring a pump. Since these costs can be

anticipated to be very small, and, in any case, apply only to a special

application of sprinkler systems not treated here, they are assumed equal to

zero in the cost analysis.

Hence, the expected value of life-cycle operating costs to the owner/occupant

(OP) based on the above assumptions are estimated to be a trivial amount that

can be omitted from the sample calculations.

3.1.2.2 Maintenance, Repair, and Replacement Costs

There is little experience upon which to base estimates of maintenance, repair,

and replacement costs. In lieu of empirical data, the approach taken is to base

the estimate on the assumption that an annual preventive maintenance and

replacement program precludes the need for other repair costs. It is assumed

that the annual preventive maintenance program consists of an inspection of one

hour's duration performed by a sprinkler or plumbing contractor. The inspection

is assumed to entail flow-tests of sprinkler heads, test of the alarm system;

check of pumps and tanks if used; inspection of all valves; replacement of

parts as needed; and a general check of all parts of the system.

^NFPA 13D-1980 recommends a minimum monthly maintenance program. It does not

specify who should perform the maintenance, but given the frequency of

recommended inspection, if done, it is likely to be done by the owner. Hence, an alternative approach to estimating the cost of maintenance would be

to estimate the opportunity cost of the owner's time. Costs were instead

based on an annual inspection by a plumber or sprinkler contractor for two

reasons: (1) a representative of a major sprinkler company advised that an annual inspection be performed by a professional in the field; and (2) wage

rates of plumbing and sprinkler contractors are more definitive and

generalizable than homeowner opportunity cost. (Telephone interview with

Kathy Vernot, Central Sprinkler Corporation, Nov. 19, 1982.)

58
The most frequent type of parts replacement is assumed to be of sprinkler

heads, because they can be damaged by painting, dust, and water corrosion over

time. NFPA 13D-1980 states that "at least 3 spare sprinklers of each type,

temperature rating, and orifice size used in the system should be kept on the

premises." However, there is no empirical data as to the actual frequency of

the replacement. The approach chosen to estimate this component of cost is to

assume that about half the sprinkler heads need to be replaced during a 30

year period, with the frequency of replacement lower during the earlier years

and higher in the later years. Figure 3 shows the specific replacement

pattern of sprinkler heads assumed for this calculation. It it assumed that

the replacements are performed as a part of the preventive maintenance

program; costs for parts but not for additional labor are estimated. Other

components of the system are assumed to last 30 years without replacement.

Equation (15) of section 2.2 is used to estimate the present value of

maintenance, repair and replacement costs, i.e. _ h

M = [(wni • hni . UPW*d,n,e) + I Kw^rj • h^rj) + m^j ] • SPW*dj,e] *

[1 - (t . A)]. (15)

The portion of equation (15) that pertains to maintenance costs can be

separately identified as follows:

^ffi = (wm • Vim • UPW*d,n,e) • [ 1- (t • A)], (23)

59
Figure 3. Assumed Annual Rate of Replacement of Sprinkler Heads During

System Life^

Replacement

Rate

(%)

1.00

x^

.05

.04

.03

.02

.01

^Thls replacement schedule allows for replacement of one-half of the 21 heads over the life of the system: an average of 2.1 during the first 10 years, 3.15

during the next 10 years, and 5.25 during the last 10 years.

60
where ,

ME = present value of annually recurring routine maintenance costs,

Wm = wage rate per hour for routine maintenance,

hjjj = length of time in hours required for routine maintenance,

t = marginal income tax rate of the owner, and

A = 1 if a rental house,

if owner-occupied.

Based on a constant dollar hourly wage rate of $27. 65^, and one hour for the

annual inspection, the present value cost to the owner-occupant over 30 years

is $380; i.e.,

ME = ($27.65) (1) (13.76) = $380.46 (24)

To the owner of a rental iinit in a 40 percent tax bracket, the present value

cost is $228; i.e.,

m = $380.46 (1 - .4) = $228.28. (25)

The portion of equation (15) that pertains to replacement and repair costs can

be separately identified as follows:

_ n R = I t^wrrj • hrrj) + nij-rj ] • SPW* • [1 - (t • A)] (26)

^R.S. Means Co., Inc., Building Construction Cost Data: 1982 , average rate for

plumbers in U.S. cities, including overhead and profit.

61
where

,

R = present value of replacement costs,

mj.j.4 = materials replacement costs in year j

,

Wj.j.4 = wage rate per hour for repair and replacements,

hj.j.j = length of time in hours required for repair and replacements,

SPW* = modified single present worth discount factor,

t = marginal income tax rate of the owner, and

A = 1 if a rental unit,

if owner-occupied.

Since it is assumed that the labor cost for replacements is included in the

preceding calculation of M and that maintenance prevents unscheduled repairs,

(*^rri * ^rrj) ^^ given a zero value and mj-rj is given the materials replacement cost of $10 per head.

If costs recur over intervals of time shorter in length than n, UPW*i ^j g

factors for each time interval can be used in conjunction with SPW*j ^j g

factors for the beginning of each time interval to calculate present value

costs. For example based on a constant dollar replacement cost per sprinkler

head of $10.00, 21 sprinkler heads of which half are replaced during the

system life, and the replacement schedule given by figure 3, the present value

cost to the owner/occupant over 30 years is $40; i.e..

62
^y

rv o o

O* V Jtr JP rs e^

eT / / / / -^- / .V 4V" / .V >^''

<& ST c7 c/

<^ cf ^^ <^ -^ <^ -^ ^ <^ ^ ^

R=($10.00) (21) [(.010) (7.360) + (.015) (7.360) (.558) + (.025) (7.360) (.312)] (27)

= $40.45

For the owner of a rental unit in a 40 percent tax bracket, the present value of

replacement is $24; i.e.,

R = (40.45) (1 - .4) = $24.27 (28)

63
3,1.3 Increased Property Taxes

Because automatic sprinkler systems are capital intensive, they will tend to

increase the value of a house, and, hence, raise its property tax assessment

basis, unless a specific waiver or exemption is granted. The purchase and

installation cost of the system is a reasonable, though imprecise, indicator of

the initial increase in the assessment basis. Thereafter, the differential

value in the yearly assessment basis may be modeled taking into account the net

effect of deterioration or obsolescence, which may lessen the value, and price

increases, which may raise the value.

Percentage assessment levels and nominal property tax rates vary dramatically

among localities, but effective property tax rates vary much less. According to

the U.S. Statistical Abstract 1980 , assessment levels in 30 large U.S. cities in

1978, for example, ranged from 98.1 percent in Washington, D.C. to 10.0 percent

in New Orleans, and nominal rates per $100 for the same group of cities ranged

from 1.25 percent in Los Angeles to 25.29 percent in Boston. Effective property

tax rates ranged from 0.82 percent in Honolulu to 7,46 percent in Boston, and

averaged 2.15 percent across the 30 cities.

Assuming a straight-line obsolescence rate, the present value increase in

property tax may be calculated by equation (16). Basing the purchase and

installation cost on 1/2 inch polybutylene pipe for a single-family residence,

using an effective tax rate of 2.15 percent (constant over the 30 years), and,

assuming no real price changes over a 30-year study period and a 6 percent

discount rate, the present value of property tax is $190; i.e..

64
_ 30

P = y ($1,718) (l-j/30) (.0215)(SPW*.,d=6%,e=0) d " ^-^^ (29)

3=1

= $189.72.

3.1.4 Cost Summary

The previous three sections, 3.1.1 through 3.1,3, have established and

illustrated cost estimating procedures for three main cost categories for

residential sprinkler systems: (1) purchase and installation costs, (2)

operating, maintenance, repair, and replacement costs, and (3) property taxes.

The purchase and installation costs were given in terms of ranges due to the

variability in these costs depending, for example, on type and size of pipe, and

system size and configuration. Because there is no "track record" of the

reliability, durability, and maintainability of these systems, it was necessary

to base operating, maintenance, repair and replacement cost estimates on a

number of assumptions about which there is considerable uncertainty. Table 5

summarizes the costs selected for the base-case analysis.

3.2. Benefits

This section focuses on the value of benefits to the homeowner of acquiring a

sprinkler system. These benefits are primarily the value of reduced risk of

death, injury, property loss, and related indirect costs; lower insurance

costs; and, depending on community actions, lower property taxes and reduced

housing costs.

65
Table 5. Summary of "Base Case" Costs for Residential Sprinkler Systems

Type of Cost

Homeowner Costs

Ovraer/Occupant

(1982 $)

Owner of a Rental House

(1982 $)

Purchase and Installation Costs,

after taxes and financing

(1/2" Polybutylene Pipe —

Component Method Estimate)

Depreciation Tax Savings

Operating, Maintenance,

Replacement and Repair Costs

Operating Costs

Maintenance Costs

Replacement Costs

Property Taxes

1,445

380

40

190

1,445

(358)

228

24

190

Total 2,055 1,529

66
3.2.1 Reduced Risk of Death and Injury

The assignment of a dollar value to deaths and injuries averted is frequently

done—either implicitly or explicitly—but not without controversy and

inconsistency. Stating all costs and benefits in dollars is desirable because

it facilitates comparisons using a variety of economic measures of

performance. Placing a dollar value on human life, pain, and suffering,

however, raises difficult philosophical, ethical, and theoretical issues. For

example, basing the value of a life on the present value of earnings potential —one of the measurement approaches that is sometimes used—tends to result in

comparatively low values for the young and the old and, in our present

economy, for women and non-Caucasians. Using court-assigned values for death,

pain, and injury inflicted—another approach that is sometimes used—results

in widely variable amounts. The values of saving lives and reducing pain and

injury implicitly assigned by other government programs concerned with safety

also vary widely among programs and projects.

1

The approach considered most consistent with economic theory is

based on the willingness-to-pay concept. The willingness- to-pay value is

computed according to how much a decision maker will invest to reduce his risk

of death by a certain fraction. In a parallel fashion the concept can be

applied to the risk of suffering injuries. While the approach and the methods

are still under debate, it is interesting to note that surveys of expressed

willingness to pay for small reductions in the risk of death have yielded

^For a discussion of approaches to measuring the value of deaths and injuries

averted, and deficiencies of these approaches, see E.J. Mishan, "Evaluation of

Life and Limb: A Theoretical Approach," Journal of Political Economy , JulyAugust 1971, pp. 687-705; or M.W. Jones-Lee, The Value of Life; An Economic

Analysis , Chicago, IL: University of Chicago Press, 1976.

67
values of life from $50 thousand to $8 million, with most values concentrated

between $250 thousand and $1 million.

Rather than attempting to develop new measures of the value of averting death,

pain and suffering, this study uses the following two approaches:

(1) In the first approach, values within the range of $250 thousand to $1

million are adopted from the NBS/SRI Fire Loss Model to convert the reduction

in lives lost and injuries to economic terms. The assumed dollar value per

life saved in the base-case example is $500,000. The assumed value per injury

averted is $20,000.

The cash flows resulting from these estimates are discounted to present value

to put them on a common time basis with the costs, and the present value of

net benefits is calculated.

