RESULTS AND METHODOLOGY OF THE LIFE-CYCLE COST ANALYSIS FOR RESIDENTIAL WATER HEATER EFFICIENCY STANDARDS

Submitted to the U.S. Department ofEnergy Office ofCodes and Standards (OCS) November 3, 1998TABLE OF CONTENTS List ofAcronyms ................................................... ... -viiRequest for Stakeholder Comments .............................................. -1- 1 Purpose ofLife-Cycle Cost Analysis ...................................... . -1- 2 Connection to Remainder ofWater Heater Standards Analysis .................. -1- 2.1 From Engineering Analysis ................................ -2- 2.1.1 Order and Combinations ofDesign Options .................... -2- 2.1.2 Estimates ofFactory Costs ofBaseline Models and Design Options .. -2- 2.1.3 Estimates ofFactory Cost ofAll Standard Size Baseline Models and Design Options ..................................... ...... -2- 2.1.4 Energy Parameters ofBaseline Models and Design Options ......... -2- 2.2 LBNL Water Heater Cost Database ............................. -2- 2.2.1 Prices ofBaseline Models ................................... -3- 2.2.2 Installation Costs .......................................... -3- 2.3 Input to Selection ofTrial Standard Levels ...................... -3- 2.4 Output toNational Energy SavingsForecast .... .................. -3- 3 Summary ofResults .......................... .......................... -3- 4 Methodology and Definitions ............ .......................... -5- 4.1 Uncertainty and Variability ............................................ .. -5- 4.1.1 Uncertainty .............. ................................. -6- 4.1.2 Variability ............................................... -6- 4.1.3 Approaches .................................. ............ -6- 5 Details ofLCC Uncertainty Analysis for Water Heaters ........................ -8- 5.1 Overview ...................................................... -8- 5.1.1 Separate Analysis for Each Fuel (Product Class) ................. -9- 5.1.2 Combinations ofDesign Options from Engineering Analysis ........ -9- 5.1.3 Five Major Modules ....................................... -10- 5.1.4 Flowchart ............................................... -10- 5.1.5 Description ofOutputs ..................................... -10- 5.2 Life-Cycle Cost Module .......................................... -12- 5.2.1 Introduction ............................................. -12- 5.2.2 Equations and General Descriptions forLCC andPayback ........ -12- 5.2.3 General Description ofSources ofData ....................... -16- 5.2.4 Life-Cycle Cost and Payback Results ......................... -17-
-ii5.3 Equipment Cost Module
............... ....................... -25- 5.3.1 Introduction to Equipment Cost ........................... ... -25- 5.3.2 Equation forEquipment Cost ................................ -25- 5.3.3 General Description ofKey Variables ......................... -26- 5.3.4 General Description ofSources ofData ....................... -27- Introduction
............................................. -27- Manufacturing Cost ....................................... -28- Retail Price ................ .............................. -29- Installation Cost ........................................ -31- Manufacturer-to-Retail Markup .............................. -33- Analytic Baseline ......................................... -33- Design Options ........................................... -34- Markup for Design Options ......... ........................ -45- 5.4 Operating Cost Module ......................................... -50- 5.4.1 Introduction to Operating Cost Module. ....................... -50- 5.4.2 Equations for Operating CostModule ......................... -55- 5.4.3 General Description ofKey Variables ......................... -57- 5.4.4 General Description ofData Sources and Calculations in Spreadsheets

.. . . . . .. .. . . .. . . .. .. .. . .. .. . .. .. . .. .. . . . .. . .. . . . .. . . .. . -59
- 5.4.5 Operating CostResults .................................... -61- 5.5 Energy Analysis Module ........................................ -65- 5.5.1 Introduction to Energy Use ................................. -65- 5.5.2 Equations forEnergy Use .................................. -65- 5.5.3 General Description ofKey Variables ......................... -66- 5.5.4 General Description ofSources ofData ....................... -67- Introduction ............................................. -67- Determining RE, UA, and Pon .............................. -67- Other Standard-Size Water Heaters ........................... -68- Determination ofthe Uncertainty Ranges for EF, RE, UA, and Pon .. -70- 5.5.5 Energy Analysis Results ................................... -76- 5.6 Hot Water Draw Module ......................................... -81- 5.6.1 Introduction to Hot Water Use ............................... -81- 5.6.2 Equation forHot Water Use ................................ -81- 5.6.5 Results ofHot Water Use Calculations ........................ -84- R

eferences ................................................................ -86-

-'ii### TABLES Table 5.1.1 Water Heater Standard Sizes ..................................... -9- Table 5.2.1 Water Heaters and Lifetime by Fuel Type ............................ -15- Table 5.2.2 Life-Cycle Cost and Payback for Electric Water Heaters ................ -17- Table 5.2.3 Life-Cycle Cost and Payback for Gas-Fired Water Heaters .............. -20- Table 5.3.1 Typical Existing Baseline Water Heaters
- Variable Cost Data ............ -29- Table 5.3.2 Other Standard-Size Existing Baseline Water Heaters -Variable Cost Data .. -29- Table 5.3.3 Electric Water Heaters
- Markup ................................... -33- Table 5.3.4 Gas-fired Water Heaters
- Markup .................................. -33- Table 5.3.5 Insulation Components Cost ...................................... -34- Table 5.3.6 Design Option Combinations
- Electric Water Heaters ................. -34- Table 5.3.7 Design Option Combinations
- Gas-fired Water Heaters ................ -35- Table 5.3.8 Electric Water Heaters
- Incremental Manufacturing Costs for Separate Design Options and Standard Sizes ................................. -36- Table 5.3.9 Gas-Fired Water Heaters
- Incremental Manufacturing Costs for Separate Design Options and Standard Sizes ................................ . -37- Table 5.3.10 Incremental Costs for Electric Water Heaters (50-gal) .................. -38- Table 5.3.11 Incremental Costs for Gas-fired Water Heaters (40-gal) ................. -40- Table 5.3.12 Electric Water Heater (50-gal)
- Variable Cost Data .................... -42- Table 5.3.13 Gas-fired Water Heater (40-gal)
- Variable CostData .................. -43- Table 5.3.14 Electric Water Heaters (50-gal)
- Fixed Cost Data ..................... -44- Table 5.3.15 Gas-fired Water Heaters (40-gal)
- Fixed Cost Data ................... -44- Table 5.3.16 All Standard Sizes Variable Manufacturing Cost
- Electric Water Heater ... -45- Table 5.3.17 All Standard Sizes Variable Manufacturing Cost
- Gas-fired Water Heater .. -45- Table 5.3.18 Equipment Costs for Electric Water Heaters .......................... -46- Table 5.3.19 Equipment Costs for Gas-fired Water Heaters ........................ -48- Table 5.4.1 Operating Costs for Electric Water Heaters ........................... -61- Table 5.4.2 Operating Costs for Gas-Fired Water Heaters ......................... -63- Table 5.5.1 Water Heater Design Characteristic Values
........................... -68- Table 5.5.2 Electric WaterHeater Modeling Parameter Variations .................. -69- Table 5.5.3 Gas-fired Water Heater Modeling Parameter Variations ................. -70- Table 5.5.4 Energy Efficiency Characteristics
- Electric Water Heaters (50-gal) ........ -71- Table 5.5.5 Energy Efficiency Characteristics
- Gas-fired Water Heaters (40-gal) ...... -71- Table 5.5.6 Water Heater Location Percentages ............................... -76- Table 5.5.7 Energy Consumption forElectric Water Heaters ....................... -77- Table 5.5.8 Energy Consumption for Gas-Fired Water Heaters ..................... -79- Table 5.6.1 Water Heater Volumes Selected for LCC Analysis ................... -84-

-ivFIGURES Figure 5.1.1 Flowchart ofLCC Analysis Spreadsheet
......... .................... -11- Figure 5.2.1 Distribution ofConsumer Discount Rates ............................ -14- Figure 5.2.2 Difference in Life-Cycle Costs by Design Option for Electric Water Heaters -18- Figure 5.2.3 Payback Period by Design Option for Electric Water Heaters ............ -19- Figure 5.2.4 Difference in Life-Cycle Costby Design Option for Gas-Fired Water Heaters -21- Figure 5.2.5 Payback Period byDesign Option for Gas-Fired Water Heaters ........... -22- Figure 5.2.6 Sensitivity Analysis forDifference in Life-Cycle Cost of2.5" Jacket Insulation on Electric Water Heater ................................. -23- Figure 5.2.7 Sensitivity Analysis for Difference in Life-Cycle Cost of2" Jacket Insulation on Gas-fired Water Heater .............................. . -24- Figure 5.3.1 Electric Water Heaters Sample Sizes ................................ -30- Figure 5.3.2 Electric Water Heaters
- Shipments vs Sample Sizes ................... -30- Figure 5.3.3 Gas-fired Water Heaters
- Sample Sizes ............................. -30- Figure 5.3.4 Gas-fired Water Heaters
- Shipments vs Sample Sizes .................. -30- Figure 5.3.5 Retail Prices
- Electric Water Heaters ............................... -31- Figure 5.3.6 Retail Prices
- Gas-fired Water Heaters .............................. -31- Figure 5.3.7 Installation Cost Sample Size
- Electric Water Heaters .................. -32- Figure 5.3.8 Installation Cost Sample Size
- Gas-fired Water Heaters ................ -32- Figure 5.3.9 Installation Cost Ranges
- Electric Water Heaters ...................... -32- Figure 5.3.10 Installation Cost Ranges
- Gas-fired Water Heaters .................... -32- Figure 5.3.11 Distribution ofIncremental Manufacturing Cost for Separate Design Options for Electric Water Heaters ................................. -39- Figure 5.3.12 Distribution ofIncremental Manufacturing Costs for Separate Design Options for Gas-Fired Water Heaters ............................... -41- Figure 5.3.13 Difference in Total Installed Cost by Design Option forElectric Water Heaters ....................................................... -47- Figure 5.3.14 Difference in Total Installed Costs by Design Option for Gas-fired Water Heaters ........................................ -49- Figure 5.4.1 Electricity Price Scenarios ........................................ -51- Figure 5.4.2 Gas Price Scenarios ............................................. -51- Figure 5.4.3 LPG Price Scenarios ............................................ -52- Figure 5.4.4 Oil Price Scenarios .............................................. -52- Figure 5.4.5 Difference in Operating Costs by Design Options forElectric Water Heaters ................................................ -62- Figure 5.4.6 Difference in Operating Costs by Design Options for Gas-Fired Water Heaters ................................................ -64- Figure 5.5.1 Variations ofEF for Electric Water Heaters .......................... -72- Figure 5.5.2 Variations ofEF for Gas-fired Water Heaters ......................... -72- Figure 5.5.3 Map ofClimate Zones ...... ..... ...................... ..... -73- Figure 5.5.4 Comparison ofSetpoint and Inlet Water Temperatures .................. -75- Figure 5.5.5 Differences in Energy Consumption by Design Option .................. -78-

-vFigure 5.5.6 Differences in Energy Consumption by Design Option
- Gas-fired Water Heaters ...................................................... -80- Figure 5.6.1 Frequency Chart ofHot Water Use
- Households with Electric Water Heaters ...................................................... -85- Figure 5.6.2 Frequency Chart for Hot Water Use
- Households with Gas-Fired Water Heaters ....................................................... -85-

