ECONOMIC ASSUMPTIONS AND EQUATIONS
APPENDIX 1 ECONOMIC ASSUMPTIONS
AND EQUATIONS
The economic assumptions and equations which define the benefit
cost analysis of seismic rehabilitation projects are summarized in
this chapter.
BenefitCost Model Without the Value of Life
The benefits of a hazard rehabilitation project are the avoided future
damages and losses (i.e., the extent to which the rehabilitation
project is effective in reducing expected future damages and
losses.). The net present value of benefits accounts for the time
value of money, because benefits, are expected to accrue in the
future and dollars received in the future have a present value which
is less than dollars received immediately. The expected net present
value of a seismic rehabilitation project is the sum of the present
value of net benefits expected to accrue each year over the life of
the project, minus the initial cost of the rehabilitation project. The
expected net present value, NPV, is defined as:
NPV= + B2 + + + BT INV
where:
Bt is the expected annual net benefit of the rehabilitation
project for year t;
i is the annual discount rate;
T is the length of the planning horizon (useful life of the
rehabilitation project); and
INV is the initial investment (the cost of the project).
ECONOMIC ASSUMPTIONS AND EQUATIONS
Each year's expected net benefit is discounted to its present value
and then added together to yield the total expected net present
value. The planning horizon, or useful lifetime of the rehabilitation
project, varies depending on the type of project, with 30 to 50 years
being common for building projects. The discount rate corrects
benefits expected in the future to their net present value.
If expected net benefits are constant each year over the life of the
project, the expected net present value equation is simplified to the
constant annual benefits and one discount term representing the
present value for the entire planning horizon. With this
simplification, the expected net present value equation is reduced to:
For completeness, we mention two other factors which could be
included in the expected net present value calculation: the salvage
value of the rehabilitation investment at the end of the planning
horizon and the annual costs to maintain the effectiveness of the
rehabilitation project. However, the present value of the salvage
value of seismic rehabilitation projects is generally quite small,
because of the long planning horizons appropriate for building
projects. Similarly, the annual maintenance costs of typical seismic
projects are generally negligible. Thus, in the present benefitcost
model, neither the salvage value nor the annual maintenance costs
are included.
ECONOMIC ASSUMPTIONS AND EQUATIONS
BenefitCost Model With the Value of Life
The benefitcost model discussed above does not include the value
of life. However, reducing the expected number of deaths and
injuries is often the principal motivation for seismic hazard
rehabilitation projects. The model can be modified to include the
value of expected deaths avoided by retrofitting.
The expected net present value including the value of life is the
expected net present value without the value of life, plus the present
value of expected annual deaths and injuries avoided by seismic
rehabilitation. The expected net present value including the value of
life is thus defined as:
NPV o = NPV + (VDA + VIA) +
where:
NPt0o is the expected net present value including the
value of life;
NPV is the expected net present value excluding the
value of life;
VDA is the annual value of expected deaths avoided;
VIA is the annual value of expected injuries avoided;
i is the annual discount rate; and
T is the planning horizon.
ECONOMIC ASSUMPTIONS AND EQUATIONS
Economic Assumptions for Modeling Benefits
Underlying The benefits of a seismic hazard rehabilitation project are the
Assumptions reduction in damages that would otherwise be expected. Expected
annual benefits are defined as the sum of expected avoided
damages and losses. There are three different types of damages
which are considered: scenario damages, expected annual
damages, and expected annual avoided damages. Definitions of
these terms are:
Scenario Damages:
the expected damages per earthquake event of a given MMI
(or range of effective peak ground acceleration, PGA) at the
building,
Expected Annual Damages:
the product of scenario damages and the expected annual
probability of an earthquake of a given MMI or PGA, and
Expected Annual Avoided Damages:
the product of expected annual damages and the
effectiveness of the rehabilitation measure in reducing
expected damages.