(2) In the second approach, total benefits, not including the benefits of

reduced risk of death and injury, are subtracted from total costs to derive a

partial net dollar cost. The estimated number of injuries averted is divided

by the estimated number of deaths averted to obtain the number of injuries

averted for each life saved. The net dollar cost is then divided by the

expected total number of deaths averted over the study period to obtain a

present value cost per life saved and so many injuries averted. 2 This

quotient represents the minimum value that a decision maker could ascribe to a

sprinkler system's benefit of reduced risk of death and injury and find the

system cost effective. Hence, the method solves for a value of life and

M, D. Graham and J. W. Vaupel, "Value of a Life: What Difference Does It

Make?", Risk Analysis , Vol. 1, No. 1, March 1981, p. 89.

^This approach is discussed by John S, McConnaughey, Jr, in An Economic

Analysis of Building Code Impacts: A Suggested Approach , NBSIR 78-1528,

October 1978, pp. 30-31.

68
injury against which the decision maker must compare his or her own value.

If, using this approach, the number of deaths averted are simply summed over

the study period, the value of all deaths and injuries, present and future,

will be weighted equally.^ In contrast, discounting the estimated dollar

value of deaths and injuries averted means that future deaths and injuries are

valued less than those current.

A further difficulty in evaluating the benefits of reduced risk of death and

injury, as well as of property loss, is that the risk reduction depends on

sprinkler system performance. This study uses the rates of deaths, injuries,

and property loss reductions developed by the NBS/SRI Fire Loss Model, based

on expert judgment and extrapolations applied to the results of laboratory and

field tests.

Two conditions of sprinkler performance are considered: (1) the sprinkler is

to be used without a functional smoke detector in the residence (i,e,, the

detector is either nonfunctional or not present), and (2) the sprinkler system

is to be used in combination with a functional smoke detector. The second

condition is much more realistic in that it is highly unlikely that a home

protection system would ever include sprinklers and not detectors. The first

condition of sprinklers used alone is included, however, to suggest the added

benefits that may accrue to a sprinkler system in the circumstance where the

benefits of smoke detectors may not be attainable.

Ipor a discussion of discounting the value of lives saved, a controversial

issue, see Richard Zeckhauser, "Procedures for Valuing Lives," Public Policy , Vol. No. 4, Fall 1975, pp. 419-464.

•^A. Gomberg, et^ al_, y A Decision Model for Evaluating Residential Fire-Risk

Reduction Alternatives , NBSIR, in preparation 1984.

69
The impact of the sprinkler system on risk of death, injury, and other losses

will differ depending on which of these two conditions exists. The first

condition —the sprinkler system used alone —results in the greatest loss

reduction attributable to sprinklers. However, since smoke detectors are very

inexpensive, provide early fire warning, are now required by many localities,

and in fact, are included as a component of the fire sprinkler kit currently

marketed, the second condition appears much more reasonable, as was noted

above. With the second case, it is necessary to separate the loss reduction

effects of the sprinkler from those of the detector. The results will depend

on whether the sprinkler is treated as an addition to the detector or vice

versa. In this analysis, the sprinkler is assumed to be an addition to the

detector because of the detector's lower cost and earlier adoption in the

marketplace.

Impact data based on the results of laboratory and field tests, shown in table

6, are used to estimate the effectiveness of sprinklers in reducing the risk

of death and injury from fires under the stated conditions. The estimates

reflect the assumption of a malfunction rate of 8 percent, corresponding to

the assumption made in section 3.1.2 for estimating operation, maintenance,

repair, and replacement costs.

From the predicted impact data, estimated percentage reductions in fire deaths

and injuries attributable to residential sprinkler systems can be derived.

These percentage reductions are shown in table 7.

The probability of fire occurring in a one- or two-family house within a given

year, P(F) , is found as the number of reported fires in one- and two-family

70
bOC

•HS ^3 ^ 3 c W CO 4-t » 03 jr (0 tfi 0) ui M

rt <U 0T3 U l-( i-> w

u

>4-« 0) <u \C ^

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0) 1-. 0) J.; ^ <r

ij a> -o c ^^ o

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•H QJ -o m j^ a

CU (U o

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Pm tJ W) 3

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)-< bOd

-H€ >-' § o ^ w C

CO 03 4J bO ^ 3

i~> (U ^T)

CO u

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4-t a oj O

U W M o

-H cfl (U 'O Q) -a

ttJ tH

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dlh 3 J.;

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-1 c C 0) n P 4-113 c T 3 m XI to

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to U •-< Q}

U OJ O t-i to t-i e a

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(0 0) t-< J= > -H C

JJ -H U-( O . CO bO -H . QJ U_| 4-) ^-• O 0) o o

U CU

QJ iH 0) J-t

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71
Table 7, Estimated Percentage Reductions in Fire Deaths and Injuries

Attributable to Residential Sprinkler Systems^

Condition 1 Condition 2 Sprinkler Detector Present

But No When Sprinkler

Detector is Added

(% Decrease) (% Decrease)

69 63

46 44

Deaths

Civilian Injuries

^Derived as follows from the estimated impact data of table 6:

Col. 3 - Col. 4

Column 1 of table 7 = of table 6

Col. 3

Col 5. - Col. 6

Column 2 of table 7 = of table 6

Col. 5

72
houses during that year, expressed as a percentage of the total number of oneand two-family houses in the housing stock at that time, i.e., P(F) =

N(F)/N(H), where N(F) = number of fires and N(H) = number of houses in the

housing stock. Using the number of reported fires in one- and two-family

houses during 1981 , and the size of the stock of one- and two-family houses in

1981, the probability of fire occuring during the year is .00856; i.e.,

522,175 X 61,000,000 = .00856.1

The conditional probability of death given that a fire occurs, P(d|F), is

equal to the joint frequency of fire and death divided by the marginal

frequency of fires, i.e., N(F&D) . The joint probability of a fire occurring

N(F)

and death resulting, P(F&D), is P(F)P(d|F).

P(F&D) can be subscripted "pc" to denote the risk "condition" just prior to

the introduction of the sprinkler, and "s" to denote the risk condition after

sprinkler installation. Applying the estimated percentage reduction in P(d|F)

attributable to the sprinkler, abbreviated p(s,f), to the joint probability of

death and fire under the prior protection state, P(F&D)pj., results in the

estimated reduction in risk of death attributed to the sprinkler system.

Multiplying the change in risk by the estimated average value of a life lost,

and the resulting product by the uniform present worth factor to discount the

^The number of fires in 1981 is from Fire in the United States , Fourth

Edition; the number of one- and two-family houses in the housing stock is

based on the latest available Census data.

73
30-year stream of annual savings to present value, yields an estimate of

present value benefits of reduced risk of death. The benefit of reduced risk

of injury can be similarly calculated.

The combined present value benefits of reduced risk of death and injury to the

homeowner can be calculated by equation (5). No difference in benefits is

estimated for the owner/occupant and the owner of a rental unit, although the

situations differ. It is assumed that the owner/ occupant will receive the

benefits of reduced personal risk directly, while the owner of the rental unit

will receive the benefits through a rent premium that reflects the tenants'

receipt of the reduced risk benefits.

Values per death (DV) of $500,000 and per injury (IV) of $20,000 are used.

The values are assumed to remain level in constant dollars over a 30 year

period. Appropriate values for P(F&D)p(, and for P(F&I)pj, are taken from table

6. Appropriate values for p(s,f) and for i(s,f) are taken from table 7. The

present value benefit to the homeowner (owner/occupant or owner of a rental

unit) is estimated to be $362 in the absence of smoke detectors, and $171 when

sprinklers are added to smoke detectors, i.e..

Condition 1: No Detector/Sprinkler System

Dr=[(0. 69) (0. 00856) (0. 00821 )($500, 000) + (0.46)(0.00856)(0.02676)($20,000)]

(13.765) = $362.85. (30)

Condition 2: Detector/Sprinkler System

Dr=[(0.63)(0. 00856) (0.00390)($500, 000) + (0.44)(0.00856)(0.02546)($20,000)]

(13.765) = $171.23. (31)

(Note that the specific number of occupants of the house at the time of a fire

is not specified, but is implicitly assumed to be equal to the average

74
occupany rate of houses in which there were reported fires and deaths and

injuries in 1981, the year for which the data were reported. Also note that

for the entire community, benefits include an additional element, firefighters' deaths and injuries averted by sprinkler systems, which are not

included in the homeowner's risk assessment.)

3.2.2 Reduced Risk of Direct Loss

The benefits from reduced risk of direct loss, that is, property loss, are

presented separately from the benefits associated with deaths and injuries

because there is less uncertainty in ascribing dollar values to property

losses than to death and injury. The evaluation procedure is, however,

similar to the foregoing, with the following difference: Unlike deaths and

injuries, property losses are reported empirically in dollars, and the

predicted impact of sprinklers on property losses is stated in terms of change

in dollar loss per fire rather than change in the frequency of loss

occurrence.

To calculate benefits of reduced direct loss, the predicted percentage

reduction in direct loss per fire is multiplied by the average direct dollar

loss per fire for the condition existing just prior to sprinkler installation,

and the result is multiplied by the marginal probability of fire and by the

discount factor to convert the yearly savings to a present value over 30

years, as provided for by equation (6). The estimated average dollar value of

direct dollar loss per fire under alternative conditions of fire protection

are shown in table 8, as are the derived percentage decreases in direct losses

attributed to sprinklers.

75
Table 8. Estimated Impact of Sprinklers on Direct Fire Loss

in One- and Two-Family Houses

Direct Loss Per Fire

Total Loss

1982 ($)

Uninsured Loss^

1982 ($)

(1) Total amount reported in 1981 ,b

adjusted to 1982 dollars

(2) Amount per fire given existing

use of fire protection devices^

(3) Amount per fire assuming no use

of smoke detectors nor sprinklers*^

(4) Amount per fire assuming use of

sprinklers but no detectors^^

(5) Amount per fire assuming use of

smoke detectors but no sprinklers'^*^

(6) Amount per fire assuming use of

both smoke detectors and sprinklers"*®

(7) Condition 1: No Detector/Sprinkler System^

(8) Condition 2: Detector/Sprinkler SystemS

1,684,000,000

3,225

3,360

994

2,626

924

645

672

199

525

185

Percentage Decrease in

Direct Loss (%)

70

65

^Insurance of property by the homeowner is assumed to cover 80 percent of any

property loss.

"Fire in the United States , Fourth Edition, Federal Emergency Management

Agency, September 1982, Washington, D, C, The 1981 estimate was adjusted to

1982 dollars by applying the Consumer Price Indices for October 1981 of 279.9

and for October 1982 of 294.1.

*^The rate of deaths and injuries per fire in the reported fire data reflects

an existing use of smoke detectors by approximately 2 in 3 households on the

average.

^Based on simulated test data from the NBS/SRI Fire Loss Model in

Alan Gomberg _et al_. , A Decision Model for Evaluating Residential Fire-Risk

Reduction Alternatives , NBSIR, in preparation 1984.

®The data reflect the assumption of a 16 percent probability that the smoke

detector will be nonfunctional at a given time, based on the results of field

survey.