-viListofAcronyms AEO Annual Energy Outlook CEC California Energy Commission CPI Consumer Price Index DOE U.S. Department ofEnergy EIA Energy Information Administration EPRI Electric Power Research Institute GAMA Gas Appliance Manufacturers Association GRI Gas Research Institute HCFC Hydrochlorofluorocarbon HFC Hydrofluorocarbon LBNL Lawrence Berkeley National Laboratory LCC Life-Cycle Cost LPG Liquefied Petroleum Gas MCF thousands ofcubic feet NES National Energy Savings NOAA National Oceanic & Atmospheric Administration RECS Residential Energy Consumption Survey WHAM Water Heater Analysis Model

-viiRESULTS AND METHODOLOGY OFTHE LIFE-CYCLE COST ANALYSIS FOR RESIDENTIAL WATER HEATER EFFICIENCY STANDARDS The Energy Policy and Conservation Act, as amended, provides energy conservation standards for waterheaters among otherproducts and authorizes the Secretary ofEnergy to prescribe amended or new energy standards for each type ofcovered product. This is a preliminary Life-Cycle Cost Analysis; it ispart ofthe analyses the Department will conduct for the water heater rulemaking. Request for Stakeholder Comments The Department specifically requests comments from stakeholders and other interested parties regarding the following items: * water heater lifetime data * updated manufacturing costs, retailprices, and installation costs * manufacturer cost-to-retail price markup values * insulation components characteristics and costs * fuel price scenarios * uncertainty ranges on EF, RE, and UA values for different design options * inlet water temperature assumptions relationship between the setpoint and inlet water temperatures * hotwater drawmodel Note: This edition ofthe LCC Report, dated November 3, 1998, is the second edition to appear on this site. The first, dated October 1998, has been superceded to correct three errors. First, a correction in the value assigned to the maximum lifetime forelectric water heaters produced a slightchange in their life-cycle costs. Second, a correction inthe ranges of uncertainty for the RE and UA energy parameters caused changes in energy consumption, operating costs, and life-cycle costs. Third, the Improved Flue Baffle design option for gas-fired water heaters was found to contain an erroneous component, which had a significant effect on the economic results for that design option. 1 Purpose ofLife-Cycle Cost Analysis This report describes the analysis ofeconomic impacts on individual consumers from possible revisions to residential water heater energy efficiency standards. Recognizing that each household is unique, variability is explicitly accounted for byperforming the calculation fora large sample ofindividual households. Variables within the household thatcannot be characterized or are uncertain are represented by arange ofvalues. The results are expressed as the fraction ofhouseholds being impacted at particular magnitudes. Life-cycle cost (LCC) -1-captures the total sum ofpurchase price and future operating expenses for water heaters. Another measure ofeconomic impact, payback period, is also calculated. 2 Connection to Remainder ofWater Heater Standards Analysis The LCC Analysis is one step inthe analysis ofwater heater efficiency standards. Much ofthe input forthis analysis comes from the Engineering Analysis'. The other major input is from a database ofwater heater specifications and costs2
. The results ofthe LCC Analysis will be used bythe Department to select the trial standard levels used in the later stages ofanalysis and decision making. The outputs will also be used bythe National Energy Savings forecast and the Utility and Environmental analyses. 2.1 From Engineering Analysis 2.1.1 Order and Combinations ofDesign Options The combinations ofdesign options are taken directly from the Engineering Analysis. They are presented in order ofascending cumulative payback period using the DOE test procedure conditions and the 1998 national average energy price. 2.1.2 Estimates ofFactory Costs ofBaseline Models and Design Options The estimates offactory cost for the baseline models andthe incremental cost ofdesign options are from data supplied bythe Gas Appliance Manufacturers Association (GAMA). For a few design options, GAMA was unable to supply estimates ofmanufacturer costs. In these cases, consultants familiar with the water heater industry were hired to supply this data. 2.1.3 Estimates ofFactory CostofAll Standard Size Baseline Models and Design Options GAMA supplied estimates offactory cost for the typical size tanks only. The range of factory costs were estimated forwater heaters with different size tanksby adding or subtracting the material costs for different amounts ofsteel, forbothjacket and tank, and offoam insulation. 2.1.4 Energy Parameters ofBaseline Models and Design Options The energy consumption in the LCC Analysis was calculated using the Water Heater Analysis Model (WHAM)3
. The energy parameters used by WHAM--RE, UA, and rated input
-- are based on the simulation models used in the Engineering Analysis. The temperatures and average daily hot water draw are selected for individual households in the analysis according to algorithms explained in later sections. 2.2 LBNL Water Heater Cost Database
-2-LBNL has developed a database ofspecifications and retail prices for residential water heaters currently on the market. The specifications are from manufacturers' product literature. Efficiency ratings are taken mostly from directories ofcertified efficiency ratings. 4Retail prices and installation costs for residential water heaters were collected through telephone calls and faxes to several dozen distributors and retail outlets throughout the United States. 2.2.1 Prices ofBaseline Models For this analysis, the price ofbaseline models was taken from the LBNL Water Heater Cost Database. The baseline models were defined asthose with five year manufacturer warranties and having no special design features. 2.2.2 Installation Costs Installation costs were also taken from the LBNL Water Heater Cost Database. In addition tothe actual costs ofinstalling water heaters, delivery, removal, and permit fees are also included. Typical costs for miscellaneous parts used in installing awater heater, such as pipe fittings, were also added. 2.3 Input to Selection ofTrial Standard Levels For the next steps in the analysis, the Department must select trial standard levels. The LCC Analysis includes all the design options that have notbeen screened out atthis stage ofthe analysis and considers each fuel type separately. The trial standard levels will be a subset ofthe design options considered in the LCC Analysis and will cover all three fuel types simultaneously. The Department will consider theresults presented here to help decide which design options to assignto trial standard levels. 2.4 Output to National Energy Savings Forecast The National Energy Savings (NES) forecast was developed from a spreadsheet that projects energy savings at the national level for different trial standard levels. The calculations it performs are based on average annual energy consumption and average installed cost ofwater heaters. The LCC Analysis includes the range ofenergy consumption and installed cost ofwater heaters for allthe design options. The average ofthese ranges will be used in the national energy savings calculations. 3 Summary ofResults This analysis estimates the portion ofthe population that will benefit from different design options in terms ofreduced life-cycle cost. The average life-cycle cost reduction is also estimated. The results ofthis study are summarized in the following table. -3-Electric Water Heaters Design Option Fraction ofPopulation Average LCC Benefitting Savings (%) ($) 1 Heat Traps 94.9 54.11 2 1+ 2" Jacket Insulation 83.9 52.93 3 1+ 2.5" Jacket Insulation 79.9 58. 67 4 3 + Plastic Tank 68.6 43.55 5 3 + Insulated Tank Bottom 59.3 22.51 Gas-fired Water Heaters Design Option Fraction ofPopulation Average LCC Benefitting Savings (%) ($) 1 Heat Traps 95.5 26.51 2 1+ 2" Jacket Insulation 97.9 60.56 3 1+ 2.5" Jacket Insulation 93.8 57.01 4 3 + Side Arm Heater 54.9 14.70 5 2 + Improved Flue Baffle 21.7 -31.27 Oil-fired Water Heaters Design Option Fraction ofPopulation Average LCC Benefitting Savings

._____________________ __ _ (%) ($) 1 Heat Traps . 2 1+ 2" Jacket Insulation 3 2 + Improved Flue Baffle 4 3 + Interrupted Ignition -- - The results fromthe analysis ofthe oil-fired water heaters will be included in a later version ofthis report.
-4-4 Methodology and Definitions Analysis ofan energy efficiency standard involves calculations ofimpacts; for example, the impact ofa standard on consumer life-cycle cost. Inorder to perform the calculation, the analyst must first: 1) specify the equation or model thatwill be used; 2) define the quantities in the equation; and 3) provide numerical values for each quantity. Inthe simplest case, the equation is unambiguous (contains allrelevant quantities and no others), each quantityhas a single numerical value, and the calculation results in a single value. However, unambiguity and precision are rarely the case. In almost all cases, the model and/or the numerical values for each quantity in themodel are not completely known (uncertainty) or the model and/or the numerical values for each quantity in the model depend upon other conditions (variability). Explicit analysis ofuncertainty and variability is intended to provide more complete information to the decisionmaking process. 4.1 Uncertainty and Variability To account forthe uncertainty and variability, the LCC model was developed using Microsoft Excel combined with Crystal Ball (acommercially available add-on). The model uses Monte Carlo simulations to perform the analysis considering uncertainty and variability. The analysis explicitly specifies both the uncertainty and variability in the model's inputs using probability distributions. The Monte Carlo simulation thentakes thousands ofrandom samples from the probability distribution for each input withinthe model to calculate the outputs. The distribution ofthevalues calculated forthe model outcome therefore reflects the probability ofthe values that would occur. This technique provides solutions to abroad range ofquestions and helps provide an insight into the likelihood ofvarious possible outcomes. An importance analysis is also produced which shows the relative contribution ofeach of the inputs to the total range ofoutputs. A variety ofgraphic displays are usedto illustrate the implications ofthe analysis results. These include: a) a cumulative probability distribution showing the percentage ofUS households which would have anet life-cycle saving by owning a more energy-efficient water heater or b) a chartthat depicts variation ofthe life-cycle cost for each design option considered. One major assumption has been made throughout the analysis. One oftwo probability distributions, Triangular or Normal, will be used where a specific form ofuncertainty or variability is totally or partially unknown. The Triangular distribution is one ofthe simplest forms ofprobability distributions. It uses three simple parameters, minimum, most-likely, and maximum, to describe the probability distribution for a given set ofdata. It iscommonly used in cases where the knowledge about the factor ofinterest is limited. Normal distribution, on the other hand, is based on an underlying assumption that the data follow a bell-shaped distribution. This is usually the case in which a variable is influenced by many factors but none ofthem is -5-dominant. When nothing but a mean and variance about arandom variable is known, the Department will use the Normal distribution to describe the variable. 4.1.1 Uncertainty When making observations ofpast events or speculating about the future, imperfect knowledge is the rulerather than the exception. For example, the energy actually consumed by a particular appliance type (such as the average U.S. water heater) has notbeen directly recorded very often. Rather, energy consumption is usually estimated based upon available information. Even direct laboratory measurements have some margin oferror. When estimating numerical values expected for quantities at some future date, the exact outcome is rarely known in advance. 4.1.2 Variability Variability means that different applications or situations produce different numerical values fora quantity. Specifying an exact value for a quantity may be difficult because the value depends on something else. For example, the amount ofhot water used per day by a household depends upon the specific circumstances and behaviors ofthe occupants (e.g., number of persons, personal habits about hot water use, etc.). Variability makes specifying an appropriate value more difficult. One's personal experience may not be representative ofthe entire population. Surveys can be helpful here, and analysis ofsurveys can relate the variable of interest (e.g., gallons ofhot water use per day) to other variables that are better known or easier to forecast (e.g., persons per household). 4.1.3 Approaches Two approaches to consider uncertainty and variability are described here: Scenarioanalysisuses a single numerical value for a quantity in the calculation, then changes the numerical values andrepeats the calculation. A number ofcalculations are done, which provide some indication ofthe extent to which the result depends upon the assumptions. For example, the life-cycle cost ofan appliance could be calculated for electricity prices of2, 8, and 14cents perkWh. The advantages ofscenario analysis are thatthe calculation is simple; arange ofestimates isused; and crossover points can be identified. When examining a given design option, a crossover point occurs when the energy price rises to apoint at which the savings in operating cost compensate for the increased purchase expense ofthe design option. The disadvantage of scenario analysis isthat there is no information about the likelihood ofeach scenario. In this analysis ofwater heaters, the only variables treated as scenarios are future energy prices. These prices are taken from forecasts by DOE's Energy Information Administration (EIA)5 and the Gas Research Institute (GRI)6
. -6-

### Probability analysisconsiders theprobabilities within arange ofvalues. Forquantities with variability (e.g., electricity prices indifferent households), surveys can beusedto generate a frequency distribution ofnumerical values (e.g., thenumber ofhouseholds with electricity prices at particular levels) to estimate the probability ofeach value. For quantities with uncertainty, statistical or subjective measures such as a triangular probability distribution can beused to provide probabilities (e.g., manufacturing cost to improve energy efficiency to some level maybe estimated tobe $10 +/- $3). The advantage isthat theprobability approach provides the greatest information about the outcome ofthe calculations, that is, theprobability that the outcome will be in anyparticular range isprovided. Themajor disadvantage ofthe probability approach is that it requires more information, namely information aboutthe shapes and magnitudes ofthe variability and uncertainty ofeach quantity. Scenario andprobability analysis provide some indication oftherobustness ofthepolicy given the uncertainties and variability. A policy is robustwhen the impacts are acceptable over a wide range ofpossible conditions.