A schematic example illustrating these damage terms is given
below:
Table I
Earthquake Scenario Annual Expected Effectiveness Expected
(MMI) Damages Earthquake Annual of Avoided
Probability Damages Rehabilitation Damages
Measure
VI $20,000 10% $2,000. 100% $2,000.
VH $25,000 5% $1,250. 80% $1,000.
VIII $35,000 2% $700. 50% $350.
IX $50,000 1% $500. 25% $125.
Total: $4,450. Total: $3,475.
ECONOMIC ASSUMPTIONS AND EQUATIONS
In this example, the scenario damages indicate the expected
damages each time an earthquake of the given Modified Mercalli
Intensity (MMI) occurs at the site of the building. Scenario damages
may also be characterized in ranges of effective peak ground
acceleration instead of or in addition to characterization by MML
Scenario damages do not depend on how frequently such
earthquakes are expected to occur. The annual earthquake
probabilities indicate the degree of seismic risk at the specific site
under consideration The expected annual damages are the product
of scenario damages and annual earthquake probability. Expected
annual damages ($4,450 in this, example) are the best estimate of
the average damages per year expected at this site; such estimates
do not indicate that these damages will occur every year. Expected
annual damages are those without undertaking the rehabilitation
measure. The effectiveness of the rehabilitation measure is an
estimate of how much expected damages will be reduced by the
rehabilitation measure under consideration. The expected avoided
damages (i.e., the benefits) are the product of expected annual
damages and the effectiveness of the rehabilitation measure. The
expected avoided damages ($3,475 in this example) are thus the
expected benefits of undertaking the rehabilitation measure.
ECONOMIC ASSUMPTIONS AND EQUATIONS
Detailed Economic Assumptions and Equations
Without the Value of Life
Scenario Scenario damages (SCDEQ) are the sum of building damages (BD),
Damages contents damages (CD), relocation costs (REL), rental income
losses (RENT), and the value of lost services (VLS) for earthquakes
of each MMI or PGA range:
SCD EQ = BD EQ + CD EQ + REL EQ + RENT EQ + VLS EQ
where:
BDEQ are scenario building damages;
CDEQ are scenario contents damages;
RELEQ are scenario relocation costs;
RENTEQ are scenario rental income losses; and
VLSEQ is the scenario value of lost government
services.
Building Building damages (BDEQ) are estimated as the product of floor area
Damages of the buildings (FA), replacement value of the building per square
foot (RV), and expected damage as a percentage of replacement
value for earthquakes of each MMI or PGA range:
BD EQ FA RV EDEQ
where:
FA is the floor area of the building (in square feet);
RV is the replacement value of the building (per
square foot); and
EDEQ is expected damage percentage for
earthquakes of each MMI or PGA range.
Contents
Damages
Relocation
Expenses
Rental Income
Losses
ECONOMIC ASSUMPTIONS AND EQUATIONS
Contents damages (CDEQ) are estimated as the product of floor area
of the buildings (FA), replacement value of the building contents per
square foot (RVC), and expected contents damage percentage
(ECDEQ) for earthquakes of each MMI or PGA range:
CD EQ = FA RVC ECD EQ
where:
FA is the floor area of the building (in square feet);
RVC is the replacement value of the building contents
(per square foot); and
ECDEQ is expected damage percentage for contents, for
earthquakes of each MMI or PGA range.
Relocation expenses (RELEQ) are defined as the product of
relocation costs per month (REL) and the expected period for which
the residence will be unusable (LOFEQ).
REL EQ = REL LOF EQ
where:
REL is the relocation cost per month; and
LOFQ is the estimated number of months of loss of
function for earthquakes of each MMI or PGA
range.
Rental income losses (RENTEQ) are included fall or a portion of the
building are rented to private tenants. Interor intraagency rents
within the Federal Government are not counted because such
payments are generally transfers and loss of such payments does
not represent a true economic loss. Other private sector economic
losses, (such as lost wages) are not considered because they are
assumed to be generally negligible for Federal Government
buildings. Rental income losses are the product of rental rate per
month per square foot of gross leasable area (RR), gross leasable
floor area (GLA), and the expected number of months that the rental
income will be lost (LOFEQ).