^Row 7 is derived as Row 3 - Row 4 . Row 3

SRow 8 is derived as Row 5 - Row 6 . Row 5

76
The value of reducing the risk of direct losses is assumed to be equal for the

owner/ occupant and the owner of a rental house, although its components

differ. The owner of a rental house is assumed to benefit directly from

reductions in uninsured losses to the structure, and to benefit indirectly

through rent premiums from reductions in uninsured and non-reimbursable losses

to tenants. Insurance is assumed to cover 80 percent of any property loss.

Using the estimates of table 8, the present value benefits to the homeowner

(owner/occupant or owner of a rental unit) of uninsured property losses are

estimated to be $55 under Condition 1 and $40 under Condition 2; i.e..

Condition 1: No Detector/Sprinkler System

PL = (.70)(.00856)(672)(13.765) = $55.43 (32)

Condition 2: Detector/ Sprinkler System

PL = (.65)(.00856)(525)(13.765) = $40.21 (33)

The present value benefits of reducing total property losses (insured and

uninsured) are estimated to be $277 under Condition 1 and $201 under Condition

2; i.e..

Condition 1: No Detector/Sprinkler System

PL = (.70)(.00856)(3360)13.765) = $277.13 (34)

Condition 2: Detector/Sprinkler System

PL = (.65)(.00856)(2626)(13.765) = $201.12 (35)

77
3.2.3 Reduced Risk of Indirect Costs

The indirect cost data in table 9 are stated as average amounts per fire.

Table 10 gives the derived estimates of indirect costs under various

conditions of sprinkler and smoke detector use. Indirect costs are assumed to

change under the various conditions proportionately to the change in direct

costs.

1

As in the cases for death, injury, and property losses, no difference in

benefits is estimated for the owner/ occupant and the owner of a rental unit.

This is because it is assumed that the owner of a rental unit will receive

benefits equivalent in amount to those of the owner/occupant through a rent

premium that reflects the tenant's benefit of reduced risk of indirect costs.

Like property losses, indirect costs are assumed to be partially insured;

therefore, there is a divergence between homeowner costs and social costs.

Using the estimates of tables 9 and 10, together with previously established

parametric values, the present value benefits to the homeowner (owner/occupant

or owner of a rental unit) of reducing out-of-pocket indirect costs are

estimated by equation (7) to be $18 under Condition 1, and $13 under Condition

2; i.e..

Condition 1: No Detector/Sprinkler System

C = (.70) (.00856) ($218) (13.765) = $17.98 (36)

Condition 2: Detector/Sprinkler System

C = (.65) (.00856) ($171) (13.765) = $13.10 (37)

^Michael J. Munson and James C. Ohls, Indirect Costs of Residential Fires , pp,

24-26.

78
Table 9. Estimated Indirect Costs of Residential Fires^

Average "Out-ofPercentage of Average Total Indirect Pocket" Cost per

Fires Involving Cost pe]r Residential Fire Given Existthe Various Fire Given Exis ting Use ing Use of Fire

Type of Types of of Fiice Protection Protection

Indirect Indirect Costs Devices c Devices^

Fire Costs^ (%) (1982 $) (1982 $)

Temporary Shelter 24.1 330 75

Missed Work 13.1 87 59

Extra Food Costs 11.

A

33 22

Demolition 0.9 13 8

Legal Expenses 1.3 10 7

Transportation 3.6 6 5

Emotional Counseling 11.2 15 3

Child Care 1.7 2 2

Other 4.4 33 29

All Typesd 29.4 529 210

^The original estimates stated in early 1977 dollars, were developed by

Princeton University and Mathematica Policy Research, Inc. for the Federal

Emergency Management Agency, as reported by Michael J, Munson and James C.

Ohls in Indirect Costs of Residential Fires , Federal Emergency Management

Agency, FA-6, April 1980 (U.S. Government Printing Office: 1980), pp. 24-26.

The estimates were adjusted to 1982 dollars by application of the Consumer

Price Indices for January 1977 of 175.3 and for October 1982 of 294.1 (U.S.

Department of Labor CPI Information Service, November 1982).

^Expenses for medical care and funerals have been omitted here. They are assumed to be accounted for in the amounts quoted in section 3.2.1 for the

respective values of deaths and injuries averted.

^Weighted average over all fires, including those not involving indirect

losses.

^^29. 4 percent of all residential fires had at least one of these components.

79
Table 10, Estimated Impact of Sprinklers on Indirect Fire Costs in One- and

Two-Family Houses

Average Indirect Costs Per Fire

Total Cost Out-of-Pocket

(1982 $) (1982 $)

(1) Amount Estimated Under Existing

Use of Fire Protection Devices^

(2) Amount Assuming No Use of Smoke

Detectors nor Sprinklers"

(3) Amount Assuming Use of Sprinklers

but No Detectors^

(4) Amount Assuming Use of Smoke

Detectors but No Sprinklers"

(5) Amount Assuming Use of Smoke

Detectors and Sprinklers"

(6) Condition 1: No Detector/Sprinkler

System

(7) Condition 2: Detector/ Sprinkler

System

529

551

163

431

151

210

218

65

171

60

Percentage Decrease in

Indirect Costs (%)

70

65

^Taken from table 9.

^Estimated trom tables 8 and 9.

80
The present value benefits of reducing total indirect costs are estimated to

be $45 under Condition 1, and $33 under Condition 2; i.e.,

Condition 1: No Detector/Sprinkler System

C = (.70) (.00856) ($551) (13.765) = $45.45. (38)

Condition 2: Detector/Sprinkler System

C = (.65) (.00856) ($431) (13.765) = $33.02. (39)

81
3.2.4 Insurance Cost Savings

A part of the cost of fire insurance premiums constitutes in effect a

prepayment of the fire losses which insured parties will on the average incur.

That is, part of the insurance costs will be returned to the insured in the

event of a loss. The effective cost of fire to the homeowner is the cost of

the insurance plus the cost of uninsured losses. In the long-run, this amount

can be expected to exceed on the average the cost of Insured plus uninsured

losses by the cost of underwriting and related transaction costs. The loss

portion of the insurance rate is that part based on the degree of risk.

Homeowners tend to insure even when the loss portion of the rate is quite

small in order to protect themselves from two types of risk: having fire

costs above the average, and having them sooner than the average.

Insurance companies typically offer reductions in homeowner's insurance

premiums of about two percent for houses with smoke detectors to reflect a

lower risk of loss. The Insurance Services Office (ISO), an advisory

organization to insurance companies, has developed a rule that calls for an

additional reduction of up to 8 percent in homeowner's insurance premiums for

a sprinkler system providing partial coverage, and up to 13 percent for one

providing full coverage, depending on underwriter judgment regarding the

^For a discussion of the theoretical basis for insurance premiums and the

strategy of private risk pooling, see Douglas C. Dacy and Howard Kunreuther,

The Economics of Natural Disasters (New York: The Free Press, 1969); and Guido

Calabresi, The Costs of Accidents; A Legal and Economic Analysis (New Haven:

Yale University Press, 1970).

82
reliability, maintainability, and performance of the system. The ISO Rule

calls for reductions in premiums on dwelling fire policies of up to 10 percent

for partial coverage, and up to 20 percent for full coverage, again depending

on underwriter judgment. For a tenant's policy on contents, the 8 percent and

13 percent recommended maximum reductions apply. At the time of this study,

the rule had been approved in 37 States.

The ISO recommendation reflects the results of a report by the Ad Hoc

Insurance Committee on Residential Sprinklers, which found in a controlled

experiment a 77 percent reduction in the damage losses subject to insurance

claims for a sprinklered house as compared to a counterpart nonsprinklered

house.

At the time of the study, however, the response of insurance companies in

adopting this recommendation appeared limited. Discussions with local

Maryland representatives of several large insurance companies revealed no

available discounts for residential sprinklers. Furthermore, it was suggested

that there might be a requirement for special coverage of the sprinkler system

for the risk of accidental discharge, offsetting to some extent any future

premium reduction. However, the ISO recommendation does not include a penalty

^Telephone interview with Dom Yezzi, Insurance Services Office, 160 Water

Street, New York, New York, December 20, 1982.

^Ad Hoc Insurance Committee on Residential Sprinklers, Report on 1980 Property

Loss Comparison Fires , reprinted by the Federal Emergency Management Agency,

November 1980, p. 12; and Ralph J. Jackson, "Insurance Incentives for

Residential Sprinklers," International Fire Chief , Vol. 47, No. 7, July 1981,

p. 11.

83
for sprinkler leakage. It appears that there is a discrepancy between the

public's perception of the significance of sprinkler system leakage and the

empirical evidence of leakage In commercial and Industrial applications. One

of the studies undertaken shows, for Instance, that over a six-year period

sprinkler-related Incidents were responsible for only about 12 percent of the

total water damage associated with the buildings studied.^

In short, the estimate of sprinkler benefits from reduced fire Insurance

premiums appears at this time to be tentative, at least In some regions of the

country. Realization of this type of benefit by the homeowner who Installs a

system today Is dependent on the responsiveness of the State and Insurance

con5)anles to the recommendations of the ISO and to test results. A

substantial period of time may be required for Insurance actuaries to

accumulate sufficient empirical data from real world experience to calculate

appropriate discounts for sprinklers. And, according to one source, there Is

a large degree of "arbitrariness and subjectivity" In Insurance rate-making,

such that changes In risk data do not necessarily lead to corresponding rate

changes.^ If this Is the case, field validation of the very favorable test

Salter W. Maybee, "A Brief History of Fire Protection In the U.S. Atomic

Energy Commission 1947-1975," A paper presented at the National Fire

Protection Association Fall Conference, 1978.

^Gelvln Stevenson, Fire Insurance: Its Nature and Dynamics . A report

prepared at Princeton University for the U.S. Department of Commerce, National

Fire Prevention and Control Administration, October 1978, pp. 75-77,

84
results for sprinkler performance may not be sufficient to Induce significant

discounts In fire Insurance premiums,^

With the foregoing caveats and cautions, the base-case analysis assumes a 13

percent reduction In homeowner's Insurance premiums, a 20 percent reduction in

premiums for dwelling fire policies, and a 13 percent reduction in the

premiums for tenant's contents Insurance, Break-even analysis solves for the

percentage discount in premiums needed to equate benefits and costs, other

factors held constant.

A premium cost basis is needed in order to calculate the value of the assumed

discount. Fire Insurance premiums for homeowner policies depend on the

construction of the dwelling, the type of occupancy, the type of structure,

and the fire protection class. The fire protection class rating is based on

the level of public protection, which is measured according to indices of

municipal fire prevention capabilities. From the Indices, an overall public

protection rating is assigned to a region or municipality, ^ There are 10

protection classes (1-10), plus categories for "Rural Protected" and

"Unprotected," A "Class 1" rating usually designates a city with a

well-equipped fire department, staffed by full-time, paid, professional fire

^An Indepth assessment of Insurance rate-making practices, procedures for

Incorporating new technological Information into the rate structure, and the

degree of adoption by companies of the ISO recommendation for discounts for

sprinkler was beyond the scope of this study. An additional Insurance issue

not addressed here is the possible need for Indemnif icatlon of sprinkler

companies against liability for losses suffered in sprinklered houses (Society

of Fire Protection Engineers, SFPE Bulletin , December 1980)

^Gelvin Stevenson, Fire Insurance: Its Nature and Dynamics, pp, 15 and 64,

85
fighters. Insurance companies refer to tables of regional and municipal fire

protection classes in establishing the premium for a given house. According

to an agent for a major insurance company, the assignment of a fire protection

class rating to a municipality or region, once established, is relatively

insensitive to changes in the number of households served by a fire department

within that municipality or region. (This information is employed as an

assumption in section 3.2.5 in connection with estimating potential municipal

cost savings from tradeoffs between community fire protection services and

residential sprinklers.)