-7-5 Details ofLCC Uncertainty Analysis for Water Heaters 5.1 Overview The LCC analysis is designed to determine the life-cycle cost and the cumulative payback for consumers for a variety ofdesign options to improve the efficiency ofresidential water heaters. To account for all the variability and uncertainty among consumers, the analysis isdone for thousands ofhouseholds from a weighted sampling from DOE/EIA's 1993 Residential Energy Consumption Survey (RECS) 7
. In additionto thevariety ofconsumers, wherever possible, other inputs for the analysis are also represented as samples drawn from arange of values. In thisway, the analysis accounts forthe full range ofcharacteristics related toresidential hot wateruse. All design options forwater heaters are analyzed as ifthey were in production levels equivalent to thetypical existing baseline models, i.e., possessing similar economies ofscale. The term "typical existing" baseline is used inthis analysis to refer to current water heater models that use HCFC-141b as ablowing agent forfoam insulation and are ofthe most common, or typical, tank size (50-gal for electric, 40-gal for gas-fired, and 32-gal for oil-fired). The criteria for the selection and an in-depth description ofthe baseline models isprovided in the Engineering Report. Manufacturers' data from GAMA's consumers directory revealed 25 different volume sizes for electric water heaters, 19 forgas, and 4 for oil. Within each volume size, there are varying numbers ofmodels. Some sizes have over 1,000 different models. Forthe purposes of this study, the assumption was made that a size with more models indicated that more ofthat size was shipped and, therefore, purchased. The sizes with the greatest number ofmodels were checked against GAMA shipment data forthe years 1988 through 1995. GAMA shipment data is reported in ranges rather than exact size volumes. After comparing consumers directory data and shipment data, standard sizes were selected asrepresentative ofcurrent market conditions. Table 5.1.1 presents a list ofall ofthe standard-size water heaters (based on rated tank volume) considered in the LCC analysis.

-8-Table 5.1.1 Water Heater Standard Sizes Water Heater Fuel Type Rated Volume (gal) (liter)* Electric 30 110 Electric 40 150 Electric (typical) 50 190 Electric 65 250 Electric 80 300 Gas-fired 30 110 Gas-fired (typical) 40 150 Gas-fired 50 190 Gas-fired 75 280 Oil-fired (typical) 32 120 Oil-fired 50 190 *rounded to the nearest 10 liters The Montreal Protocol bans use ofHCFC-141b as ablowing agent for polyurethane foam insulation after2003. For this analysis, HFC-245fa is assumed tobe the substitute blowing agent. Polyurethane foam made with HFC-245fa may be slightly less effective as an insulation. Costs maybe slightly higher as well. Additionally, theU.S. Consumer Product Safety Commission, an independent Federal regulatory agency, is currently working with the water heater industry to design gas-fired water heaters that will not ignite flammable vapors. Both of these changes will be in effectby the time anynew efficiency standard becomes effective. The future baseline models, which will incorporate these two changes, are referred to as the "analytic" baseline models inthis analysis. These will be the baselines against which design options are compared. 5.1.1 Separate Analysis for Each Fuel (Product Class) The LCC analysis is done separately for each energy source: electric, gas, and oil. This analysis does not address fuel choice orfuel switching. These issues are addressed in the National Energy Savings analysis. 5.1.2 Combinations ofDesign Options from Engineering Analysis The design options used in this analysis are described in more detail in the Engineering Report. Design options are combined by order ofcumulative payback as determined in the Engineering Analysis. Hot water use and energy costs inthis analysis reflect the range ofvalues among consumers, unlike the Engineering Analysis, which is based onthe DOE Energy Factor test procedure and average national energy prices.

-9-5.1.3 Five Major Modules A spreadsheet model with five major modules isthe basis ofthe LCC analysis. The major modules are LCC and Payback, Operating Cost, Equipment Cost, Energy Analysis, and Hot Water Draw. The individual modules are described in more detail later in this report. Several ofthese modules have accompanying data tables that are used forreference. Each module has its own inputs and outputs, with some modules using as inputs the outputs ofother modules. As a default, the spreadsheet opens to a main page that allows the user to select scenarios for future energy prices, and then initiates aMonte Carlo run by sampling all ofthe inputs 10,000 times. There isa separate spreadsheet available foreach type ofwater heater being considered; electric, gas-fired, and oil-fired. The spreadsheets are written in Microsoft Excel 97. The Monte Carlo capabilities are enabled by Crystal Ball, an add-on program that helps analyze therisks and uncertainties associated with models. Crystal Ball is available from Decisioneering, Inc. The LCC spreadsheets will be available later in November 1998 on the DOE, Office of Codes and Standards web site at <http://www.eren.doe.gov/buildings/codes_standards/reports/index.htm>. Ifyouhave any questions or are unable to access the web site, please contact Ms. Brenda Edwards-Jones at (202) 586-2945 or byfax at (202) 586-4617. 5.1.4 Flowchart To provide a general overview, a flowchart showing the major sections ofthe spreadsheet and the data flow between the modules is shown in Figure 5.1.1. 5.1.5 Description ofOutputs The main outputs ofeach module are summarized as tables and charts in the individual sections. The summaries for each module give outputs by design option, except for the draw module. The draw module calculates hot water use for each household. The amount ofhot water use is not affected by water heater efficiency, so it is not calculated separately for each design option.

-10-

### Life-Cycle Cost Analysis

Water Heater LCC Model Main Page RECS93 sample Water Heater Design Option Data Table / Energy price scenarios

- Recovery M Cost Efficiency Maintenance / I Cost -Standby l Cost In s ta l ost

-Rated input \ \ P

AT W A T E R W A T E R DRAW HEATER HEATER MOD I ANALYSIS _COST \ M P L jMMODEL MODELODEL

/ Discount DELTA LCC & Water Discount PAYBACK Heater

Rate / \ CALCULATIONS / Lifetime

-LCC Comparisons,

Payback, and Importance Charts 

### Figure 5.1.1 Flowchart ofLCC Analysis Spreadsheet The summarytables list the average value for each output and thepercent ofhouseholds that would benefit by usingthat design option. For example, in the LCC and Payback module, thevalues reported inthe tables are LCC and Payback. In other modules, other outputs are reported as appropriate. -11-The impact ofindividual design options are shown in combined histogram and cumulative frequency charts. These charts show the output (LCC or payback) by percent ofthe population in order ofascending value. The bars ofthe histograms show the relative frequency ofdifferent results out of 10,000 samples from 5,788 RECS households (2,559 with electric water heaters, 2805 with gas-fired, 248 with LPG, and 176 with oil-fired). RECS household weightings were used to develop the samples. The lines show cumulative percentages ofthe results for each value. Thehigher the absolute value ofthe correlation, the more influence the input has on the output. Anegative correlation indicates adecrease in output in response to an increase in the input. Forexample, in Figure 5.2.6, the higher the discount rate, the larger the difference in LCC. The final type ofchart is a tornado chart, which shows the impact ofthe inputs ofeach module on the output in question. The sensitivity ismeasured asthe rank order correlation between each input and the output ofinterest. The higher the correlation the more influence that inputhas onthe output. 5.2 Life-Cycle Cost Module 5.2.1 Introduction The life-cycle cost isdefined as the total consumer expense overthe lifetime ofa water heater, including purchase price and operating expenses (which includes energy expenditures). Future operating expenses are discounted to the time ofpurchase, and summed over the lifetime ofthe water heater. 5.2.2 Equations and General Descriptions forLCC and Payback Life-cycle cost is defined by the following equation: LCCoption = EquipCostoption+ NPV(Drate,OprCostoption,Lifetime)
where: EquipCost = cost ofbuying and installing awater heater ($) = (equipment cost) + (sales tax) + (installation cost) options = one of5design options for electric, 5for gas, and 4 for oil-fired NPV = Net present value ($) is defined by the following equation:

-12-Lifetime OrCost 

### NPV= 

## I

- -lar year=I (1+

### Drate) Dte = Discountrate (real) (%) OprCost = cost ofoperating a water heater ($/year) = (energy usage) x (energy rate) + (maintenance cost) Lifetime = Lifetime ofwater heater (years) EquipCostis defined as the costs associated with buying and installing awater heater. This includes the cost ofawater heater plus sales tax, installation charges, and, ifthe water heater is 

### being replaced, charges for theremoval ofthe old waterheater. NPV (Net PresentValue ) is the present value today ofa future stream ofexpenditures. Dae is defined as therate at which future expenditures are discounted to establish their present value. A distribution ofdiscount rates was derived to represent the variability in financing methods consumers use inpurchasing appliances. The resulting distribution ofdiscount rates will be usedto calculate adistribution oflife-cycle costs for water heaters. Consumers purchase appliances in new homes and as retail purchases. The retail purchases are paidby cash, credit cards, or retailer loans. A comment 8(Whirlpool, 1990) indicated that for white goods about 40% ofretail purchases are paid in cash, 35% use credit cards, and 25% use retailer loans. The same comment indicates 25% ofappliance purchases are for new homes. (Forwater heaters, it isestimated that purchases for new homes are now about 20%.) The method ofpurchase used byconsumers is assumed to be indicative ofthe source of the funds and the type offinancing used bythese consumers. A range ofinterest rates that may reasonably be expected to apply in the future to different types ofconsumer savings orfinancing were estimated. For newhousing, the estimated nominal mortgage rate ranges from 5-8%, the derived after-tax rate is based on ataxof28%, and an inflation rate of2% is subtracted from the total. The result is arange ofreal mortgage rates of 1.60-3.76%. (Example: 5% * (100%-28%)
- 2% = 1.60%) For cash, the minimum rate is 0%. This rate applies to purchasers making cash purchases without withdrawing from savings accounts. For the maximum, the opportunity cost is represented bythe interest that could have been earned in a savings account. The historical nominal maximum savings rate ranged from 4.5-5.5% from 1970 to 1986 (real rates of-8.27 to +3.58%). A real rate of3%was selected as indicative ofthe maximum. -13-The interest rates forretailer loans and credit cards are assumed to have the same range. The minimum credit card rate is taken as 6% real. Introductory rates on some credit cards today are 5.9% nominal, but after the introductory period (often 6months), the rate becomes much higher. Maximum rates are over 20% nominal. However, ifthe purchase ispaid for initially by acredit card and the consumer pays offthe balance in less thanthe life ofthe water heater, then the effective interest rate is lower thanthe nominal credit card rate. The current assumption is a range of6-15% real. DOE recognizes that otherfactors might be considered in the estimation ofreal consumer discount rates, such as the actual impacts ofappliance purchases onconsumer savings, indebtedness or consumption, and expressed or imputed consumer preferences. While such data, ifit were tobecome available, mightprovide a stronger analytical basis forDOE's choice of discount rates, it is considered unlikely that such data would have a significant effect on the range ofvalues considered in the current analysis. Figure 5.2.1 shows the distribution ofreal discount rates, ranging from 0to 15%, with a mean of6%. 