RENTEQ = RR GLA LFEQ
ECONOMIC ASSUMPTIONS AND EQUATIONS
Government
Services Lost
where:
RR is the rental rate per month per square foot;
GLA is gross leasable floor area in square feet; and
LOFEQ is the estimated number of months of loss of
function for earthquakes of each MMI or PGA
range.
For public sector buildings, the value of government services lost
(VLSEQ) when the building becomes unusable during an earthquake
must be included. Government services are valued using the Quasi
Willingness to Pay (QWTP) model. QWTP is a simple methodology
that assumes that government services are worth what we pay to
provide the services. A detailed review of the assumptions in the
QWTP model is given as Chapter 2 of Volume 2.
VLSEQ is the sum of agency wages (WAGE) plus benefits (BENE)
and support budget (SUPP) per day, multiplied by the number of
days of loss of agency function (LOAFEQ). The period of lost
services depends on the agency's ability to find alternative quarters
and to establish normal functions. This period may vary depending
on the structure, size and function of the agency and the availability
of suitable quarters after the earthquake. Note that the period of
loss of agency function may be much shorter than the period of
relocation necessary due to seismic damage, because agencies will
resume their functions in temporary quarters, where:
VLSEQ = (WAGE + BEN + SUPP) LOAF EQ
where:
VLSEQ is the value of lost agency services for an
earthquake of a given MMI or PGA range;
WAGE is the total wages paid to the resident work force
per day;
BENE is the total benefits paid to the resident work
force per day;
SUPP is the support expenditures per day; and
LOAFEQ is the period of loss of agency function for an
earthquake of a given MMI or PGA range.
A8
ECONOMIC ASSUMPTIONS AND EQUATIONS
Expected
Annual
Damages
Expected
Avoided
Damages
Expected
Annual
Benefits
Expected annual damages (AD"'),are the product of scenario
damages (SCDEl) and the expected annual probability of an
earthquake of a given MMI or range of PGA (EAEEQ):
ADEQ = SCD EQ EAEEQ
where:
SCDEQ are scenario damages (as defined previously);
and
EAEEQ is the expected annual number of earthquakes
of a given MMI or PGA range.
Expected avoided damages (AVDEQ) are the product of scenario
damages (SCDEQ), the expected annual probability of an earthquake
(EAEEl), and the effectiveness of the rehabilitation measure
(EFFEQ):
AVDEQ = SCDEl EAEEQ EFFEQ
where:
SCDEQ are scenario damages for each damaging
earthquake of a given MMI or PGA range;
EAEEQ is the expected annual probability of an
earthquake of a given MMI or PGA range; and
EFFEQ is the effectiveness of the rehabilitation measure
in reducing expected damages for earthquakes
of a given MM[ or PGA range.
The expected annual benefits (AB) of a seismic hazard rehabilitation
project are the sum of expected avoided damages (AVD) summed
over the full range of damaging earthquakes considered (e.g., MMI
VI to MMI XII or ranges of effective peak ground accelerations,
PGA).
max
AB = E AVD EQ
EQ=min
where:
EQ is the damaging earthquake considered (MMI or
PGA);
ECONOMIC ASSUMPTIONS AND EQUATIONS
min is the minimum damaging earthquake
considered;
max is the maximum earthquake considered; and
AVDEQ are the expected annual avoided damages from
earthquakes of each MMI or PGA bin being
considered.
Detailed Economic Assumptions and Equations:
With the Value of Life
The benefitcost model discussed above does not include the value
of life. However, reducing the expected number of deaths and
injuries is often the principal motivation for seismic hazard
rehabilitation projects. The model can be modified to include the
value of expected deaths avoided by retrofitting to lifesafety
standards.