In light of the factors that influence insurance rates, it is not surprising

to find substantial variation in them, A 1976 compilation, by State and type

of protection, of average property insurance costs for $20,000 of coverage for

one- or two-family dwellings of masonry or masonry veneer construction inside

the city limits of a municipality with a Class 3 fire protection rating, was

used to derive the high, low, and mean insurance rates in 1982 dollars shown

in table 11.

To develop estimates of the annual insurance premium, the estimated mean rates

in table 11 are applied to an assumed structure value of $71,300^ and to a

contents value of $50,000. (The mean rate for the homeowner's policy is

assumed to cover structure and contents combined and is applied only to

structure value to develop an estimate of annual premium.)

^The 1982 average sales price for new houses sold in the U.S. was $83,900

(from U.S. Department of Commerce, Construction Review , May-June 1983). This

price is reduced by 15 percent to adjust for land costs.

86
Table 11. Estimated Property Insurance Rates in the U.S. for One -or Two-Family Dwelling and Contents^

(Inside City Limits, Class 3 Fire Protection Rating, Masonry Veneer

Construction)

Cost Per Thousand Dollars of Coverage^

(1982)

Low High Mean

Homeowner's Policy

Residential Commercial Policy

(Dwelling Fire Policy)

Tenant's Policy on Contents

1.02

1.11

0.85

7.23

9.69

4.87

2.96

3.47

2.38

^Derived from 1976 data for 40 States giving the average cost of policies in

each state for $20,000 of coverage, as reported by Gelvin Stevenson, Fire

Insurance; Its Nature and Dynamics . The costs were converted to costs per

thousand dollars of coverage and adjusted from 1976 dollars to 1982 dollars by

applying the consumer price indices for property insurance for January 1977 of

238.6 and for October 1982 of 405.8 (U.S. Department of Labor). The adjusted

lowest and highest values among the forty provided are shown to indicate the

large degree of variation. The adjusted mean value is used in the sensitivity

analysis. The data base from which these estimates were developed reflected

substantial deviation in type and condition of coverage and the data are not

entirely comparable. For example, the high end of the range for homeowner's

and residential commercial insurance are derived from rates in states that did

not have separate rates for masonry and frame construction.

"It should be recognized that the cost per $1,000 of coverage tends not to be

a linear function of the total amount of coverage, as is implicitly assumed in

applying the above rates to larger amounts of property value. However, the

adjusted average rates shown above correspond quite closely to actual

quotations obtained by the study for homeowner's and residential commercial

policies for $85,000 of coverage in suburban Maryland.

87
For the homeowner/ occupant , the present value benefit of a discount in

insurance premiums due to sprinklers is calculated as follows:

Condition 1: No Detector/Sprinkler System

IN = id^ (in^i • IS) UPW* (40)

d,n,e,

Condition 2: Detector/Sprinkler System

IN = idh (l-id^) (inh • IS) UPW* (41)

d,n,e

(Definitions follow equation 43.)

For the owner of a rental house, the procedure for estimating the present

value benefit of discounts in insurance premiums due to sprinklers is as

follows:

Condition 1: No Detector/Sprinkler System

* IN = [idg (ing • IS) + idc (inc • IC)] UPWd,n,e d " t) (42)

Condition 2: Detector/Sprinkler System

* IN = [idg (1-idd) (ing • IS) + id^ (l-id^) (in^. • IC)] UPW^j^^^g

(1 - t), (43)

where

,

IN = present value to the homeowner (owner /occupant or owner of a rental

house) of insurance premium discounts,

id^i = the fractional discount in premiums for homeowner's insurance for a sprinklered house,

idg = the fractional discount in premiums for dwelling fire insurance

for a sprinklered house,

idjj = the fractional discount in premiums for homeowner's insurance for

a house equipped with a smoke detector,

in^ = the insurance rate per $1,000 of homeowner's coverage,

ing = the insurance rate per $1,000 of fire coverage on the structure.

88
IS = the amount of insurance coverage on the structure,

idj, = the fractional discount in premiums for tenant's insurance in a sprinklered house,

in_ = the insurance rate per $1,000 of coverage on the contents.

IC = the amount of insurance coverage on contents, and

t = the marginal income tax rate of the owner of a rental house.

For an owner/ occupant purchasing a homeowner's policy which includes coverage

of both structure and contents, in^ and IC need not be separately assessed.

For an owner of a rental house, any discount on the tenant's contents

insurance is included as a benefit to the owner of the house, reflecting the

assumption of an equivalent higher rent to the owner for benefits to the

tenant.

Using the above assumptions and the upper end of the range of recommended

discounts, the present value benefits to an owner/occupant of reduced

insurance premiums over 30 years, under Condition 1, are $378; i.e.,

Condition 1: No Detector/ Sprinkler System

71,300

IN = (.13) (2.96)( ) (13.765) = $377.66 (44)

1,000

Condition 2: Detector/Sprinkler System

Under Condition 2, where there is an initial 2 percent reduction in premiums

to reflect smoke detectors, present value benefits of the additional

reductions to reflect sprinklers are $370.

89
To the owner of a rental house, present value benefits, under Condition 1, are

$536;

Condition 1: No Detector/Sprinkler System

71,300 50,000

IN = (.20)(3.47)( ) + (.13)(2.38)( •)(13.765) (1-.4) = $536.42

1,000 1,000

(45)

Condition 2: Detector/ Sprinkler System

Under Condition 2, where reductions due to smoke detectors are first taken

into account, present value benefits due to the addition of sprinklers are

$526.

(The difference between estimated savings for the owner/ occupant and the owner

of a rental house reflects the difference in applicable insurance rates and

the fact that rental income is taxable to the owner, while insurance costs

are a tax deductible expense for the owner.)

By their payment of insurance premiums, individual property owners exchange

relatively small certain costs for protection against uncertain losses. To

avoid double counting of homeowner benefits, it is necessary to coordinate the

assumptions regarding direct (property) losses (section 3.2.2) and insurance

cost reductions. That is, the inclusion of insurance cost savings means that

the loss reductions should be lessened to reflect the assumption of fire

insurance. This was done in sections 3.2.2 and 3.2.3. For the base-case

analysis, it is assumed that all but 20 percent of property losses are covered

by insurance, as well as a substantial share of indirect costs. Fire

insurance also often includes death and injury benefits in variable amounts,

but the value for life and injury are assumed to be over and above any

insurance reimbursements, and no additional adjustment is made.

90
3.2.5 Municipal Cost Savings in Fire Protection Services (Potential Property

Tax Savings to the Homeowner)

In 1982 the more than 18.8 thousand municipalities in the U.S. are estimated

to have spent about $5.7 billion on fire protection. This was an average

expenditure of about $300 thousand per municipality. ^ With increasing

budgetary pressures, many municipalities are seeking ways to cut costs without

unacceptable cuts in service. Some are looking to residential sprinkler

systems as one possible way to reduce, stabilize, or control the growth in

municipal fire protection costs. For example, equipping the houses of a new

development with sprinklers might reduce or eliminate the need for increased

municipal fire protection capacity. The resulting savings might be passed

back to homeowners in the form of lower property taxes or used by the

municipality for other purposes.^

The tradeoff between residential sprinklers and municipal fire protection

services is highly dependent on local conditions, and the estimate of an

"average" value of potential municipal cost savings from sprinklers is

uncertain and very rough at best. The approach used here is (a) to estimate

the cost of providing fire protection to a new residential development by

building, equipping, and staffing a fire station (or adding to an existing

'^The 1982 dollar expenditure is estimated by adjusting the 1978 expenditure as reported in the 1980 Statistical Abstract to 1982 dollars. The number of

municipalities is as reported for 1977.

^An issue which may arise in this context but which is not addressed in this

study is the question of equity in matching of incidences of tax changes with

incidences of homeowner costs.

91
fire station), and (b) to assume that the new station (or addition) need not

be built, equipped, and staffed if all houses in the development are equipped

with sprinklers. It is assumed that the existing level of fire protection

services will continue to be adequate if the new houses are equipped with

sprinklers because the necessary response time to these houses will be reduced

for most fires. '• The fire department cost savings are interpreted as community

benefits. The cost savings divided by the number of houses in the new

development are interpreted as potential homeowner benefits—"potential"

because they are dependent on the action taken by the municipal government.

The costs of the fire department are based on the following highly simplified

assumptions regarding the area and houses served:

(1) The size of the "New Development" corresponds to the size of the area to

be served by a new fire station, and comprises 5.85 square miles. This area

was derived according to a theoretical approach depicted in Figure 4.^

^It should be recognized, however, that if the assumed change were to alter

the community's fire protection class rating, the reduction in community fire

protection costs could be more than offset by higher insurance rates to

homeowners. An example of the effect of fire protection services on insurance

rates was given in a recent article: "... in an area with no fire protection,

which insurance people in New England call 10-F, the annual insurance premium

for an average $20,000 home would be $96.60. The annual premium for the same house in an area rated 5-C would be $41.80, or an annual (difference) of

$54.80. (Chief Edmund Stone, "How to Estimate Value of Department Rating on Insurance Savings," Fire Engineering , March 1978). However, as was noted in

section 3.2.4, there may be sub^antial leeway in changing the ratio of fire

protection services to households, without affecting the fire protection

call rating of the community.

•^The Rand Corporation, Fire Department Deployment Analysis: A Public Policy

Analysis Case Study , Ed. W. E. Walker, J. M. Chaiken, and E. J. Ignall (New

York: North Holland, 1979).

92
Figure 4. Determining the Area of the "New Development" for Which Fire

Station Costs Will be Avoided^

O

^According to a theoretical approach to fire company location (as described by

the Rand Corporation in Fire Department Deployment Analysis: A Public Policy

Analysis Case Study) , a hexagon shape was assumed for the area—the optimal

shape for efficiently utilizing a fire station. And, a maximum distance of a house from the station of 1 1/2 miles was assumed based on a required flow

rate. The area of the hexagon was then determined.

o = Engine Company

93
(2) The area is assumed to contain 2,106 people and 642 houses. The

population density was established according to the average density of people

per square mile inside Standard Metropolitan Statistical Areas (SMSA's) in

1970, the latest year for which these data were found. ^ Using the average

SMSA density of 360 people/ sq. mile and multiplying by the number of miles

results in an estimate of 2,106 people in the New Development (i.e.,

360 people/sq.mile • 5.85 sq.mile = 2,106 people.