## Consumer Real Discount Rate 20% l 16% 2 12%/° 40/0 4%00/0 2% 4% 6% 8% 10% 12% 14% 16% 

### Discount Rate Figure 5.2.1 Distribution ofConsumer Discount Rates OprCost isdefined as the expenditures necessary to keep the water heater operating. Ithas two parts, fuel and maintenance. Fuel costs are calculated by multiplying annual water heater energy use by the energy rate paid by the household. Maintenance costs are repair charges. Lifetime isthe period oftime the water heater will provide service. Table 5.2.1 shows lifetimes -14-for waterheaters by fuel type. Oil-fired water heaters are assumed to have the same distribution oflifetimes as gas-fired water heaters. Table 5.2.1 Water Heaters and Lifetime byFuel Type9 Fuel Lifetime (years) Minimum Average Maximum Electric 4 12 19 Gas and LPG 3 9 15 Fuel Oil 3 9 15 The simple payback period measures the amount oftime needed torecover the additional consumer investment in increased efficiency through lower operating costs. The payback period equation can be expressed as: EquipCost
- EquipCost, Paybackopi.mO = pti OprCost,
- OprCostp where: option = one of5 design options forelectric, 5for gas-fired, and 4 for oil-fired waterheaters base = thetypical analytic baseline design Numerically, the simple payback period is the ratio ofthe increase in purchase (and installation) price to the decrease in annual operating expenditures (including maintenance) from replacing the analytic baseline water heater with awater heater incorporating another design option. Payback periods are expressed in years. Apayback period ofthree years means that the increased purchase price is equal to three times the value ofreduced operating expenses in the year ofpurchase, or that the increased purchase price is recovered in approximately three years because oflower operating expenses. Payback periods greater thanthe life ofthe product mean thatthe increased purchase price is never recovered in reduced operating expenses.

-15-5.2.3 General Description ofSources ofData Residential Energy Consumption Survey The analysis uses as its underlying data source the 1993 RECS. RECS provides information concerning energy consumption in the residential sector and contains a more complete set ofdata for water heater analysis than any other survey reviewed for this study. The survey contains basic data concerning household characteristics from an interview questionnaire and annual fuel consumption and expenditures (excluding transportation fuel) derived fromthe records offuel suppliers. Also included are weather data (in the form ofheating and cooling degree days) and aweighting variable. The 1993 RECS survey consists ofa total of7,111 sample households from across the contiguous U.S. Most, but not all, ofRECS household records are used in the analysis and are assumed, with their weighted averages, to be representative ofhousing ona national scale. The households that are included in the analysishave three defining features: 1.Running hotwater 2. Anindividual water heater 3. One offour fuels: electricity, oil, gas, orLPG Households without these features are not used in the analysis. RECS sometimes reports ranges, rather than precise numbers, forvariables, and there are also certain omissions ofcrucial information forvariables needed forthis analysis. In orderto correct for these missing or insufficient data, two methods were used: (1) when ranges were given, best point estimates were made within the range; and (2) when the RECS data did not cover particular areas ofinterest, other studies were used to develop the necessary information for each RECS housing unit. National Oceanic and Atmospheric Administration The National Oceanic and Atmospheric Administration (NOAA) ofthe U.S. Department ofCommerce, operates the National Climatic Data Center, which isthe world's largest active archive ofweather data.The analysis uses NOAA's 30-year (1961-1990) average air temperatures t° . Gas Appliance Manufacturers Association The Gas Appliance Manufacturers Association (GAMA) is a national trade organization which represents hot water heater manufacturers inthe U.S. It collects and disseminates data on water heating equipment. This analysis uses GAMA's shipment data, consumers' directory. and manufacturer costs for most design options. -16-ManufacturerProduct Literature Most manufacturers ofwater heaters provide dealers (and consumers) with literature describing their models, including their efficiency ratings. 5.2.4 Life-Cycle Cost and Payback Results Electric WaterHeaters Table 5.2.2 lists the portion ofthe population benefitting from each design option, in terms ofreduced life-cycle cost. The average LCC savings and payback are also shown. Table 5.2.2 Life-Cycle Cost and Payback for Electric Water Heaters Design Option Fraction of Average LCC Average* Population Savings Payback Benefitting ($) (yrs) (%) 1 Heat Traps 94.9 54.11 1.07 2 1+ 2" Jacket Insulation 83.9 52.93 3.49 3 1+ 2.5" Jacket Insulation 79.9 58.67 4.14 4 3 + Plastic Tank 68.6 43.55 5.76 5 3 + Insulated Tank Bottom 59.3 22.51 6.79 *medianFigure 5.2.2 shows the cumulative frequency ofdifferences inLCC by design option for electric waterheaters. The percent ofthe population benefitting and being disadvantaged are also shown onthe graphs. Note that a negative difference in life-cycle cost for a given design option indicates a savings. The width ofthe plot shows the spread ofsavings inthe population. In general, the design optionswith higher efficiencies tend to show a wider spread in the population. Figure 5.2.3 shows cumulative frequency ofpayback period by design option. The percent ofpopulation which would have apayback ofless than or equal to three years is indicated. A three-year payback period was chosen because it was assumed that design options which satisfy this criteria are most likely to be included in the proposed standard. In general, the design options with higher efficiencies tend to show a wider spread in the population.

-17-Delta Life Cycle Cost of Heat Trap compared to Delta Life Cycle Cost of 2"Jacket Insulation Analytic Baseline (1998S) compared to Analytic Baseline (1998$) 95% Benefit 5% Disadvantage 84% Benefit 16% Disadvantage 4000 . ..- 100% 2500
- -- -- 100% 3000

D 80% s I 2000 - 80% i 2000S | 60% J i 15 00 -IAl 60% Z 40% 1 00 000 0% 500

- 20% :.:-: - _ _._1N ,I N . No20% -5 I 0 0 0% 0 -l0% Delta LCC(S) Delta LCC($)

Delta Life Cycle Cost of2.5' Jacket Insulation j Delta Life Cycle Cost of Plastic Tank compared compared to Analytic Baseline (19985) to Analytic Baseline (1998$)

80% Benefit 20% Disadvantage 69% Benefit 31% Disadvantage 2000 - ------- 100% | 1500 ' ° °

- 100% 1 1coon ." 80% S - 80% 1

tc -'°°° j ; : - 1 60% X 60%
; S N 1000 s40% e

Delta LCC($) Delta LCC($) I , 40% 40%

i Delta Life Cycle Cost ofTank Bottom Insulation [ compared to Analytic Baseline (19985) 59% Benefit 41% Disadvantage 1500 20 2100% iS~ 1000 ) jfti 60% 1 80%

. 500 lN , _n 40%
Delta LCC($)

.. Frequency -mCumulative %
Figure 5.2.2 Difference in Life-Cycle C osts by Design Option for Electric Water Heaters

-18-Payback Period of HeatTrap compared to Payback Period of2" Jacket Insulation compared Analytic Baseline (Years) toAnalytic Baseline (Years) 82% payback =3 years 42%payback <= 3years 6000
. . ... 100% 2500 100% 4000 5 4^000 *80% e >,2000 80% o 400000 e 3000k r60%
_ ' 1500 11 60%

- 2000 40V S -% E 1000

- 40% U.- 1000 - 20% 3 IU 500 20% o 0 l 0% 0 a JlilH| lsiB-i-.-..-.--- 0% Years Years

PaybackPeriod of 2.5" Jacket Insulation Payback Period ofPlasticTankcomparedto comparedto Analytic Baseline(Years) Analytic Baseline (Years) 32% payback <= 3 years 12% payback<= 3years 2000 ---- 100% 2000 -- 100% 1500 2 80% 1500 80%

,, t 0 I, '['R'R a Mia-:- 'r-i-:-:- , B0 %

.. . ... cO Uu N 0
_ ( ) N. 00 I U . In %e u< o 150

0 100%

I Ln I8% - Years YrYears
Payback Period ofTank Bottom Insulation -compared toAnlytic Baseline (Years) ij ~8% payback ' 3 years 1500 - 100% 80% e i y 10 0 0 lir 60%

2 5 00

# L hni 40% -1 

# nnn a

5 ~. _ _ . n20% 5

- n O IU) N 00 Years
ryAFrequency Cumulative % Figure 5.2.3 Payback Period by Design Option for Electric Water Heaters

-19-Gas-fired WaterHeaters Table 5.2.3 lists the portion ofthe population benefitting from each design option, in terms ofreduced life-cycle cost. The average LCC savings and average payback are also shown. Table 5.2.3 Life-Cycle Cost and Payback for Gas-Fired Water Heaters Design Option Fraction of Average LCC Average* Population Savings Payback Benefitting ($) (yrs) _____________(%)________ 1 HeatTraps 95.5 26.51 0.70 2 1+ 2" Jacket Insulation 97.9 60.56 1.87 3 1+ 2.5" Jacket Insulation 93.8 57 . 01 2. 62 4 3 + Side Arm Heater 54.9 14. 70 6.25 5 2 + Improved Flue Baffle 21.7 -31.27 9.35 *median Figure 5.2.4 shows the cumulative frequency ofdifferences in LCC by design option for gas-fired water heaters. The percent ofthe population benefitting and being disadvantaged are also show onthe graphs. Figure 5.2.5 shows cumulative frequency ofpayback period by design option. The percent ofpopulation which would have apayback oflessthan or equal to three years is indicated.

-20-Delta Life Cycle Cost of HeatTrap compared to Delta Life CycleCost of 2" Jacket Insulation Analytic Baseline (1998$) compared to Analytic Baseline (1998$) 96% Benefit 4% Disadvantage 98% Benefit 2% Disadvantage 10000 ---- - 100% 1 8000 --.... 100% 8000. .s80%
_ 1 86000 8o0% 6000l +60% i 40 60% | 400o% r_ 4000 40% E 40%

. 2000 20% 000 20% v OQOQOQOQQQ I O% & 0 '0%

_ -0
_ _ -0% Delta LCC($) Deta LCC($)

Delta Life Cycle Cost of2.5" Jacket Insulation Delta Life Cycle Cost of Slde-Arm Design (w/ comparedto Analytic Baseline (19985) MetalTank) comparedto Analytic Baseline

94% Benefit 6% Disadvantage (1998$) 55% Benefit 45% Disadvantage 8000 .......-- . 100% 6000o 80% 3000 *** 100% 60% 1 . 80% >

Delta LCC(S) I Delta LCC(S)

Delta Life Cycle Costof Improved Flue Baffle

compared toAnalytic Baseline (1998$) 4022% Benefit 78% Dsadvantage

8000 2 -* 100% 00 S-6 000- - 80%

_ I4000 2 A I60%2 000% 0 0%

e 2000.
_ 0o- §% 0
,,o o o o.o.o ooo %n CD, uo rD
- 8- U? - Doe LCC($)Delta LCC(C($)
Figure 5.2.4 Difference in Life-Cycle Cost by Design Option for Gas-Fired FluWater Heaters compa -21d toAnalyticBaselin ( 22%Benefit 78% Disadvantage 4000
40%

DeltaLCC($)

[~ ~-lFrequency = Cumulative % Figure 5.2.4Difference in Life-Cycle Cost by Design Option for Gas-Fired Water Heaters

-21-Payback Period of HeatTrap compared to Payback Period of 2' Jacket Insulation compared Analytic Baseline (Years) to Analytic Baseline (Years) 95% payback<= 3 years 83% payback <= 3years 8000