Value of Deaths The annual value of avoided earthquake death loss is assumed to
Avoided be the product of the area of the building in square feet, times the
average occupancy per square foot, times the difference in expected
death rates between unrehabilitated and rehabilitated buildings,
times the dollar value of one human life. The annual value of
reducing the earthquake death loss due to rehabilitation is thus
defined as:
max
VDA = E EAE EQ (FA OCP (DR EQ DRR EQ)) VOL
EQ=min
where:
VDA is the annual value of expected deaths avoided
by rehabilitating buildings to lifesafety
standards;
EAEEQ is the expected annual probability of an
earthquake of given MMI or PGA range;
FA is the floor area of the building in square feet;
OCP is the average occupancy rate per square foot;
DREQ is the expected death rate;
Value of Injuries
Avoided
ECONOMIC ASSUMPTIONS AND EQUATIONS
DRREQ is the expected death rate after rehabilitation;
and
VOL is the dollar value of one statistical human life.
Similarly, the value of injuries avoided, VIA, is, estimated:
max
where:
IREQ is the expected injury rate in the existing
building;
IRREQ is the expected injury rate after rehabilitation;
and
Vol is the dollar value of one statistical injury.
In the benefitcost model, injuries are considered in two categories:
minor injures, which do not require hospitalization and major injuries,
which do require hospitalization.
Benefitcost results are always presented both with and without
including the value of life so that the benefits of avoiding physical
damages and the benefits of avoiding deaths and injuries can be
analyzed separately.
BenefitCost
Analysis
CostBenefit
Analysis
Cost
Effectiveness
Analysis
ECONOMIC ASSUMPTIONS AND EQUATIONS
Definitions of Economic Terms
Benefitcost analysis provides estimates of the "benefits" and "costs"
of a proposed project or change. The term "benefitcost analysis" is
used to denote economic analyses that apply either the maximum
present value criterion or the benefitcost ratio criterion to evaluate
prospective actions. Both costs and benefits are discounted to their
net present value. The maximum present value criterion subtracts
costs from benefits to determine if benefits exceed costs.
Benefit/cost ratios provide an alternative evaluation: prospective
actions in which benefits exceed costs have benefitcost ratios
above one. The logic of benefitcost analysis requires that benefit
cost ratios, and/or the present value criterion, be compared across
competing alternatives.
Costbenefit analysis has identical economic assumptions to benefit
cost analysis and differs only in the nomenclature used to describe
the analysis. Subtle differences in meaning between benefitcost
and costbenefit analysis have been discussed by Hurter et al.
(1982). These authors prefer the term benefitcost for three
reasons:
1) determining benefits is often the most difficult aspect of the
analysis; if costs are placed first, the emphasis is wrong;
2) when ratios are used to compare projects, the ratio used is
benefitcost, not cost/benefit; and
3) placing the word "costs" first seems to suggest a negative
attitude toward projects. It should be noted, however, that
economic concepts, particularly as reflected in benefitcost
analysis, are completely neutral with respect to the
undertaking of projects.
Costeffectiveness analysis identifies the leastcost way to achieve a
stated objective; it is strictly a comparison among means to a given
end (Andrews, 1982). Thus, cost effectiveness is the ability to
achieve a given benefit at a minimum cost. In cost effectiveness
analysis. the merits of the objective itself are not evaluated in
economic terms. This approach is typically used to select methods
of achieving specific environmental standards.
The Stafford Act uses costeffectiveness when it means that benefits
exceed costs in §404, Hazard Mitigation, and §406, Public
Assistance.