The number of households was derived by relating the number of people per

household to the number of people. The 1980 average number of people per

family was reported as 3,28.^ Assuming single-family houses, the number of

houses is found as 642 (i.e., 2,106 people/3.28 people/family = 642 families).

The cost of the fire station structure (including site preparation, architects

and engineers fees, supervision and administrative overhead, and materials and

labor, but excluding land costs) was developed by the General Estimate Method

of construction cost estimating, according to the following building

specifications

^

^ 1981 Statistical Abstract , p. 15.

^Ibid. , p. 42.

%cGraw-Hill Information Systems, Dodge Building Cost Calculator and Valuation

Guide, Edition 41, New York, New York, January-March 1981,

94
Fire Station

Construction: Masonry Wall

Quality: Good

Structure: Reinforced concrete foundation, footings, walls and

slabs. Exterior walls: face brick and block with

stone trim and finish. Good quality wood or metal

sash. Interior masonry bearing walls with plaster

finish. Structural steel floor and roof decking with

concrete fill. Built-up roof and insulation. Resilient

flooring and ceramic or quarry tile. Suspended acoustical

tile ceiling in office area. Remaining areas dry-wall or plaster.

Plumbing: Locker and shower rooms. Water coolers. Utility and

service sinks.

Heating and Ventilation: Boiler - oil or gas fired low pressure steam or hot water heat. Suspended heaters in truck

area.

Electrical: Special wiring and circuitry for alarm systems, extensions,

outlets, clock, trouble and reading lights.

Functional Areas: Apparatus and truck parking areas, hose drying,

storage, mechanical work area, watch room, office

and living area, lounge, dormitory, and kitchen.

Size: 4,000 square feet.

The basic cost data in the Dodge Building Cost Calculator are at a 1970 level,

and must be adjusted by cost multipliers for the desired location. For use

in this study, the average of the local cost multipliers for 183 U.S.

Metropolitan Areas was computed. This figure was 2.3, and its use resulted in

costs stated in 1981 dollars. To adjust the cost to 1982 dollars, the

price indices for State and local government purchases of structures for 1981

(230.3) and the 2nd quarter of 1982 (seasonally adjusted) (235.2) were used,

235.2

i.e., ($111,520) (2.3)( '—) = $261,953. The resulting estimate, in 1982

230.3

dollars and rounded to the nearest hundred, is $262,000.

95
Land costs, estimated as 20 percent of total cost (building and land), are

$65,500 in 1982 dollars, rounded to the nearest hundred (i.e., $261,953 +

.2TC = TC and .2TC = $65,488).

Structure and land costs combined are estimated to be $327,500, i.e., $262,000

+ $65,500 = $327,500. The cost of operating the station to supply fire

services (including costs of equipment and manpower, but not the building) is

developed from the per capita supply costs reported for five western cities

(and, hence, may not be typical for the U.S. as a whole). The reported costs,

in adjusted 1982 dollars, ranged from a low of $19.59/person/year to

$41.27/person/year, and averaged $32.04/person/year.^

Using constant dollar costs and a assumed 6 percent municipal discount rate,

the present value costs of supplying fire services to the new development over

30 years is estimated to be $928,800 in 1982 dollars, rounded to the nearest

hundred (i.e., ($32.04) (13.765) (2,106) = $928,810.44).

Summing the supply costs and the building costs yields an estimated total

present value cost of providing fire services to the new community by

conventional means of $1,256,300 in 1982 dollars, (i.e., $327,500 + $928,800 =

$1,256,300). This is the estimated benefit to the municipality of not

^Based on per capita supply costs for Glendale, Yuna, Flagstaff, Tempe, and

Phoenix as reported by Roger Aklbrandt in "Efficient Output of a Quasi-Public

Good-Fire Services" (Ph.D. Dissertation, Department of Economics, University

of Washington, 1972, table A.). The supply costs, stated in 1971 dollars, were

adjusted to 1982 dollars by application of the price indices for State and

local government purchases of goods and services.

96
building, equipping, and staffing a fire station to serve the new

development.

The owners of the sprinklered houses would derive a corresponding benefit only

if the municipality shared this savings through, for example, lowered local

taxes. Assuming an annual pass-through of the present value savings

amortized over 30 years at a real discount rate of 6 percent from the

municipality to the homeowners who install sprinklers, the annual tax rebate,

or tax reduction, would be $143 per household (i.e., ($1 ,256,000)(0.073) v 642

= $142.82). For both an owner/ occupant and an owner of a rental house, the

estimated after-tax present value benefit (MTS) is $1,179 (i.e., MTS =

($142. 82)(13. 765X1-0.4) = $1,179.49). This takes into account the fact that

local taxes are a tax deductible expense in computing Federal income taxes for

owner-occupied and rental houses.

3.2.6 Governmental Incentives

To encourage a type of action or behavior deemed in the public interest,

local. State, and Federal Governments sometimes provide subsidies to lower

the effective cost of the desired action to the individual and, thereby

increase its likelihood of occurrence. For example, governmental incentives

have been made available in recent years to promote homeowner investment in

energy conservation and alternative energy sources.

^For an analytical treatment of financial incentives and their impact as applied to solar energy investments, see Rosalie T. Ruegg, Evaluating

Incentives for Solar Heating , National Bureau of Standards, NBSIR 76-1127,

September 1976.

97
Financial incentives may take the form of income tax credits, increased

allowable income tax deductions, direct cash subsidies in the form of grants

and cost-sharing arrangements, special low interest loans and loan guarantees,

and waivers or reductions in property taxes that would otherwise accrue.

Although there are currently no incentives offered by the Federal Government

to homeowners who purchase sprinkler systems, there is a possibility that such

incentives may become available in the future, and, hence, the potential

impact of incentives is of interest to the study. As of the time of this

study, pending incentive legislation is limited to tax credit provisions for

profit-making establishments which install sprinklers. For example. Senate

Bill 878, introduced by Senator Howard Cannon (D-NV) would have allowed a 20

percent tax credit for sprinklers installed in properties eligible for the

regular investment tax credit.

At least one state, Alaska, has enacted a law which exempts from taxation 2%

of the assessed value of any structure that is protected with a "fire

protection system. "^

For the purpose of the base-case analysis, no governmental incentive is

included. However, the value of a tax credit necessary to cause a break-even

investment outcome for the homeowner is calculated for several different

^The bill as written did not extend the credit to one-and two-family

residences, a point that has been inaccurately reported in the press (see, for

example, "Dousing Home Fires," The Washington Post , July 10, 1982). [Telephone

interview with staff assistant to Senator Howard Cannon, Dec. 10, 1982,

J

Several House Bills (HR.1958 and HR. 73795) contained similar provisions.

[U.S. Legislative Status Office, U.S. Capitol].

^Reported by John A. Viniello, "An Old Idea With a New Technology," Grinnel

Fire Protection Systems Company, Inc. (Undated).

98
conditions in section 3.3. Also, the sensitivity analysis includes the case

of a 20 percent Federal income tax credit, plus the local incentive of

eliminating the estimated value of the higher property taxes that are included

in the base-case analysis. The value of the tax incentive is based on the

assumption that the total cost of purchasing and installing the system is

eligible for the credit. Using the $1,718 estimated cost of a system with 1/2

inch diameter polybutylene piping (table 5) and assuming receipt by the

homeowner of the credit at the end of the year in which it is installed

results in an estimated present value benefit of $324; i.e.,

GI = ($1,718) (.2) (.943) = $324.01, (46)

where GI = present value of a governmental incentive.

Note that the value of this benefit is equivalent for the owner/occupant, the

owner of a rental unit, as well as for the builder/developer, because it

constitutes a direct reduction in the investor's tax liability by the

designated amount.

3.2.7 Other Potential Benefits

A different type of incentive that may be offered in some localities to

builders/developers who install sprinkler systems is a relaxation in local

codes to allow increased building density and less fire-resistant

construction. By reducing land and construction costs, these allowances

constitute benefits to the builder/developer who installs sprinkler systems.

To the extent that the resulting cost reductions are passed through to

purchasers of the houses, they are also benefits to the homeowner. However,

the increased housing density that may result could give rise to "disbenef its"

99
that are partially offsetting of the cost reduction benefits. The changes in

construction requirements may also have other effects which affect homeowner

satisfaction with the house. Because of the large degree of uncertainty about

the impact of these types of code changes on the homeowner, they are not

included in this estimation of homeowner benefits and costs.

Another potential benefit to the homeowner that is sometimes cited is a higher

resale value of the sprinkler-equipped house. That benefit is treated

implicitly in this study in conjunction with the assumed life of the system.

In the base-case analysis, it is assumed that the system gives service for 30

years and that ownership is maintained over that 30 year period.

3.2.8 Summary of Benefits Estimates

The preceding seven sections, 3.2.1 through 3.2.7, have discussed benefit

estimation for reduced risk of death and injury and direct and indirect costs,

insurance cost savings, reduced costs of municipal fire protection services,

governmental incentives, and other potential benefits. Benefit estimates have

been developed for the owner/ occupant of a house and the owner of a rental

house. Table 12 summarizes the estimates of current and potential benefits.

100
Table 12. Summary of Benefits Estimates^

Homeowner Benefits

Sprinkler Impact

Owner/

Occupant

(1982 $)

Owner

Rental

House

(1982 $)

Reduced Risk of

Death & Injury

Reduced Risk of

Property Loss

Reduced Risk of

Indirect Costs

171

40

13

171

40

13

Insurance Cost

Savings

370 526

Subtotal 594 750

Reduced Need for

Community Fire

Protection

Services Reflected

In Lower Property

Taxes

1,173b 1,173^

Subtotal

Governmental

Incentives

324c

1,767

324c

1,923

Total $2,091 $2,247

^Summarized from sections 3.2.1 through 3.2.7.

"Based on the assumption of a full pass-through to homeowners of local

government cost savings. Not included in base-case analysis.

^Based on a 20 percent tax credit not currently available. Not included in

base-case analysis.

101
3.3 Case Study Results

3.3.1 Base-Case Results

This section brings together the estimates of costs from section 3.1 and

benefits from section 3.2 and enters them in the benefit-cost framework.

Nine benefit-cost case studies demonstrate how the model can be used, and the

results provide insight to the potential economic feasibility of residential

sprinkler systems under specified conditions.

Table 13 summarizes the data and assumptions for benefits developed in section

3.2, and table 14 those for costs developed in section 3.1. These data and

assumptions are used in the first case illustration, referred to as the base

case. Table 15 summarizes the data and assumptions used in the other selected

case illustrations, which are presented in the context of sensitivity

analysis of the base case. Table 16 lists the values of economic parameters

used in all of the illustrations. (Notes to each of the tables summarize

briefly the basis for selecting the values shown. For a more in-depth

explanation, the reader can refer back to sections 2.3, 3.1 and 3.2.)

Table 17 gives the net benefits results for the base-case study. It may be

seen that in this illustration the sprinkler system is not a cost-effective

investment. Costs are estimated to exceed benefits by nearly $1,500 in

present value dollars over a 30 year period.