- -- *** ---- * 100% 1 5000- - 100% 8 6000 80% i > 4000 80% e 

# B

4000 

## T i60% | J 3000 60% 40% | a 2000 40%

. 2000 20% 1000 20% I 0%I
- 0% Years Years

PaybackPeriod of 2.5' Jacket Insulation Payback Period ofSide-Arm Design (w/Metal comparedto Analytic Baseline (Years) Tank) compared toAnalytic Baseline (Years) 59% payback<= 3years 3% payback = 3years 4000

- ---- '----'-_ 100% 2000 ...-.-. 100% 3000 80% * S o 1500- HB» - 80% *

1 2000 60% 1000 60 OaR 40% j i 40% 51000 20% 20% 0 !--rlU ..- 'a . ,:_ o ; Ii;!0% 0 SL_:1, II'a,

-- : : 0% Years Years
Payback Periodof Improved Flue Baffle compared to Analytic Baseline (Years) 0%payback< 3years 2000 -_ --- 100% &1500.n 1" 80% e 3 g 160% I

1000 F U 40% E 500 20%

0 * r -- , 0% Years

Frequency + Cumulatie %
Figure 5.2.5 Payback Period by Design Option for Gas-Fired Water Heaters
-22-The following two sensitivity charts (Figures 5.2.6 and 5.2.7) show the results of sensitivity analysis for differences in LCC for the design options with the highest average lifecycle cost savings for electric and gas-fired water heaters. Sensitivity charts for other design options are found in Appendix A. Figure 5.2.6 and Figure 5.2.7 show therank order correlation ofinput variables with the incremental LCC for the 2.5" Jacket Insulation on electric water heaters and the 2" Jacket Insulation design option on gas-fired water heaters. Variables are ordered with maximum correlation (positive or negative) on top and minimum correlations on the bottom.
SensitivityAnalysis - ElectricWater Heaters DeltaLife Cycle Cost of2.5' Jacket Insulation compared toAnalytic Baseline (19985)
Discount rate 8

Water Heater Lifetime (years) -0.31
Total Cost to Buy and Install a2.5'

Jacket insulation Water Heater 0 (19985$).:. 02 Annual Operating Cost in2003 of Analytic Baseline Water Heater -0.19 (19985) Annual Operating Cost in2003 of 2.5' Jacket Insulation Water Heater -0.16 (1998,$) Total Costto Buy and Installan l Analytic Baseline Water Heater 0.12 (1998$) -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 Figure 5.2.6 Sensitivity Analysis for Difference in Life-Cycle Cost of2.5" Jacket Insulation on Electric Water Heater

-23-SensitivityAnalysis - Gas-fired Water Heaters Delta Life Cycle Cost of2' Jacket Insulationcompared toAnalytic Baseline (1998$)
Water Heater Lifetime (years) -0.50 -

Discount Rate 0.45
Annual Operating Cost in2003of Analytic Baseline Water Heater -.27 (1998$) Annual Operating Cost in2003 of2'

Jacket Insulation Water Heater -0.25
Total Cost to Buy and Installa 2' Jacket Insulation Water Heater 0.12 (1998$) Total Cost to Buy and Install an Analytic Baseline Water Heater 0.10 (1998$) -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Figure 5.2.7 Sensitivity Analysis for Difference in Life-Cycle Cost of2" Jacket Insulation on Gas-fired Water Heater

-24-5.3 Equipment Cost Module 5.3.1 Introduction toEquipment Cost The equipment costrepresents the sum ofthe retail price, sales tax, and installation costs. Theretail price is calculated from themanufacturer's cost multiplied by an overall markup. The first halfofthis discussion addresses the typical existing baseline model; the analytic baseline model is the basis for the later description ofthe design options. 5.3.2 Equation for Equipment Cost The waterheater cost (equipment cost only) is calculated usingthe equation: EquipCostopion,si:e = MfrCoStopton. sie,

### x Markupsiex (1 + SalesTax) + TotlInstCostop,o where: MfrCost = cost to manufacture water heater ($) Markup = markup from manufacturer's cost to retail price SalesTax = sales tax on water heater (%) TotlnstCost = total cost ofinstallation ofwater heater ($) The markup is calculated using the following ratio: Markups,,e =RetlPricese/MfCost,,s where: RetlPrice = water heaterprice atthe retail outlet, all standard-size existing baseline models ($) Total installation cost is based on: TotInstCostop,,o. =InstCost +AddInstCostP,,O n where: InstCost = cost to install baseline water heater ($)
-25-AddlnstCost = additional cost(s) to install fuel-fired water heater with certain design options ($) The additional installation cost iscalculated as follows: AddInstCostp,,, =AddElecCostop,,o, +AddVentCosto,, 0 o +AddTubeCostopo. where: AddElecCost = additional cost ofinstalling a new electric circuit for gas-fired water heaters with design options that require electricity ($) AddVentCost = additional cost ofupgrading the venting system for gas-fired water heaters with designs that increase recovery efficiency ($) AddTubeCost = additional costto install aburnertube extension for oil-fired water heaters with certain design options ($) 5.3.3 General Description ofKey Variables MfrCost is the manufacturing cost to produce awater heater. This cost is the sum ofthe variable and the fixed costs. The variable costs are composed ofthe direct costs to the manufacturer, which are defined as the sum ofthe material, labor, and overhead costs. The variable manufacturer cost is also called afull production cost. The fixed costs, the costs to convert to the production ofa newwater heater design, are the sum ofthe capital cost and the product design cost. The fixed manufacturer cost is sometimes called a conversion cost. Markupis defined asthe ratio between the retail price to the manufacturer's cost. This is an overall markup; it may include several intermediate markups applied by awholesaler or other intermediate sellers. SalesTax isthe local, state or county tax applied to the water heater atthe point ofsale. RetlPrice is defined asthe retail outlet price ofthe water heater paid directly bythe customer. This price does not include the installation cost or any other miscellaneous fees such as delivery fee, removal fee, permit fee, and partsfee. TotInstCost is the total installation cost ofthe water heater. It is the price paid directly by the customer to have the water heater installed including the additional cost ofadding a new electrical circuit and/or upgrading the venting system in the case ofsome gas-fired water heater design options. InstCost isthe installation cost ofthe baseline water heater. It is the price paid directly by the -26-

### customer to have the waterheater installed, including any miscellaneous fees such as delivery fee, removal fee, permit fee, and parts fee. It does not include the cost ofadding anew electrical circuit and/or upgrading the venting system inthe case ofgas-fired waterheaters with design options thatmay require these. AddInstCost is the additional installation costto install an electric circuit and/or to upgrade the venting system ofa gas-fired water heater, orto install aburner tube extension for oil-fired water heater. AddElecCost isthe additional cost ofinstalling an electric circuit forthe gas-fired water heater when the design option includes an intermittent ignition device and/oran electromechanical flue damper and there is nopre-existing electrical outlet near thewater heater. AddVentCost is the additional costto install anupgraded venting system orupgrade an existing venting systemto eliminate condensate problems ingas-fired waterheaters withdesign options that increase recovery efficiency. As discussed intheEngineering Report,the flue lossefficiency has been limited to 80.0%. Consequently the only upgrades considered are the installation of Type-B vent connectors between the water heater andthe existing vent system. AddTubeCost isthe additional installation cost to install aburner tube extension for an oil-fired water heaterwiththicker insulation thanthe baselineunit. 5.3.4 General Description ofSources ofData Introduction To determine the equipment cost, manufacturing cost,retail price, installation cost, and sales tax information are needed. GAMA provided estimates ofwater heater manufacturing costs for typical existing baseline models". LBNL contracted with aconsultant'2

### recommended by GAMA for additional data. (Fixed manufacturing costs, becausethey applyonly tocosts associated with converting to new waterheater designs, are discussed later inthis section in conjunction withthe analytic baseline.) The source ofthe retail price, the sales tax, and the installation cost isthe LBNL Water Heater Cost Database which contains data collected from largeretail chains and various wholesale distributors. The following variables fromthe database are used toidentify theretail price data:

-27-RatedVolume Volume ofthe water heater tank WHModel Model name YearsWarranty Number ofyears covered in the model's warranty WHFuel Type offuel used RetailPrice Retail price DeliveryFee Charge for transporting water heater to the customer's house InstallFee Charge to install water heater RemovalFee Charge to remove old water heater from the customer's house PermitFee Fee (where required) to install water heater PartFee Charge for (any) extra parts Markup is based on manufacturing cost and retail price. The retail prices forall standardsize existing baseline models are drawn from the collected data. The criteria for the existing baseline models are a 5-year manufacturing warranty and no special design features. Manufacturing costs for otherthan typical existing baseline water heaters, i.e., all other standard sizes, are based on the manufacturing cost forthe typical waterheater plus (or minus) incremental costs for extra (or less) foam insulation and sheet metal. ManufacturingCost VariableManufacturingCost.The variable component ofthe manufacturing cost for the typical existing model is the sum ofdirect material, direct labor, overhead, andtransportation costs. The overhead cost includes the factory overhead cost only. The non-production costs, which include selling, general, and administrative costs, research and development costs, and interest costs, are considered apart ofthe fixed manufacturing cost and are not included in the variable manufacturing cost. The typical existing baseline variable manufacturing cost data used in the analysis for electric, gas-fired, and oil-fired water heaters are presented in Table 5.3.1.

-28-Table 5.3.1 Typical Existing Baseline Water Heaters
- Variable Cost Data Typical Existing Average Variable Costs Cost Uncertainty Range Baseline Material Labor Overhead' Total Minimum Maximum ($) ($) ($) ($) Electric (50-gal) 62.16 12.41 50.99 125.56 84.96 171.92 Gas (40-gal) 75.02 12.49 50.10 137.61 104.31 174.40 Oil (32-gal) 'includes transportation As explained above, the manufacturing costs for other size waterheaters are based onthe manufacturing cost for thetypical existing baseline water heaterplus (or minus) incremental costs for extra (or less) materials, i.e., foam insulation and sheet metal. Table 5.3.2. presents the calculated incremental costs for all other standard-size existing baseline models. Table 5.3.2 Other Standard-Size Existing Baseline WaterHeaters -Variable Cost Data Rated Volume Incremental Material Cost Total Variable Cost _____________________($) ($) Electric 30-gal -7.78 117.78 Electric 40-gal -2.83 122.73 Electric 65-gal 3.87 129.43 Electric 80-gal 7.39 132.95 Gas-fired 30-gal -3.15 134.46 Gas-fired 50-gal 2.23 139.84 Gas-fired 75-gal 7.50 145.11 Oil-fired 50-gal Retail Price Theretail price is defined as the retail outlet price ofthe water heater equipment paid directly by the customer. This price does not include the installation cost nor any other miscellaneous fees such as delivery fee, removal fee, permit fee, or parts fee. The retail price analysis isbased onthe LBNL WaterHeater CostDatabase which contains data collected from retail chains and wholesale distributors. The models selected for the analysis are baseline models with a 5-year manufacturing warranty and no special design features. Figure 5.3.1 presents the sample sizes for electric water heaters, showing the number ofretailer responses on which the retail cost data is based. Figure -29-5.3.3 presents the sample sizes for gas-fired water heaters. Forexample, the retail price forthe 50-gal electric waterheater isbased on a sample of50 responses regarding the retail price of existing baseline water heaters and theretail price for the 40-gal gas-fired waterheater is based on a sample of52 responses. The size ofthe data samples generally reflects that ofthe 1996 GAMA-reported shipment share ofeach water heater size (rated volume)'3
. The comparisons of GAMA water heater shipments vs. water heater sample size byrated volume are shown in Figure 5.3.2 for electric water heaters and in Figure 5.3.4 for gas-fired water heaters. As can be seen in the figures, the fit is quite close, although much better for electric than gas-fired. This indicates that the samples generally reflect actual shipments. |