Economic
Efficiency
Economic
impact
Assessment
Informal
BenefitCost
Analysis
ECONOMIC ASSUMPTIONS AND EQUATIONS
Economic efficiency is attained when the economy is functioning in a
way that maximizes the value of society's consumption over time
(Ward and Deren, 1991). Economic efficiency may also be viewed
as the contribution to overall social welfare (Leman, 1989). It is
generally accepted that a benefitcost ratio above one indicates an
improvement in economic efficiency. Benefitcost analysis however
does not indicate whether the project is the "most efficient"
allocation of scarce resources for two reasons. First, benefitcost
analysis is an average rather than a marginal concept. The ratio
indicates the relationship between benefits and costs for a given
project size. Economic efficiency, however, requires that a project
be sized where marginal benefits equal marginal costs, which
maximizes the total net benefits. Second, the typical project benefit
cost analysis does not survey the complete array of spending
alternatives for all public projects/programs unrelated to the project
under analysis. Economic efficiency under a budget constraint
would require that the marginal benefits for all public spending
alternatives be equal.
Economic impact assessment is both simpler and broader than
either benefitcost analysis or costeffectiveness analysis in that it
does not necessarily require aggregation or even categorization of
effects as costs or benefits. It requires only the projection of
economic effects of proposed actions and the listing of these for
consideration. Impact assessment is broader than benefitcost or
costeffectiveness analysis, because it includes identification of all
economic impacts: the changes in total (direct, indirect and
induced) regional employment and income created by the proposed
project. The inclusion of indirect and induced regional economic
benefits and costs in the formal benefitcost analysis is not generally
accepted by the economics profession. Many economists maintain
that such indirect and induced economic impacts represent a
change in the distribution of economic activity and should not be
confused with true gains in economic efficiency.
Informal benefitcost analysis embraces an indefinite range of
procedures for the general identification and balancing of desirable
and undesirable effects of proposed actions on society. Thus,
informal benefitcost analysis simply approximates pure common
sense, and it should not be compared with formal economic
analyses of prospective projects.
ECONOMIC ASSUMPTIONS AND EQUATIONS
RiskBenefit Risk benefit analysis compares the economic benefits of a proposed
Analysis project with the environmental and/or healthsafety risks that are
also created by the project. Ideally, the environmental and/or
healthsafety risks should be quantified in economic terms which in
many cases is almost, if not impossible.
BENEFITCOST MODEL EXAMPLE
APPENDIX 2: BENEFITCOST MODEL EXAMPLE
This appendix consists of a full printout of an example benefitcost
analysis for the Veterans' Administration Medical Center, Memphis,
Benefit/Cost Analysis of the Seismic Rehabilitation federal Buildings Version 1.0, August 4, 1994
Benefit Cost Analysis of the Seismic Rehabilitation of Federal Buildings Version 1.0, August 4, 1994
BenefitCost Analysis of the
Seismic Rehabilitation of Federal Buildings
Version 1.0
August4, 1994
Building Name: Veterans' Administration Medical Center
Address: 1030 Jefferson Ave.
City, State, Zip: Memphis, TN 38104
Analyst: Goettel & Horner Inc.
Rehabilitation Project: Add shear walls and moment frame
Run Identification: Final
Prime Contractor: Technical Assistance:
VSP Associates, Inc. Goettel & Horner Inc.
455 University Avenue, Suite 340 2725 Donner Way
Sacramento, CA 95825 Sacramento, CA 95818
Telephone: (916) 6489112 Telephone: (916) 4514160
Benefit Cost Analysis of the Seismic Rehabilitation of Federal ullkfinp3 Version 1.0, August4, 1994
I I
Building Name:
Address:
City, State, Zip:
Analyst:
Run ID:
Managing Agency
Contact Person:
Address:
City, State, Zip:
Telephone:
Building type: enter CAPITAL letter code in the green box.
Click button if building type is changed.