Table 18 shows the break-even values of critical parameters that would be required

to make the sprinkler system of table 17 minimally cost effective, with other

variables at their base-case values. For example, with no municipal cost

reductions or special incentives , the value placed on life would have to be

102
Table 13. Summary of Data and Assumptions for Estimating Benefits for the

Base-Case Illustration

Parameter Assumed Value

Probability of Fire P(F)a

Prior Protection State

Probability of Death Given Fire P(d|F)'5

With Smoke Detector But Without Sprinklers

With Smoke Detector and With Sprinklers

Value per Life^

Probability of Injury Given Fire P(I|F)'^

With Smoke Detector But Without Sprinklers

With Smoke Detector and With Sprinklers

Value per Injury*^

Average Direct Property Loss Per Fire^

With Smoke Detector/Without Sprinklers

With Smoke Detector/With Sprinklers

Average Indirect Cost Per Fire'^

With Smoke Detector/Without Sprinklers

With Smoke Detector/With Sprinklers

Insurance Premium Discount—Homeowner's

Policye

Homeowner's Premium Rate per $1,000

Coverage^

Insured Value of HouseS

.00856

Smoke Detectors Present

.00390

.00146

$500,000

.02546

.01436

$20,000

$2,626 (total) $525 (uninsured)

$924 (total) $185 (uninsured)

$431 (total) $171 (out-ofpocket)

$151 (total) $60 (out-ofpocket)

13%

$2.96

$71,300

^Number of reported fires in one- and two-family houses in the U.S. in 1981

divided by the number of one- and two-family houses in the U.S. housing stock.

"Estimated from reported data and simulated results based on laboratory and

field fire tests for single-family dwellings, as described in Alan Gomberg, et

al. , A Decision Model for Evaluting Residential Fire-Risk Alternatives , NBSIR,

in preparation 1984. (Implicit in the probability estimate is an occupancy

level of the house equal to the 1981 U.S. average for houses in which people

were killed or injured by fire.)

^Based on assumptions made in section 3.2.1.

"Derived from estimates reported by Michael J. Munson and James C. Ohls,

Indirect Costs of Residential Fires , by assuming that indirect costs are affected by sprinklers proportionately to the impact of sprinklers on direct

costs.

^Percentage discount recommended to insurance companies by the Insurance

Services Office (ISO), as reported by the Ad Hoc Insurance Committee on Residential Sprinklers.

^Derived by averaging and updating 1976 reported insurance rates for one- and

gtwo-family dwellings from 40 U.S. States.

Mean sales price of all new houses in the U.S. ($83,900 in 1982), less a 15%

adjustment for land costs.

Note: All monetary values are in 1982 U.S. dollars.

103
Table 14. Summary of Data and Assumptions for Estimating Costs for the

Base-Case Illustration

Parameters Assumed Value

House Occupancy

Sprinkler System Contract Cost^

Piping

Installed Cost/L.F.

Number of Fittings

Installed Cost of Fittings

Fire Sprinkler Kit, Installed

Other Costs

Total System Cost

Operating Costs

Water Charge^

Probability of Properly Functioning

System^

Activation of System*^

Maintenance, Repair and Replacement Costs

Annual Routine Inspection by Plumber

Hourly Wage Rate®

Plumber

Replacement of Sprinkler Heads^

Yearly Replacement Rate, Years 1-10

Yearly Replacement Rate, Years 10-20

Yearly Replacement Rate, Years 20-30

Property TaxS

Initial Assessment Basis Contract Cost

Ending Assessment Basis Contract Cost

Owner-0ccupied

1/2" polybutylene - 205 L.F.

$2.03

30

$149

$1,120

$33

$1,718

.00078«^/gal

0.92

Activation of 3 Sprinkler Heads

for 30 Minutes

1 hour

$27.65

1%

1.5%

2.5%

($1,718)

^Developed by applying the Component Method of Construction Cost Estimating to a hypothetical system design for a 2-story colonial-type house.

°U.S. mean marginal price per gallon of water for a household of four.

^Based on study by Alan Gomberg, et _al .

, A Decision Model for Evaluating

Residential Fire-Risk Reduction Alternatives . ^Pessimistic assumption, since normally only one head will activate and

activation will not last for 30 minutes.

®U.S. average wage rates in cities, including overhead and profit, in 1982

dollars.

f Sprinkler heads can be damaged by painting, dust, and water corrosion over

time. This replacement schedule allows for replacement of one half of the 21

heads over the system life and assumes failure to be an increasing function of

age.

^Assumes straight-line decline in tax basis.

104
Table 15. Summary of Data and Assumptions for Other Illustrations

Parameters Assumed Value

Pass-through to Homeowner of Municipal

Cost Savings (New Housing Development)

Geographical Area^

Population Density''

Number of Houses^

Fire Station Structure Cost Avoidance^

Fire Station Land Cost Avoidance®

Equipment and Manpower Cost Avoidance^

"Regular" Property Taxes on Capitalized Value

of Sprinkler Systems

Federal Income Tax CreditS

Copper Piping (average 1 1/4")^

Water Demand ("Stand-by") Charge^

No Insurance

House Occupancy

Prior Protection State

5.85 sq. miles

2, 106 people

642 houses

$262,000

$65,488

$32/pers on/year

Waived for Cases

II and III

20% of

contract cost

$3,724 contract

cost

$2,000

All losses out-of-pocket

Decision Not to Insure;

(1) Attributed to Sprinkler

System

(2) Independent of

Sprinkler System

Tenant Occupied

Smoke Detectors Not Present

^Estimated according to theoretical approach to optimal fire company

location.

"Reflects average U.S. population density per square mile inside SMSA's.

^Number of people ^average number of people per household in U.S.

^Developed by the General Estimate Method of Construction Cost Estimating

according to specifications for a masonry wall fire station of 4,000 square

feet.

^Estimated as 20 percent of total building and land cost, i.e, $261,953 +

.2TC = TC.

^Developed from the average per capita fire services supply cost of equipment

and personnel reported for five western U.S. cities, updated to 1982 dollars.

SProvision included in U.S. Senate Bill 878 for profit-making establishments

which install sprinklers.

"Estimated according to the Con5)onent Cost Estimating Method.

^Reflects the current practice of some utilities to charge a special "water

stand-by fee" for connecting a house equipped with a sprinkler system

to the municipal water system.

105
Table 16. Summary of Economic Assumptions Used in Case Studies

Parameter Assumed Value

System Life^

Study Period

Remaining Value at End of Life

Discount Rate^

Mortgage Rate*^

Mortgage Life*^

Inflation Rate^

Homeowner ' s Marginal Income Tax Rate^

Effective Property Tax Rate®

Downpayment

30 Years

30 Years

6% (real) 11.3% (nominal)

10% (real) 15.5% (nominal)

30 Years

5%

40%

2.15%

^The life of fast-response sprinkler systems, with polybutylene piping, has

not been empirically validated for residential use; however, plumbing

systems in houses and sprinkler apparatus in commercial buildings appear to

have relatively long lives. The specific choice of a 30 year study period

is based on the customary 30 year mortgage lending period for residential

housing,

^Based on the average, real, after-tax rate of return to investors in all

grades of nonflnancial common stock and long-term corporate bonds over recent

decades, and the implied discount rate ranging from 5.1% to 8.9% for households with incomes between $35,000 and $50,000, as derived by Hausman,

^Reflective of approximate conditions at the time of the study,

"For the tax year, 1983, the marginal tax rate of 40% applies to single

individuals with at least $34,000 of taxable income and to married couples

with at least $45,800.

®The average effective rate for 30 large U.S. cities in 1978.

106
Table 17. Base Case: Net Benefits Calculation

Benefits Present Value ($)

Deaths and Injuries Averted

Property Losses Averted

Indirect Costs Avoided

Insurance Cost Savings

Total Benefits

171

40

13

370

594

Costs

Purchase and Installation Costs

(after taxes and financing)

Operating, Maintenance, Repair,

and Replacement Costs

Property Taxes on the System

Total Costs

1,445

420

190

2,055

Net Benefits -1,461

107
Table 18. Base Case: Break-even Analysis

(Note: Assumptions Are Initialized to Base-Case Values After Each Break- even Calculation)

Parameter Break-Even Value

Purchase and Installation Cost

(after taxes and financing)

Probability of Fire

Value of a Life Saved^

(Discounted)

Value of a Life Saved Plus 3.56 Injuries^

Averted^ (Not Discounted)

Average Value of Uninsured Property

Loss Per Fire Without Sprinklers

Percentage Discount in Homeowner's

Insurance Rate

Homeowner's Insurance Premium Per

$1,000 of Coverage

Annual Property Tax Reduction Reflective

of Municipal Cost Savings (Constant $'s)^

Reduction in Builder's Costs (assuming a full pass-through to home buyer)

Federal Income Tax Credit

(as a % of Initial Purchase and

Installation Cost)

.064

$5 million

$2.6 million

$19,500

64%

$14.64

$92

$1,461

90%

^Assumes an occupancy level equal to the 1981 U.S. average for houses in which

people were killed or injured by fire. Hence, the break-even value would be

smaller than that shown for houses with greater than average occupancy or larger for houses with smaller than average occupancy.

"According to Approach 2 described in section 3.2.1.

^Tax reductions in addition to a waiver of property tax on the capitalized

value of the sprinkler system.

108
about $5 million in present value dollars _or the total value placed on life

and injuries averted would have to be about $2,6 million in undiscounted

dollars. As other examples, the homeovmer would have to have a risk over

seven times the average rate, _or incur about $19,500 in uninsured

property loss on the average per fire without sprinklers in order for a breakeven outcome to result, all other factors remaining the same.

3.3.2 Additional Case Results

Table 19 summarizes the results for eight additional hypothetical case studies

to show what happens when the values of key parameters and assumptions are

varied from those of the base case illustration.

Columns 1 and 2 of Table 19 show that the combination of a waiver of property

taxes on the capitalized value of the sprinkler system and a pass-through to the

homeowner of estimated municipal cost avoidance are sufficient, given the other

data and assumptions, to eliminate most of the losses. If, in addition, a 20

percent Federal income tax credit is granted, positive net benefits of about

$200 dollars are estimated.

Columns 3 and 4 of Table 19 show the result of two pessimistic cases.

Substantial net losses are estimated for systems using large copper piping and

subject to a "water standby fee." These two estimates may be regarded as "worst

case results" because piping as large as 1 1/4 inch would seldom be used

throughout a system, and most municipalities probably would not levy a water

demand charge

.

109
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110
Columns 5 and 6 show estimated results assuming no insurance. Column 5

attributes the cost savings from not insuring, directly to the sprinkler;

i.e., the assumption is that the sprinkler reduces the risk of loss to a level

that causes the homeowner to accept the risk without insuring. Positive net

benefits are estimated. These two cases are unlikely to be widely applicable

because most homeowners either are required to carry fire insurance as a

condition of obtaining a mortgage loan, or, in any case, do not elect to

"self-insure" because they are risk averse. The results reflect primarily the

fact that fire dwelling insurance is not cost effective, on the average, in

terms of the expected value of net dollar benefits, although it may be

rational in terms of expected utility.

Column 6 assumes that the decision not to insure is made independently of the

sprinkler decision, and, hence, attributes no insurance savings to sprinklers.

Net losses result. In both cases, the full estimated value of losses averted

(not just uninsured losses) is credited to sprinklers.