# _ BElectric Water Heaters - Electric Water Heaters - Retail CostSample Shipmentsvs Sample Data ! _Rated Vol I 60__________ 1 ! 0.40 1 (sample data) 50 I GAMA

Sample Sizes Shipments vs Sample Sizes Shipment 30 ° 0.20

0200 Retail Cost Sam(ple Gasired Water Heaer Shipments | I
_ Rated 60 0.10 Volume 0 1 0.00 30gal 40gal 50gal 6 5 80gal 30 gal 40gal 50 gal 65 gal 80 gal Rated Volume, gal Rated Volume, gal Figure 5.3.1 Electric Water Heaters Figure 5.3.2 Electric Water Heaters
- Sample Sizes Shipments vsSampleSizes

Retail CostSample Gas-fired Water Heater Shipments Gas Water Heaters vs Water Heater Sample Data I Rated 60 0.70 Volume 50represt te samplve data) 4 0 -3, 0.50

.. 40 ; Shipment

30 Z 0.30 o 20 0.20- 10 i p ~ L~4~ 

### 1 i 0.10

- 0 

## O0.00 30 gal 40 gal 50 gal 75 gal 30 gal 40 gal 50 gal 75 gal Rated Volume, gal Rated Volume, gal Figure 5.3.3 Gas-fired Water Heaters
- Figure 5.3.4 Gas-fired Water Heaters
- Sample Sizes Shipments vs Sample Sizes The retail prices for all standard-size existing baseline water heaters are shown in Figure 5.3.5 for electric water heaters and in Figure 5.3.6 for gas-fired water heaters. The mean values represent the average reported retail price for each standard-size water heater. The figures also -30-show the minimum and maximum values forthe retail price ranges obtained through the survey. For example, themean retail price for the 50-gal electric water heater is $178.88, with the minimum retail price reported to be $128.00 and the maximum as $297.00. Inthe case ofgasfired water heaters, the mean retail price forthe 40-gal size water heater is $149.94, with the minimum of$115.00 and the maximum of$260.00. Note that these retail prices do not include sales tax. RtaI Price Retail Price BectricWater Heaters Gas-fired Water Heaters $600 $600 s600 5$56 .23 $500 _5
. $ 5.5007_-___--sl'____ | 1~~~~~~~~~$~~~5- -U400 $ 'S400 .____ _ _ _ _ _4 _)

_ 29 a n 0 9 400 _-- __ _--_ -------- _.45 .36 i I s357O8 

### r 58 8 $35 .00 $300 - -srm -B97.001--41Z 

## _ $300

- - -- xS20 | 51D53 |I 516036

# f 7
_ _ 

# i
tS200 U240$00 $ S260.00 .$256.00 $100 s D - - - - - 100 133.00

_ 30g 40ga 50l 65l 80gal- g Figure_______ 5__RtilPics-_lcti30 gal 40gal 50gal 75 gal Figure 5.3.5 Retail Prices
- Electric Water Figure 5.3.6 Retail Prices
- Gas-fired Water Heaters Heaters InstallationCost The installation cost ofthe water heater is the price paid by the customer to have the water heater installed. This price does not include the retail price, but does include other miscellaneous fees such as delivery fee,removal fee, permit fee, and parts fee. Installation costs are included in the LBNL Water Heater Cost Database used forthe development ofthe water heater retail prices. The baseline models were selected using the same criteria used for the retail price determination: a 5-year manufacturing warranty and no special design features. Figure 5.3.7 presents the sample sizes forelectric water heaters, showing the number of retailer responses onwhich the installation cost data is based. Figure 5.3.8 presents the sample sizes for gas-fired water heaters. For example, the installation cost for the 50-gal electric water heater is based on a sample of41 responses about installation costs forthe existing baseline water heaters and the installation cost for the 40-gal gas-fired water heater is based on a sample of48 responses.

-31-Installation Cost Sample Size Installation Cost Sample Size Electric Water Heaters Gas Water Heaters 60 50 50 I 40 40 30 5 30 10 -u 20 tO1 10 0 0 30gal 40gal 50gal 65 gal 80gal 30 gal 40 gal 50 gal 75 gal Rated Volume, gal I Rated Volume, gal Figure 5.3.7 Installation Cost Sample Size
- Figure 5.3.8 Installation Cost Sample Size
- Electric Water Heaters Gas-fired Water Heaters The installation costs for all standard-size existing baseline water heaters are shown in Figure 5.3.9 for electric water heaters and in Figure 5.3.10 forgas-fired water heaters. The mean values represent the average reported installation cost foreach water heater size. The figures also show theminimum and maximum values for installation costs obtained through the survey. For example, the mean installation cost forthe 50-gal electric waterheater is $160.73, with the minimum reported tobe as little as $65.00 and the maximum as high as $258.00. The relatively narrow installation cost range for 65-gal electric waterheaters isprimarily due to the small installation cost sample size for this particular tank size (see Fig. 5.3.7). Inthe case ofgas-fired water heaters, the average installation cost forthe 40-gal size water heater is $159.52, with a minimum of$65.00 and a maximum of$258.00.
4tallatfin~CaI-st InstallationCost BectriVterHeaters [ ts-fired Water Heaters $350 t $300 $300 $25__ _____________$25ao 

### o_ 25 o 0 o ___0 _____5 2 1 00 0 $200

- _ 0

. 16262 $159.52 $156.52 15&71 ° $150
__ - 16£ 6 $1 

# ! 6 a 5 6 0 73J $ 1 6_ao !j $150------_--------$15 X$1l00 65.00 s65.00 $175.00 $6500 $600 $65.00 50 0 6500 $- _ _ _ ; $- 30ga 40gal 50ga 65g9 8gal 30ga 40gl 50ga 75gal Figure 5.3.9 Installation Cost Ranges
- Figure 5.3.10 Installation Cost RangesElectric Water Heaters Gas-fired Water Heaters

-32-

### Manufacturer-to-Retail Markup The manufacturer-to-retail markup isdefined as the ratio ofthe retail price to the manufacturer cost. The retail prices reflect those ofwater heaters sold in 1998. Since theretail price and the estimated manufacturer cost differ foreach fuel type and for each size (rated volume), the markup is different for each standard-size existing baseline model. Tables 5.3.3 and 5.3.4 show the average estimated markups for electric and gas-fired water heaters, respectively. Themarkup includes the average national value fortaxes of5.20% (A.D.L., 1998). Note that the retail prices are calculated using an exact value forthe multipliers. Table 5.3.3 Electric Water Heaters
- Markup Rated Volume Manufacturer Cost Retail Price Markup ($) ($)________ 30-gal 117.78 165.72 1.41 40-gal 122.73 168.70 1.37 50-gal 125.56 188.18 1.50 65-gal 129.43 375.65 2.90 80-gal 132.95 399.32 3.00 Table 5.3.4 Gas-fired Water Heaters
- Markup Rated Volume Manufacturer Cost Retail Price Markup ($) ($) 30-gal 134.46 153.31 1.14 40-gal 137.61 157.74 1.15 50-gal 139.84 205.42 1.47 75-gal 145.11 475.88 3.28 AnalyticBaseline As explained in the Engineering Report, the HCFC-141b blowing agent currently in use will be replaced by 2003. This report assumes thatthe new blowing agent will be HFC-245fa. The analytic baseline model developed for this analysis utilizes foam insulation blown with HFC-245fa. The assumed costs forthe insulation components forboth blowing agents are shown in Table 5.3.5. The total cost perpound offoam with the newblowing agent is $1.32 as compared to $1.00 forfoam blown with HCFC-141b. Additionally, as also discussed in the Engineering Report, for health and safety reasons, future gas-fired water heaters must be able to resist ignition offlammable vapors. The new analytic baseline model for gas-fired water heaters includes the cost ofdesign changes to prevent ignition offlammable vapors. All ofthe following discussions are based on the analytic baseline models. The rated tank volumes ofthe analytic baseline models are the same as the tank volumes ofthe existing baseline models. -33-Table 5.3.5 Insulation Components Cost Foam Components Fraction Component Cost Cost(141b) Cost (245fa) (%) ($/lb) ($/lb) ($/lb) Blowing agent (141b) 13 1.50 0.20 Bowin ant (245a 13 4.00 0.52 Isocyanurate 51 0.75 0.38 0.38 

### Polyols 31 0.65 0.20 0.20 Catalysts, refractants, etc. 5 4.50 0.22 0.22 Total 100 1.00 1.32 Source: Williams, 1998' 4. Design Options The incremental manufacturing costs for the design options were supplied primarily by GAMA. GAMA did notprovide data for 2.5 " Jacket Insulation forelectric waterheaters, 2.5" Jacket Insulation, Plastic Tank, and Side Arm Heater for gas-fired, nor any ofthe design options for oil-fired water heaters. The missing data was supplemented byinformation obtained from consultants M. Minnear and E. West'5
. LBNL recalculated the costs ofthe insulation and the sheet metal to reflect the characteristics ofthe HFC-245fa blowing agent. DesignOption Combinations.As shown in Appendix F ofthe Engineering Report, many combinations ofdesign options were initially analyzed. Most ofthe selected designs consist of combinations ofbasic design options. The Engineering Report gives a detailed explanation ofthe selection ofdesign option combinations and the payback calculations. Energy costs forordering and combining design options for allthree fuel types were based onAEO's national average energy prices for theyear 2003. A list ofdesign option combinations is shown in Table 5.3.6 for electric water heaters and in Table 5.3.7 for gas-fired water heaters. Table 5.3.6 Design Option Combinations for LCC Analysis
- Electric Water Heaters # Design Option Combinations 0 Typical Analytic Baseline 1 0 + Heat Traps 2 1+ 2" Jacket Insulation 3 1+ 2.5" Jacket Insulation 4 3+ Plastic Tank 5 3+ Insulated Tank Bottom

-34-Table 5.3.7 Design Option Combinations for LCC Analysis
- Gas-fired Water Heaters # Design Option Combinations 0 Typical Analytic Baseline 1 Heat Traps 2 1+ 2" Jacket Insulation 3 2 + 2.5" Jacket Insulation 4 3 + Side Arm Heater 5 2 + Improved Flue Baffle For each design option combination, the incremental variable and fixed costs were developed from the costs ofeach design component. The uncertainty ranges ofthe incremental total costs for most ofthe design options were provided byGAMA. Some ofthevariations (2.5" Jacket Insulation, Plastic Tank, and Side Arm Heaters) were developed using the rangesprovided by M. Minniear and E. West. Since the uncertainty values were provided for the existing models, the next step was to recalculate the data tobe applicable for the design options based on the analytical model. Incremental ManufacturingCosts The LCC analysis uses individual design options that are then grouped together in combinations ofdesign options according to the resultsofthe Engineering Analysis. This analytic procedure requires incremental manufacturing costs ofindividual design options. The distributions ofthe manufacturing costs formost design options were provided by GAMA as cumulative frequency tables. GAMA data only applied to 50-gal electric water heaters and to 40-gal gas-fired water heaters. This datais used as abasis for the development of the incremental manufacturing costs. Table 5.3.8 for electric water heaters and Table 5.3.9 for gas-fired water heaters show a schematic view ofthe methodology used in the development. A detailed explanation ofthe procedure is presented in Appendix B ofthis report. The general methodology is as follows: 1)GAMA distributions ofthe manufacturing cost for each design option (aside from the existing baseline) are adjusted for HFC-245fa foam by adding or subtracting the cost ofthe foam. 2) The GAMA distributions ofthe manufacturing cost for the other standard sizes are adjusted by adding or subtracting the cost ofextra foam and extra sheet metal. No size adjustments forcosts ofthe Plastic Tank or Insulated Tank Bottom design options were made. 3) The distributions ofthe manufacturing cost forthe design options not provided by GAMA are based on distribution ranges provided by LBNL consultants.