FEMA Letter
178 Code Common Building Types
W/ A Wood Light Frame
W2 B Wood (commercial or industrial)
Si C Steel Moment Frame
S2 D Steel Braced Frame
S3 E Steel Light Frame
S4 F Steel Frame with Concrete Shear Walls
S5 G Steel Frame with URM Infill
C H Concrete Moment Frame
C2 I Concrete Frame with Concrete Shear Wall
C3 J Concrete Frame with URM Infill
PCI K Precast Concrete Tiltup w/ Flexible Diaphragm
PC2 L Precast Concrete Frame w/ Concrete Shear Walls
none M Precast Frame w/o Shear Walls
RM1 N Reinforced Masonry w/ Flexible Diaphragm
RM2 0 Reinforced Masonry w/ Precast Concrete Diaphragm
URM P Unreinforced Masonry Bearing Wall
none 0 Mobile Homes
OTHER (Please specify)
______7R
Total Floor Area (square feet): Calculated
Building Replacement Value per square foot ZI
Total Building Replacement Value ZZLZ 86CAO 040
Number of Stories Above Grade:
Date of Construction
Historic Building Controls?
Anaors1: Goettel &Homer Inc
Benefd[Cost Analysis of the Seismic Rehabilitation of Federal Buildings Version 1.0, August 41 994
Building Replacement Value: x x sq ft.
1,000 Total
Demolition Threshold Damage Percentage:
DEFAULT ESTIMATES FOR EXISTING BUILDING:
MMI MVI VII I VII I IX X Xi XII I
Modified MDF:
DESCRIPTION & VALUE OF BUILDING CONTENTS: $ sq. ft. Total ($1,000)
MEAN DAMAGE FUNCTION FOR CONTENTS:
MMI I VI I Vii I VII I iY I xl I Y I ill I
PGA (percent of g)
Default (%damage)
User Entered (%damage)
Default Estimate (days)
User Entered (days)
I
Relocation costs ($/sflmo) Rental Cost ($/sffmo) Total Relocation Costs ($/sq.ft.imo)
a_ A *_~~~~~~~~~~9& mm
II II
Default Minor Injury Rate
User Entered Estimate:
I I
Default Major Injury Rate
User Entered Estimate:
I
I
I
Default Death Rate
User Entered Estimate:
I
.1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Analyst Goene & Homer Inc.
Analyst: UOOOCI &turner ICC.
A18
OCCUPANCY:
Average Number of Occupants:
Days per Week:
Hours per Day
Average Occupancy (24 hours, 7 days per week):
Complete EITHER Section or 2 (they are equivalent):
1a. Total annual operating budget of government functions in this building.
(DO NOT count pass through funds such as social security payments.)
lb. Does this include rent? (1yes, 2=no)
2a. Number of fulltimeequivalent persons working in the building:
2b. Average annual salaryplusbenefits paid to the above.
2c. Average annual utilities, and other nonwage operating expenses:
Rental Values For Support of Agency Functions
3a. Amount of floor space occupied by government tenants (sq. ft.): 5
3b. Proxy annual rent estimate (if la. does not include rent): L" 885 $ 3
Daily cost of providing services from this building: 02,0
PostEarthquake Continuity Premium
Based on the nature of the services in this building, how much extra cost per day would the tenant agencies be willing to spend to maintain agency functions after an earthquake: 1,000
TOTAL VALUE OF LOST SERVICES PER DAY: ($ 802J1
Functional downtime is the number of days to restore government service after an earthquake, either
in the existing building or in temporary quarters. Functional downtime is different from relocation time
and may be much shorter
Building Damage (%)
Default Downtime (Days)
Space Rented to Private Entities Average Rental Rate Total Private Rent
Analyst Goetel & Homer Inc.