By comparing column 6 of table 19 with the base-case results of table 17, it

may be seen that net losses are estimated to be greater for the sprinkler used

in the uninsured house than in the insured house unless the savings from not

insuring are tied to the sprinkler investment. This reflects the allowance of

significant discounts in insurance premiums under the base case. If there

were no premium discounts for the insured house, the sprinkler system would be

more cost effective in the uninsured house than in the insured house, as one

might expect. A corollary of this result is that fire insurance makes less

economic sense for a sprinklered house than for an unsprinklered house, unless

111
the risk reduction from sprinklers is reflected in insurance premium

discounts.

Column 7 of table 19 shows net benefits for sprinklers evaluated under

Condition I, that is, without the presence of a smoke detector. The net

losses are lower than under the base case (Condition II with smoke detectors),

because of the larger impact of sprinklers in reducing risk of loss. However,

this case is for the most part unrealistic because sprinklers generally would

be used in conjunction with smoke detectors. It is highly unlikely that a

home protection system would include sprinklers and not the much lower priced

smoke detector. The case of sprinklers used alone is included in order to

suggest the added benefits that may accrue to a sprinkler system when the

benefits of smoke detectors may not be attainable, such as when occupants are

incapacitated and cannot response to a smoke detector. Of course, in such a

situation the occupants' risk exposure would likely be higher than the average

risk data used in the case studies, and therefore the case studies results are

tentative.

Column 8 of table 19 shows net benefits for sprinklers evaluated for a rental

house. The sprinkler system is estimated to be somewhat more cost effective

for the owner of a rental house than for the owner/occupant, other things

being equal, although net losses of about $800 are estimated for this case

illustration. Larger tax deductions of system expenses, such as for

depreciation and operating, maintenance and repair costs, account for the

better showing of the rental house. These results are, however, also

contingent on the assumption that the landlord will receive a rent premium

112
fully reflective of the tenant's reduced risk of fire loss, in addition to the

owner's direct benefits of increased protection on the structure.

Table 20 shows the results of a break-even analysis based on Case II

assumptions, i.e., a waiver of property taxes and a pass-through to the homeowner of the estimated value of municipal cost avoidance. It shows that,

other factors remaining the same, estimated net losses for this case

illustration could be eliminated by adding any one of the following changes to

the Case II assumptions; (1) a risk of fire one and a half times as high as

the U.S. average rate; (2) a value of life of roughly $850,000 using

discounted values, or as low as about $400,000 using non-discounted values;

(3) a 16 percent discount in homeowner's insurance rates; or (4) a passthrough of reductions in builder's costs of about $98.

113
Table 20. Case II: Break-Even Values

(Note: Assumptions Are Initialized to Case II Assumptions After Each BreakEven Calculation)

Parameter

Break-Even

Value

Case II

Value

Purchase and Installation Cost

(after taxes and financing)

Probability of Fire

Value of a Life Saved

(Discounted)

Value of a Life Saved Plus 3.56

Injuries Averted^ (Not Discounted)

Average Value Uninsured Property

Lo. = Per Fire Without Sprinklers

Percentage Discount in Homeowner's

Insurance Rate

Homeowner's Insurance Premium Per

$1,000 of Coverage

Annual Property Tax Reduction Reflective

of Municipal Cost Savings (Constant $'s)^

Reduction in Builder's Costs (assuming

a full pass-through to home buyers)

Federal Income Tax Credit

(as a % of Initial Purchase and

Installation Cost)

$1,347

.012

$839,000

429,000

$1,800

16%

$3.74

$7.11

$98

$1,445

.00856

$500,000

$525

13%

$2.96

$85.16 Reduction

(Waiver of property tax on the system)

^Derived according to Approach 2 described in section 3.2.1.

^Tax reductions in addition to a waiver of property tax on the capitalized

value of the sprinkler system. The break-even solution indicates that an additional reduction of $7.11 annually is required to bring net losses to zero,

i.e., a total reduction of $92.27.

114
4. SUMMARY AND CONCLUSIONS

This paper has developed a model for evaluating the expected value of net

benefits to the homeowner of a fire sprinkler system, and has illustrated the

model in a series of hypothetical case studies for new, single-family

dwellings in the U.S. The results of the case studies are based on many

assumptions, and actual net benefits from a sprinkler system may be

considerably different from those estimated here. The cases may provide

insight as to how the cost effectiveness of these systems is affected by

particular conditions.

Some inferences that may be drawn from the hypothetical case studies are the

following: (1) The cost effectiveness of residential sprinkler systems is

improved by code changes which allow the use of approved plastic pipe; (2)

sprinkler systems may be uneconomical under low-to-averege conditions of risk

for the homeowners who independently purchases a system; but they may be cost

effective under conditions of high risk; (3) sprinkler systems are more likely

to be cost effective, other factors being the same, for homeowners who are

part of a community of sprinkler users and who receive the benefit of

attributed cost avoidance by local government or by the home builder; (4)

homeowners who live in localities with "water standby fees" or who use

commercial sprinkler systems are unlikely to have a cost-effective sprinkler

systems under average probabilities of fire and related death, injury, and

property loss; (5) sprinkler systems are more likely to be cost effective when

used in situations where additional protection is needed, such as situations

where the benefits of smoke detectors alone may not be attainable, for

example, when occupants are incapacitated and cannot respond to the alarm.

115
These findings, though based on hypothetical cases, are helpful in

Identifying the following critical areas for further exploration: (1) the

potential of municipal cost savings from sprinklered houses and the

feasibility of corresponding tax reductions, (2) the feasibility of

cost/performance tradeoffs between sprinklers and fire resistant construction

methods and materials, (3) the availability of discounts on insurance

premiums, (4) the practice of levying water demand charges for sprinklered

houses, (5) approaches to lowering the cost of sprinklers, (6) retrofit

capability, (7) partial systems for fatality-prone areas of the house, and (8)

benefits accruing to households with different behavioral and demographic

characteristics and living in houses of different construction and age.

Studies of municipality experience with mandated sprinkler systems would be

useful in estimating municipal cost avoidance. An investigation of the

technical substitutability of different building approaches to residential

fire safety should contribute to the estimation of construction cost tradeoffs. Further testing and validation of the impact of sprinklers on fire

losses might facilitate appropriate changes in insurance rate structures. The

issue of water demand charges will require cooperation between local water

utilities and local governments who wish to encourage the widespread use of

residential sprinklers.

The model in its present form is not appropriate as a decision tool for the

homeowner. Incorporation of utility analysis is one requirement for such an

extension. The models of builder/developers and for municipal government

116
decisions (as given in the appendix) also require further refinement to make

them convenient for use by builders, developers, and municipalities. Research

efforts are needed to address issues related to the computation of expected

values and expected utilities of fire mitigation strategies for use in the

various decision models. These issues include the appropriate methodology for

assigning monetary values to future lives saved, to injuries of different

degrees of seriousness, and to unique properties, as well as the appropriate

procedures to follow in regard to discounting lives saved and injuries averted

in the various decision models. Data is needed to support applications of the

models to a variety of real-life situations.

117
SELECTED REFERENCES

Ad Hoc Insurance Committee on Residential Sprinklers, Report on 1980 Property

Loss Comparison Fires . Reprinted by Federal Emergency Management Agency, U.S.

Fire Administration; National Fire Data Center, Washington, D.C.) November

1980, 22.

Aklbrandt, Roger, "Efficient Output of a Quasi-Public Good-Fire Services,"

Ph.D. Dissertation, Department of Economics, University of Washington, 1972.

Arrow, K. J., Social Choice and Individual Values , Second Edition (New Haven,

Connecticut: Yale University Press, 1963).

Battelle Columbus Laboratories, Development of an Experimental Prototype LowCost Electronic Sensor/Actuator for a Residential Automatic Sprinkler Head , (prepared for the Federal Emergency Management Agency), undated.

Budnick, Edward K. , Estimating Effectiveness of State-of-the-Art Detectors

and Automatic Sprinklers on Life Safety in Residential Occupancies , National

Bureau of Standards, NBSIR 84-2819, January 1984.

Calabresi, Guido, The Costs of Accidents: A Legal and Economic Analysis . (New

Haven, Connecticut: Yale University Press; 1970).

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122
Appendix, Related Decision Models for the Builder/Developer and the

Municipal Government

A.l Decision Model for the Builder/Developer

Because the majority of houses being constructed today is on a speculative

"for sale" basis, the builder/developer is a key decisionmaker regarding the

characteristics and features of new housing. A builder/developer of new

housing may assess the market demand for houses equipped with sprinkler

systems and install them as a standard feature or offer them as an option to

potential buyers. Emphasis in marketing might be on safety and/or costeffectiveness.

In offering sprinklers as a standard feature, the builder/developer weighs the

costs of purchasing and installing the systems against the ability to sell the

houses at an effectively higher selling price, and against any offsetting cost

reductions that may be realized by including sprinklers in the housing.

Offsetting cost reductions may include lower land costs due to higher density

of buildings, lower construction costs due to reduced requirements for fire

resistant materials, and reduced land set-aside for fire lanes and fire

stations. The ability of a builder/developer to charge a higher price for

speculative houses equipped with fire sprinklers depends on consumer

acceptance and perceived value.

Based on patterns observed in the market acceptance of other new technologies

for the home, developers of higher-priced housing, for which the sprinklers

would add a smaller percentage increase to first costs and to mortgage

A-1
payments, could be expected to be more successful in covering their costs.

By making the systems standard, the builder/developer of a sizable number of

houses might be able to install the systems at a lower cost than could a

custom builder, through, for example, quantity discounts on materials,

increased labor efficiencies, and smaller markups for overhead and profit.

The large-scale builder/developer is more likely to attain the cost offsets

mentioned earlier, such as reduced expenditures for fire resistant

construction, than the small-scale custom builder because of the critical

minimum level of community participation required to justify these kinds of

cost reductions.

In offering sprinklers as an option, rather than as a standard feature, the

builder/developer avoids the risks of an uncertain market. However, by making

the systems optional, builders/developers may not attain any economies of

scale in their provision. More importantly, the level of community

participation may be inadequate to justify the allowance by public officials

of offsetting cost reductions in land and construction.

The following three investment cases can be identified for the speculative

builder/developer:

Case I . The builder/developer voluntarily installs sprinkler systems as

a standard feature in a subdivision or community of speculative "for

sale" houses.

^Reiger, Marketplace Realities and Solar Economics .

A-2
Case II . The builder/developer voluntarily offers the system as an

option to homebuyers who request it.

Case III . The builder/developer installs the systems in all houses built

in compliance with a mandatory requirement set by public officials.

In each of these cases, all of the relevant decision variables to the

builder/developer involve more-or-less up-front cash amounts that require no

time adjustments for estimating the economic efficiency of the investment.

Furthermore, Case II, whereby the builder/developer installs a sprinkler

system only at the request of the homebuyer, can likely be dismissed as not

requiring analysis. This is because the builder/developer may be assumed to

shift the full cost of the system to the homebuyer, and, thereby, avoid the

risk of an uncertain selling price. And, because of a probable lack of full

community participation in electing the sprinkler option, the builder/

developer would likely receive little in the way of offsetting cost

concessions from the local government.