-35-Table 5.3.8 Electric Water Heaters
- Incremental Manufacturing Costs for Separate Design Options and Standard Sizes Design 30-gal 40-gal 50-gal 65-gal 80-gal Option Existing GAMA Level 1 GAMA Level 1 GAMA Level 1 GAMA Level 1 GAMA Level 1 Baseline

- (change tank size)
- (change tank size) + (change tank size) + (change tank size) Analytic GAMA Level I GAMA Level 1 GAMA Level 1 GAMA Level 1 GAMA Level I Baseline

- (change tank size)

- (change tank size) + (HFC-245fa) + (change tank size) + (change tank size) + (HFC-245fa) + (HFC-245fa) + (HFC-245fa) + (HFC-245fa) Heat Traps GAMA Level 2
- GAMA Level 2
- GAMA Level 2
- GAMA Level 2
- GAMA Level 2
- Level 1 Level 1 Level 1 Level 1 Level 1 2"Jacket GAMA Level 3
- GAMA Level 3
- GAMA Level 3
- GAMA Level 3
- Level GAMA Level 3
- Level 1 Insul Level 1- (change tank Level 1- (change tank Level 1+(HFC-245fa) 1+(change tank size) + (change tank size) size) size) + (HFC-245fa) + (HFC-245fa) + (HFC-245fa) + (HFC-245fa) 2.5" Jacket scale 2" Jacket Insul scale 2" Jacket Insul scale 2" Jacket Insul scale 2" Jacket Insul scale 2" Jacket Insul Insul Plastic Tank Plastic Tank Plastic Tank Plastic Tank Plastic Tank Plastic Tank (from M. Minniear) (from M. Minniear) (from M. Minniear) (from M. Minniear) (from M. Minniear) Insul Tank GAMA Level 6
- GAMA Level 6
- GAMA Level 6
- GAMA Level 6
- GAMA Level 6
- Bottom Level 1 Level 1 Level I Level 1 Level 1 Note: GAMA levels for electric water heaters: Level I

- Baseline Level 2
- Heat Traps Level 3
- 2"Jacket Insulation Level 6
- Insulated Tank Bottom

-36-Table 5.3.9 Gas-Fired Water Heaters
- Incremental Manufacturing Costs for Separate Design Options and Standard Sizes Design Option 30-gal 40-gal 50-gal 75-gal Existing Baseline GAMA Level 1 GAMA Level 1 GAMA Level 1 GAMA Level 1

- (change tank size) + (change tank size) + (change tank size) Analytic Baseline GAMA Level 1 GAMA Level 1 GAMA Level 1 GAMA Level 1

- (change tank size) + (HFC-245fa) + (change tank size) + (change tank size) + (HFC-245fa) + (flammable vapor) + (HFC-245fa) + (HFC-245fa) + (flammable vapor) + (flammable vapor) + (flammable vapor) Heat Traps GAMA Level 2
- Level 1 GAMA Level 2
- Level I GAMA Level 2
- Level 1 GAMA Level 2
- Level 1 2" Jacket Insul GAMA Level 3
- Level 1 GAMA Level 3
- Level 1 GAMA Level 3
- Level 1 GAMA Level 3
- Level 1

- (change tank size) + (HFC-245fa) + (change tank size) + (change tank size) + (HFC-245fa) _+ (HFC-245fa) + (HFC-245fa) 2.5" Jacket Insul scale 2" Jacket Insul scale 2" Jacket Insul scale 2" Jacket Insul scale 2" Jacket Insul Side Arm Heater Side Arm Heater Side Arm Heater Side Arm Heater Side Arm Heater (from M. Minniear) (from M. Minniear) (from M. Minniear) (from M. Minniear) Electronic GAMA Level 6
- Level 1 GAMA Level 6
- Level 1 GAMA Level 6
- Level 1 GAMA Level 6
- Level 1 Ignition (IID)* Improved Flue GAMA Level 5

- Level 1 GAMA Level 5

- Level 1 GAMA Level 5

- Level 1 GAMA Level 5

- Level 1 Baffle____ *Although IID isincluded as a separate design option in this table, it is only used in conjunction with a Side Arm Heater. Note: GAMA levels forgas-fired water heaters: Level I

-Baseline Level 2
- Heat Traps Level 3
- 2" Jacket Insulation Level 5

- Improved Flue Baffle Level 6
- Electronic Ignition (IID)

-37-Table 5.3.10 lists the incremental costs forthe individual design options for the typical 50-gal electric water heater. Table 5.3.10 Incremental Costs for Electric Water Heaters (50-gal) Design Options Average Incremental Manufacturing Cost 

### ($) Heat Traps 6.68 2" Jacket Insulation 24.41 2.5" Jacket Insulation 43.01 Plastic Tank 27.93 Insulated Tank Bottom 32.89 Figure 5.3.11 shows the distribution ofthe incremental manufacturing costs ofseparate design options for the 50-gal electric water heater.

-38-Incremental Manufacturer Cost of HeatTraps Incremental Manufacturer Costof 2" Jacket Insulation 5000 4000 5000

. l 

### e 4000 30003000 C 2000 2000
. | I 1000

- 1000

00008~88~~8 0000000000 $ $

Incremental Manufacturer Costof2.5 Jacket Incremental Manctrer CostofPlastic Tank Insulation 12000 2500 10000 200 2000 8000 1500 6000 1000

- I 4000 U 500 2000 00000000000 00000000000

- )ooooooo Coo0oCUo ooooo ooo oo $ $

Incremental Manufacturer Costof Insulated Tank Bottom 4000 3000 2000 I 1000

Figure 5.3.11 Distribution ofIncremental Manufacturing Cost for Separate Design Options for Electric Water Heaters

-39-Table 5.3.11 lists the incremental costs forthe individual design options for the typical 40-gal gas-fired water heater. Table 5.3.11 Incremental Costs for Gas-fired Water Heaters (40-gal) Design Options Average Incremental Manufacturing Cost ($) Heat Traps 2.38 2" Jacket Insulation 16.41 2.5" Jacket Insulation 27.76 Side Arm Heater w/ nD 7.18 Improved Flue Baffle 108.11 Figure 5.3.12 shows the distribution ofthe incremental manufacturing cost ofseparate design options forthe 40-gal gas-fired water heater.

-40-Incremental Manufacturer Costof HeatTraps Incremental Manufacturer Cost of 2' Jacket Insulation 10000 S" & 5000 18° 600_0 !] 6000 8 600 0 |8 l 4004000 o 4000 3000 u . 2000 2000 00000000000 00000000000 $ $

Incremental Manufacturer Cost of 2.5"Jacket Incremental Manufacturer Costof Side Arm Insulation Heater and ID 5000 4000 » 4000 3000

3000 2000 1000 a. U 1000 1000

> 8000 6000 2 4000 I 2000-_
$ u 100g 0 10 0

Figure 5.3.12 Distribution ofIncremental Manufacturing Costs for Separate Design Options for Gas-Fired Water Heaters

-41-VariableManufacturingCost. The variable manufacturing cost for each design option is calculated asthe sum ofthe analytic baseline manufacturing cost plus the associated incremental variable manufacturing cost for that design option. The incremental variable manufacturing cost is the sum ofthe incremental material, labor, and overhead cost to produce the design option. The typical analytic baseline variable manufacturing costs andthe incremental variable costs for design options used in the analysis for electric water heaters are presented in Table 5.3.12 and forthe gas-fired water heaters in Table 5.3.13. These costs come from the Engineering Report.Asmentioned earlier, for health and safety reasons, future gas-fired water heaters must resist flammable vapor ignition. Because ofthis, the variable manufacturing cost for the analytic baseline model includes a cost of$15 for a design to prevent ignition offlammable vapors. Since the added variable cost is included in the typical analytic baseline design, it does not impact the cost-effectiveness ofany design improvement. Note that the incremental insulation costs for thebaseline electric water heatertank (50-gal) are lower than for gas-fired (40-gal), because the insulation forthe baseline electric water heater tank is 1.5 inches thick compared tol inch for the baseline gas-fired tank. Table 5.3.12 Electric Water Heater 50-gal)
- Variable Cost Data Design Options Average Variable Costs Material Labor Overhead Total 

### ($) ($) ($) ($) 0 Analytic Baseline 64.30 12.41 50.99 127.70 1 0 + Heat Traps 2.59 0.20 0.83 3.62 2 1+ 2" Jacket Insulation 8.59 0.51 3.66 12.76 3 1+ 2.5" Jacket Insulation 14.41 1.02 7.32 22.75 4 3+ Plastic Tank 5.25 0.80 3.20 9.25 5 3 + Insulated Tank Bottom* 0.00 0.00 0.00 26.98 *GAMA provided only total incremental costs.

-42-Table 5.3.13 Gas-fired Water Heater (40-gal)
- Variable Cost Data Design Options Average Variable Costs Material Labor Overhead Total 

### ($) ($) ($) ($) 0 Analytic Baseline 91.13 12.49 50.10 153.72 1 0 + Heat Traps 2.75 0.16 0.21 3.12 2 1+ 2" Jacket Insulation 9.59 0.60 4.93 15.12 3 1+ 2.5" Jacket Insulation 14.49 1.20 9.86 25.55 4 3 + Side Arm Heater 68.28 5.38 26.02 99.68 5 2 + Improved Flue Baffle 0.97 1.29 1.32 3.58 FixedManufacturingCost. The fixed component ofthemanufacturing cost is the cost to convert the production line tomanufacture anew water heater design. Some ofthe fixed costs used in the analysis were submitted by GAMA; the consultants provided therest ofthe fixed costs. The fixed cost is the sum ofthe capital cost and theproduct design cost. Production volume has a significant impact onthe perunit conversion cost, particularly on the capital cost. GAMA did not provide the range ofproduction volume usedto calculate the fixed costs, because ofthe need toprotect specific manufacturer responses. Thefixed manufacturing cost for each design option isthe sum ofthe incremental capital cost and the incremental product design costto produce the design option. The incremental fixed manufacturing cost data used in the analysis for electric water heaters ispresented in Table 5.3.14 and for the gas-fired water heaters in Table 5.3.15. The fixedmanufacturing cost for the gas-fired analytic baseline model includes a capital cost for a design toprevent ignition offlammable vapors. Since the added fixed cost is included inthe typical analytic baseline design, it does not impact the cost-effectiveness ofany design improvement. The assumed fixed cost of$20.00 for the ignition prevention design forgas-fired water heaters is included in the data for the analytic baseline model in Table 5.3.15. No attempt was made to disagregate the $20.00 between capital and product design costs. Note that GAMA provided both capital and product design costs for 2" insulation for gas-fired water heaters, but only atotal fixed cost for electric water heaters.