Benefit Cost Analysis of the Seismic Rehabilitation of Federal Buildings Version 1.0, August 4 1994
Building Type:
Project Description:
Objective of Rehabilitation: Io
Direct Construction Costs
Base Year of Costs
A&E Fees, Testing, Permits
Project Management
Other Costs
Duration of Occupant Relocation (months)
Lost of Occupant Relocation per sq. ft. per month
Cost of Relocation of occupants
Total Seismic Rehabilitation Costs 1
BUILDING MEAN DAMAGE FUNCTIONS:
MMI VI I  VI I VIII IX X Xl XII
PGA (percent of g) 48  816 1632 3255 5580 I 80100 I >100
EXSITING BUILDING: _A mm
REHABILITATION EFFECTIVENESS: (percentage of damage avoided)
00 1 V1,14, 411 V31M108IMP,11 1 I 11110K0ii 4i
BUILDING
CONTENTS Default:
User Entered Estimate:
Estimated
Before Rehab
Estimated Before Rehab
Estimated After Rehab
User Entered Estimate:
Major
Estimated Before Rehab
Estimated After Rehab
User Entered Estimate:
DEATHS I
Estimated Before Rehab
Estimated After Rehab
User Entered Estimate:
To estimate the expected annual number of earthquakes at the site under consideration:
a) specify the soil type (SO, Si, S2, S3, or S4) in the green box below
b) choose ONE of the seismic risk assessment methods below:
SEISMIC RISK ASSESSEMENT METHODS:
I) DEFAULT METHOD: Enter two .3 second spectral acceleration values in the green boxes below.
These values may be obtained from the Seismic Risk Table for about 300 cities which is in the Users Guide,
or may be read from the 1991 NEHRP maps.
spectral Acceleration Contours Effective Peak Acceleration Click button
Adjustment Factor if seismic data
11% o a 11 I Time Period
2) SITESPECIFIC GEOTECHNICAL METHOD. Enter numbers from a sitespecific geotechnical seismic risk
assessment, if available, in the blue line below
SEISMIC RISK TABLE
PGA (percent of g)
Default Estimate
Geotechnical Estimate:
Benefit/Cost Analysis of the Seismic Rehabilitation of Federal Buildings Version 1.0,August 4, 1994
Facility Class:
Project Description I S~5
SCENARIO DAMAGES ($ per earthquake event):
PGA (percent 2_5599 I 80100 I >100fn
Building Dam
Contents Dan
Relocation
Rental Income
Value of Lost
Total Losses
EXPECTED ANNU
Building Damages
Contents Damages
Relocation Expenses
Rental Income Losses
Value of Lost Service
Total Losses
RESIDUAL A
Building Damage
Contents Damage
Relocation Exp
Rental Income I
Value of Lost S
total Losses
Analyst: Goentel & Homer Inc.
0MI
DGA (percent of g)
VI
48
VII
816
VII
1632

I
IX
3255
X
5580
Xi
80100 j Xl
>100
%Mean Damage Function ; 1 7 100 0 100 100
SCENARIO INJURIES & DEATH
Number of Minor Injuries
Number of Serious Injuries
Number of Deaths
EXPECTED INJURIES & DEA1
Number of Minor Injuries
Number of Serious Injuries
Number of Deaths
SCENARIO INJURIES & DEATHS WITH REHABILITATION:
Number of Minor Injuries
Number of Serious Injuries 3 I8
54SE01 1 `48E
143E
Number of Deaths W 8_2600
Number of Minor Injuries
Number of Serious Injuries
Number of Deaths
Number of Minor Injuries
Number of Serious Injuries
Number of Deaths
Analysis o the Seismic Rehabilitation of Federal Buildings Version 1.0,August 4, 1994
Bene8UtCost
Facility Class:
Project Description: E
k. ECONOMIC PARAMETERS:
discount Rate: percent
Planning Period: ears
Present Value Coefficient:
3. SUMMARY OF DAMAGES AND ECONOMIC LOSSES:
II I I Present value or
3uilding Damages
Contents Damages
Relocation Expenses
Rental Income Losses
Value of Lost Services
Total Damages and Losses
PRESENT VALUE OF TOTAL DAMAGES AND ECONOMIC LOSSES AVOIDED: 109~'2199MEc$Xy
L71
TOTAL COSTS OF THE SEISMIC REHABILITATION PROJECT: TF4SWl!