Cases I and III are similar in that they both involve total participation of

new houses in the use of sprinklers and therefore might involve cost

concessions to the builder/developer. They may differ, however, in the

ability of the builder/developer to recoup the purchase and installation costs

of the systems. In Case I, where sprinkler systems are voluntarily installed

as a standard feature, the builder/developer accepts fully the vagaries of

market demand for the systems and may or may not be able to pass on the costs

to homebuyers. In Case III, where all new housing in a community is required

by law to have sprinkler systems, builders/developers of new, sprinklered

housing do not face competition within the community from new, non-sprinklered

A-3
housing. They, therefore, are more likely to be able to pass along fully to

the homebuyer the cost of the sprinkler system, other things being equal.

The following net benefits model evaluates the economic efficiency to the

builder/developer of either of these cases:

NBb/d = LCRo + CCRo - TPIg/D + ^^o + OGIq,

where,

NBg/j) = net benefits to the builder/developer from including sprinkler

systems in houses,

LCRq = reduced initial land costs due to higher building density

and smaller land set-asides as allowed by public building

officials,

CCRq = reduced initial construction costs due to lessened code

requirements for fire resistant materials,

TPIg/p = initial total purchase and installation costs of the sprinkler

systems to the builder/developer,

RSq = differential selling price of the sprinklered house as compared

with a counterpart non-sprinklered house, times the number of houses.

For Case I (non-mandatory) , the differential selling price reflecting

the sprinkler only, with all other factors held constant, could be

expected to approximate the value

n

(1 + d)''

derivable from the homebuyer model in section 2.2.

For Case III (mandatory) , the value PI could be expected to set a lower boundary on the differential selling price.

OGIq = other government-provided incentives, such as income tax credits,

grants, or subsidized loans.

A-4
A. 2 Decision Model for the Municipal Government

While public officials do not directly purchase and install residential

sprinkler systems, they can make decisions which critically affect the

investment decisions of those who do. Public officials may weigh the costs to

new and existing communities of meeting increased needs for fire loss

abatement through the use of conventional fire protection strategies, and may

determine that installing sprinkler systems in houses is the least-cost

alternative to the community. They may then influence the investment

decisions of builders/developers regarding sprinklers through legislative

mandates or through the provision of incentives such as those cost reduction

provisions mentioned above, or through both. They may influence homeowner

investment decisions by effectively reducing system costs, through, for

example, waiver of property tax on the capitalized value of the systems,

pass-throughs of municipal cost savings, tax credits, and depreciation

allowances.

Three economic questions at the community decision level are: (1) Is it

economically efficient to the community at large to mandate or encourage the

use of residential fire sprinklers? (2) What level of cost concessions to

builders/developers can be justified on economic grounds to encourage their

installation of sprinkler systems? (3) What will be the likely effects on

local governmental costs?

The life-cycle cost model developed in this section on an exploratory basis is

intended to address the first question and to determine upper boundary

estimates for the second and third questions.

A-5
The municipal decision model below encompasses the total of individual

households in the community, all under average conditions. It takes into

account the cost of firefighter deaths and injuries, fire department costs,

differential housing construction costs, and differential community

infrastructure costs, in addition to the total of uninsured direct and indirect

homeowner fire losses, total insurance costs, and aggregate sprinkler system

costs.

Find the least-cost alternative, LCCp or LCCg:

LCCc = H •?fLVc(f) + DLVc(f) + ILVc(f)+FFLVc(f) + IV^Cf)]* P(F) + IP^s '(BV+CV)}

UPW* + FDCc + FCCc + OCCc

n,d,e

LCCg = H [PLVgCf) + DLVgCf) + ILVgCf) + FFLVg(f + IVgCf)]. P(F)+ IPg.(BV+CV).

UPW* + PI + OP + M + OC + FDCg + FCCg + OCCg,

n,d,e

where.

LCC(, = total life-cycle cost of the conventional approach to

community fire protection,

LCCg = total life-cycle cost of a new approach to community fire

protection which relies primarily on self-protection

through the use of sprinkler systems,

H = the number of houses affected.

^Note that tax effects are excluded from the community model because they are assumed to be transfers that do not affect overall costs. Note also

that resale value is excluded from the community model because the useful

life of the system, rather than the Investor's holding period, is assumed to

be used for the study period.

A6
PLV (f) = the average annual dollar value of uninsured and non-reimbursed

property loss if a fire occurs, where subscript c indicates the

absence of sprinkler systems, and a given level of community

fire protection services as reflected by the values of FDC^,,

FCCj,, and OCC^., and subscript s indicates the presence of

sprinkler systems in combination with a given level of

comnainity fire protection services as reflected by the values

FDCg, FCCg, and OCCs,

DLV (f) = the average annual number of occupant deaths if a fire occurs times an estimated dollar value per death, where subscript c indicates the absence of sprinkler systems, and a given level

of community fire protection services as reflected by the

values of FDC(,, FCC^,, and OCC^,, and subscript s indicates the

presence of sprinkler systems in combination with a given level

of community fire protection services as reflected by the

values of FDCg, FCCg, and OCCg,

ILV (f) = the average annual number of civilian injuries if a fire occurs times an estimated dollar value per injury, where subscript c Indicates the absence of sprinkler systems, and a given level

of community fire protection services as reflected by the

values of FDC^,, FCC^,, and OCC^,, and subscript s indicates the

presence of sprinkler systems in combination with a given level

of comminity fire protection services as reflected by the

values of FDCg, FCCg, and OCCg,

FFLV (f) = the average annual number of firefighter injuries if a fire occurs times an estimated dollar value per injury, where

subscript c indicates the absence of sprinkler systems, and a given level of comnEinity fire protection services as reflected

by the values of FDC^,, FCC^,, and OCC^,, and subscript s Indicates the presence of sprinkler systems in combination with

a given level of community fire protection services as reflected by the values of FDCg, FCCg, and OCCg,

IV (f) = the average annual dollar value of out-of-pocket indirect costs

if a fire occurs, where subscript c indicates the absence of

sprinkler systems, and a given level of community fire

protection services as reflected by the values of FDC^,, FCC^,,

and OCCj., and subscript s indicates the presence of sprinkler

systems in combination with a given level of community fire

protection services as reflected by the values of FDCg, FCCg,

and OCCg,

P (F) = probability of fire in a year

IP = annual insurance premium rate, where subscript ns indicates no sprinkler and s indicates sprinklers installed,

A7
BV = average value of the structure to be insured,

CV = average value of the contents to be insured,

FDC = the life-cycle cost per house of providing, operating and

maintaining a fire station, and subscripts c and s indicate two

levels of protection as measured by average response time,

level c being shorter time than s,

FCC = the average initial cost per house of using fire resistant

materials, where subscripts c and s indicate two levels of fire

resistance, level c being a greater level of resistance than s,

OCC = other costs to the community per house associated with

collectively provided fire protection, such as fire lanes,

where subscripts c and s indicate two levels of protection,

c indicating a greater level of protection than s,^ and

n = the average economic life of residential sprinkler systems

which is assumed to be identical to its average useful life.

PI, OP, M, OC are as defined previously for the homeowner model.

The alternative which minimizes total life-cycle costs will be the

economically efficient approach for the community, other things being equal.

If LCC(, is greater than LCCg , the amount by which the former exceeds the

latter provides a rough estimate of the maximum amount which the community

should be willing to spend to encourage (or require) the switch from

"Alternative c" to "Alternative s".

Note in interpreting the model that it is assumed that the homeowner evaluates

the cost-effectiveness of a personal investment in sprinklers in light of a

fixed level of comnRinity fire-protection service, while the local government

evaluates the decision in light of a variable level of community fire

protection service.

•'^OCC encompasses, in principle, effects associated with variable housing

densities; however, quantification of density benefit-cost effects is very

difficult in practice.

A-{
Hence, in the case of the homeowner, If PLV(f) Is the expected value of

uninsured property loss without a sprinkler system, then Z(s,f) • PLV(f) is the

reduction in that loss attributable to a sprinkler system, where £(s,f) = the

percentage reduction by sprinklers. In the case of the municipal government,

however, the value of fire property loss (PLV) may vary as the values of FDC,

FCC, and OCC are changed.

Note also that the above model is expandable to a more general cost

minimization model covering many alternative combinations of sprinkler use and

collective fire protection, rather than just two alternatives as modeled here.

The direct costs to the community of purchasing, installing, operating, and

maintaining a "saturation level" of sprinkler systems, i.e., H [PI + OP + M +

OC] can be used in a break-even context to determine the aggregate value

of increased benefits and cost reductions that must be achieved to make

it cost effective for the community to provide a given level of fire safety

through the use of sprinklers. That is, at the break-even point,

H . [Pr+OP+M+OC=H .j [PLVc(f ) - PLVgCf ) + DLV^Cf ) - DLVg(f )) + (ILV^Cf

)

- ILVs(f)) + (FFLVc(f) - FFLVs(f)) + IV^Cf) - IVgCf)] • P(F) + [(IP^g " IPg) •

(BV + CV)]| • UPW*n^d,e + i^^^^ " FDCg) + (FCC^ - FCCg) + (OCCc - OCCgA

A9

NBS-IUA IREV. 2-6C) U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO.

NBS/TN-1203

2. Performing Organ. Report No 3. Publication Date

November 1984

4. TITLE AND SUBTITLE

A Benefit-Cost Model of Residential Fire Sprinkler Systems

5. AUTHOR(S)

Rosalie T. Ruegg and Sieglinde K. Fuller

6. PERFORMING ORGANIZATION (If joint or other than N6S. see ;n struct/on s) NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

GAITHERSBURG , MD 20899

7. Contract/Grant No.

8. Type of Report & Period Covered

Final

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State, ZIP)

Fire Safety Technology Division

Center for Fire Research

National Engineering Laboratory

National Bureau of Standards

Gaithersburg, MD 20899

10. SUPPLEMENTARY NOTES

I I Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here)

This paper develops and applies decision models for evaluating the economic

efficiency of providing fire loss mitigation in houses through the use of a new

technology: fast-response sprinkler systems. A model is developed for calculating

present value net benefits as they would accrue to an owner-occupant or an owner

of a rental house who installs a sprinkler system. Costs and benefits of owning a system are estimated for selected hypothetical cases pertaining to a new, singlefamily dwelling in the United States. The estimates are then used to illustrate

the model. Minimum or maximum values that key decision variables must take in order

for sprinkler systems to be cost effective in the selected applications are calculated through break-even analysis. Related models are developed for evaluating

the economic merits of sprinkler systems from the standpoint of developers and

local governments. Implications for the research and building communities are discussed.

12. KEY WORDS (S/x to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

building economics; economic analysis; fire protection; life-cycle costing; net

benefit analysis; residential fire safety; risk-benefit analysis; sprinkler systems.

13. AVAILABILITY

[T] Unlimited

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[^3] Order From National Technical Information Service (NTIS). Springfield, VA. 22161

14. NO. OF

PRINTED PAGES

14Q

15. Price

SCOMM-DC »04J-P(IC

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