TOTAL BENEFITS MINUS TOTAL COSTS WITHOUT THE
VALUE OF AVOIDED INJURIES & DEATHS: (129. 7O2,1
BENEFIT COST RATIO WITHOUT THE VALUE OF AVOIDED INJURIES & DEATHS: LIS "I
C.VALUE OF INJURIES AND DEATHS:
Value of Avoiding a Minor Injury:
Value of Avoiding a Serious Injury:
Statistical Value of Life:
I Annual Expected I Annual Avoided I Annual Residual I Present Value of I
Minor Injuries
Serious Injuries
Deaths
PRESENT VALUE OF TOTAL DAMAGES, ECONOMIC LOSSES, DEATHS AND
INJURIES AVOIDED:
TOTAL BENEFITS MINUS TOTAL COSTS WITH THE
VALUE OF AVOIDED INJURIES & DEATHS:
BENEFIT COST RATIO WITH THE VALUE OF AVOIDED INJURIES & DEATHS: 1' 2.42
Analyst: Goettel & Homer Inc.
A24
08/04194.
12:56:50.
Benefit Cost Analysis of the Seismic Rehabilitation of Federal Buildings Version
SUMMARY Run Identification Final
Veterans' Administration Medical 1030 Jefferson Ave. Memphis, TN 38104
Rehab Project Description: Add shear walls and moment frame
Facility, Class: Concrete Frame with Concrete Shear Wall
Data used for this analysis:
Building Replacement Value per square foot $115.00
Total Floor Area (square feet): 805,700
Total Building Replacement Value $92,655,500
Demolition Threshold Damage Percentage: 50%
Total Contents Value $96,000,000
Cost of Providing Services per day $302,701
Continuity Premium $1,500,000
Value of lost services per day $1,802,701
Total Private Monthly Rental Revenue $0
Total Relocation Costs ($/sq. ft month)$2.50
Total Seismic Rehabilitation Costs $40,457,800
Average Day Occupancy 3,000,
Average Night Occupancy 2,900
Soil Type S2
Data used in this analysis that varies by MMI:
mmI VI VII VIII IX X Xl xi
PGA (g) 48 816 1632 3255 5580 80100 >100
Mean Damage Function (%) 1 25 75 100 100 100 100
Modified MDF (%) 1 25 100 100 100 100 100
Minor Injury Rate 000 3.00E02 .400E+00 1.00DE+02 S.OOE+01 5.00OE401 5.aOOE+01 E.OOOE+01
Major Injury Ratel10 00 4.0oaE03 1.120E+00 3.000E+02 2.500E+02 2.00OE402 1.500E+02 1.500E+02
Death Rate ll 000 1.OOOE03 2.80OE01 5.000E+01 5.OOOE+02 7.000E+02 8.000E402 8.OOOE+02
Content MDF (%) 1 25 75 100 100 100 100
Functional Downtime (days) 1 25 30 30 30 30 30
Days of Relocation Necessary, 0 150 365 365 365 365 365
Building Rehab Effectiveness () 1 o 83 94 88 81 73 67
Contents. Rehab Effectiveness () 100 83 94 88 81 73 67
Rehab Minor Injury Ratel1000 3.000E03 8.400E01 1.OO0E+01 5OOOE+OO S.OOOE*OO S.OOOE+O 5.000E+00
Rehab Major Injury RatelO000 4.000E05 1.120E02 3.000E+00 2.50OE+0O 2.000E+00 1.SOE+OO 1 .5005+00
Rehab Death Ratel1O O 1.0OOE06 2.800ED4 S.OOOE02 5.000E01 7.OOE01 8.OOOE01 8.00OE01
Annual Number of Earthquakes 5.1 O8E02 1.34SE02 3.541E03 8.196E04 2.293E04 7.675E05 1.412E04
SUMMARY OF DAMAGES AND ECONOMIC LOSSES: Without Value With Value
of Life of Life
PRESENT VALUE OF TOTAL DAMAGES AND ECONOMIC LOSSES AVOIDED: $33,385,616 $97,892,529
TOTAL BENEFITS MINUS TOTAL COSTS: ($7,072,184) $57,434,729
Benefit cost ratio: jn0.83 2.42
A25
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