-43-Table 5.3.14 Electric Water Heaters (50-gal)- Fixed Cost Data Design Options Average Fixed Costs Capital Cost Product Design Total ($) ($) ($) 0 Analytic Baseline 0.00 0.00 0.00 1 0 + Heat Traps**
- -- 0.39 2 1+ 2" Jacket Insulation**

- - 0.73 3 1+ 2.5" Jacket Insulation* -- -- 1.02 4 3 + Plastic Tank* 15.00 3.00 18.00 5 3+ Insulated Tank Bottom** -- - 3.39 *design options 3 &4 are adjusted based on data from M. Minniear **GAMA provided only total incremental costs.
Table 5.3.15 Gas-fired Water Heaters (40-gal)
- Fixed CostData Design Options Average Fixed Costs Capital Cost Product Design Total ($) () ($)($) 0 Analytic Baseline* 20.00 0.00 20.00 1 0 + Heat Traps 0.07 0.13 0.20 2 1+ 2" Jacket Insulation 0.85 0.59 1.44 3 1+ 2.5" Jacket Insulation ** 1.28 1.18 2.46 4 3+ Side Arm Heater** 6.34 3.49 9.83 5 2 + Improved Flue Baffle 1.17 1.72 2.89 *with flammable vapor resistant design **design options 3 &4 are adjusted based on data from M. Minniear OtherStandard Sizes
- ManufacturingCost. The typical analytic baseline models represent the common size water heaters with an efficiency equal to the minimum allowed by the existing energy efficiency standards. These units have the largest market share in their product class. Other standard water heater sizes are manufactured in addition to the typical size. The methodology used to select water heaters with rated volumes other than the typical size is explained in Section 5.1 ofthis report. The manufacturing costs for all sizes were -44-

### estimated from the variable manufacturing cost forthe typical existing baseline water heaters by adding or subtracting the cost ofincremental amounts ofinsulation and sheet metal. It was assumed thatthere would be no differences inthe fixed manufacturing costs forother size water heaters. The variable manufacturing costs for Heat Traps, Plastic Tank, and Insulated Tank Bottom for electric water heaters, and SideArm Heater and Improved FlueBaffle for gas-fired water heaters, were assumed to bethe same for all sizes. Thevariable manufacturing cost data used inthe analysis for electric waterheaters are presented inTable 5.3.16 and for the gas-fired water heaters in Table 5.3.17. Table 5.3.16 All Standard Sizes Variable Manufacturing Cost
- Electric Water Heater Design Options 30-gal 40-gal 50-gal (typical) 65-gal 80-gal ($) ($) ($) ($) ($) Existing baseline 117.78 122.73 125.56 129.43 132.95 Analytic baseline 119.29 124.67 127.70 131.86 135.63 2"Jacket Insulation 11.96 12.53 12.76 13.09 13.38 2.5" Jacket Insulation 21.01 22.25 22.75 23.44 24.05 Note: Costs ofincreasedjacket insulation are presented asincremental variable manufacturing costs and are based on the typical analytic baseline. 

### Table 5.3.17 All Standard Sizes Variable Manufacturing Cost
- Gas-fired Water Heater Design Options 30-gal 40-gal (typical) 50-gal 75-gal _($) 

### ($) ($) ($) Existing baseline 134.46 137.61 139.84 145.11 Analytic baseline 150.40 153.72 156.06 161.59 2" Jacket Insulation 14.41 15.12 15.55 16.62 2.5" Jacket Insulation 24.47 25.55 26.21 27.82 Note: Costsofincreasedjacket insulation are presented as incremental variable manufacturing costs and are based on the typical analytic baseline. 

### As explained inthe Engineering Report, multiple design optionswere developed for each water heater fuel type. Markup forDesign Options 

### The manufacturer-to-retail markupwas assumed toremain constant forall ofthe design options within a standard size model. Thus,theretail price forany design was determined simply bymultiplying its manufacturer cost bythe derived markup for the existing baseline water heater ofthat size.

-45-5.3.5 Results Electric Water HeaterEquipment Costs Table 5.3.18 lists the average manufacturing and total installed cost for the analytic baseline and the design option combinations for all sizes ofelectric water heaters, where total installed cost is the final total cost to the customer, i.e., the sum ofthe retail price, salestax, and any installation cost. Table 5.3.18 Equipment Costs for Electric Water Heaters (All Sizes) Design Options Average Manufacturing Average Total Installed 

### Costs ($) Costs ($) 0 Analytic Baseline 121.13 345.09 1 0 + Heat Traps 127.81 355.58 2 1+ 2" Jacket Insulation 148.43 388.35 3 1+ 2.5" Jacket Insulation* 163.97 413.08 4 3 + Plastic Tank 191.90 456.98 5 3 + Insulated Tank Bottom 196.86 464.68 Figure 5.3.13 shows, foreach design option and for all standard sizes,the difference in total installed cost compared tothe analytic baseline forelectric water heaters. Variations in total installed cost include variations in manufacturing cost, mark-up, and installed cost. In general, design options with higher efficiencies have a wider spread in total incremental installed cost. Note that Table 5.3.18 shows average manufacturing cost and average total installed equipment cost, while Figure 5.3.13 shows the spread ofthe incremental total installed cost.

-46-DeltaTotal Installed Cost ofHeat Trap Water Delta Total Installed Cost of2" Jacket Insulation Heater compared toAnalytic Baseline (1998$) Water Heatercompared toAnalytic Baseline (1998$) 1 0000
- 100% 80D00 80% I 4000 -** * 100% 6000 6 3000 80% 2 I8i6000 1 W

% 1 ! l~o: jf 60%
_ 0 ' 40 4 000 0% E 0% 40%~ 20% ' 2000 20% 5 O 0% E

.- N N N > N S $ $

DeltaTotal Installed Cost of 2.5' Jacket Delta Total Installed Cost ofPlasticTank Water Insulation Water Heater compared to Analytic Heatercompared to Analytic Baseline (1998$) Baseline (1998S) 2500 - ***** 100% 3000 100% 2000 80% 2500 80% s E 1500 I 60% 1 2000 

# i

~ m

* sM150~ -60% ~ 1000 40% '4 1500 

### IF I 40% 500 20% 3 .1000 20% 0 - 0% 0 500 aN0 _ : 0%

Delta Total Installed Cost ofTank Bottom InsulationWater Heatercompared to Analytic Baseline (1998S)

C5~~~~~~~ 60% 1000 0% u '500 fi 8~~40% 2 500 20% g 0 0 %



### _ doa 

### NI 11,111 ,j $ Frequency a Cumulative % Figure 5.3.13 Difference in Total Installed Costby Design Option for Electric Water Heaters

-47-Gas-fired WaterHeaterEquipment Costs Table 5.3.19 lists the average manufacturing and total installed cost forthe analytic baseline and the design option combinations for all sizes ofgas-fired water heaters, where total installed cost isthe final total cost to the customer, i.e., retail price, sales tax, and any installation cost. Table 5.3.19 Equipment Costs forGas-fired Water Heaters (All Sizes) Design Options Average Manufacturing Average Total Installed 

### Costs ($) Costs ($) 0 Analytic Baseline 175.56 385.76 1 0 + Heat Traps 177.94 388.86 2 1+ 2" Jacket Insulation 194.50 411.47 3 1+ 2.5" Jacket Insulation 205.93 427.04 4 3 + Side Arm Heater w/IID 314.05 602.15 5 2 + Improved Flue Baffle 201.67 530.50 Figure 5.3.14 shows, for each design option and all standard sizes, the difference in total installed costs compared to the analytic baseline for gas-fired water heaters. Variations in total installed cost include variations in manufacturing cost, mark-up, and installed cost. In general, design options with higher efficiencies have awider spread in total incremental installed cost. Note that Table 5.3.19 shows average manufacturing cost and average total installed equipment cost, while Figure 5.3.14 shows the spread ofthe incremental total installed cost.

-48-Delta Total Installed Cost ofHeat Trap Water Delta Total Installed Cost of2' Jacket Insulation Heater compared toAnalytic Baseline (1998$) Water Heatercompared toAnalytic Baseline (1998$) 12000 100% 10000 80% I 8000 - ------------100% 8000 600 80% 6 606000 | 

### - 60% 4000 400 40% U- 2000 20% o E 2000 20% °0 ... 8 |. 80% 0% - .. $ $

Delta Total Installed Cost of2.5' Jacket i Delta Total Installed Costof Side-Arm Heater Insulation Water Heater compared toAnalytic I WaterHeatercompared toAnalytic Baseline Baseline(98 (1998) 99$) 6000 -....-- u.. 100% 1500
- 100% 5000 1 80% 100 8% 4S000 ; 40000 160% 100 60% 12000 0 40% I fzooo| E o 1500 !_ - 0 % I O 0% '; 10(o M - ___M + 0 g ° , M. S $

Delta Total Installed Costof Improved Flue Baffle

Water Heater compared to Analytic Baseline (1998$) 8000 ------ 100% g 6000 - 80% S 60% i |4000 10%

2000 0% 0 0% $

= Frequency _ Cumulative % Figure 5.3.14 Difference in Total Installed Costs by Design Option for Gas-fired Water Heaters

-49-5.4 Operating Cost Module 5.4.1 Introduction to Operating Cost Module. Operating a waterheater involves two costs. A residential consumer pays for fuel to operate the water heater and formaintenance tokeep the water heater running properly. Fuel costs depend on the waterheater energy usage and the per unit cost offuel. Maintenance costs depend on water heater design. There are four types offuel commonly used in residential water heaters--electricity, gas, liquefied petroleum gas (LPG or propane), and distillate fuel (oil). Depending onthe particular type ofwater heater, more than one type offuel may be used in its operation. Forinstance, electric water heaters use only electricity, whereas gas-fired water heaters use gas (orLPG) plus electricity for some designs. Future fuel costs will vary from house to house. There are two primary factors that contribute to this variation. One isthe existing variability in energy price, which depends on the rate schedule charged by the utility andthe consumption pattern ofthe particular household. The other is theuncertainty offuture energy prices' 6
. The uncertainty in the future trend ofprices is further complicated bythe current restructuring ofthe electricity supply industry. To deal with the variations in energy prices, the fuel rates reported in energy bills ofthe sample in the 1993 RECS are used to represent the variability ofenergy price from house to house. To account for future uncertainties, various scenarios ofprojected future energy prices (trends bynational average) are applied to each household's energy price. Four possible fuel price scenarios are built into the LCC calculations. They are: EIA Annual Energy Outlook 1998, High Economic Growth EIA Annual Energy Outlook 1998, Reference Case EIA Annual Energy Outlook 1998, Low Economic Growth GRI 1998 Baseline Projection

Other scenarios will be considered in the analysis as they become available. Figures 5.4.1, 5.4.2, 5.4.3, and 5.4.4 show the trends for the projected future prices foreach ofthe four fuel prices, namely, electricity, gas, LPG, and oil,respectively.

-50-U.S. Average Residential Electricity Price - Four Scenarios 10 9 

# {, 0) 8

S 6 - GR°IM 5 D _LOw Growth

1995 2000 2005 2010 2015 2020 year Figure 5.4.1 Electricity Price Scenarios U.S. Average Residential Natural Gas Price - Four Scenarios

7

U ; AEO 1N8 'OOW. 45 6J GRIexmIc

4 1995 2000 2005 2010 2015 2020 year Figure 5.4.2 Gas Price ScenariosU.S. Average Residential LPG Price - Four Scenarios 1.40,

-1.00 - .20 i 0.80

0202 - mLowGro1th
year Figure 5.4.3 LPG Price Scenarios U.S. Average Residential Oil Price - Two Scenarios

- 

### 7

GRI1986 _GRI . e.xtd 'C -DOTHEO INS 1995 2000 2005 2010 2015 2020 year Figure 5.4.4 Oil Price Scenarios The figures show that all electricity price projections share a declining pattern, while the price projections for gas and LPG are more varied. Oil prices remain relatively flat. After adjusting for inflation and energy price changes, energy prices for the RECS households are scaled from the starting year by the projected average future energy prices. Thus each sampled house from RECS has four different future annual energy price series associated -52- Fiue544Ol8rc cnro

The~~~~~~~~~~~~~~~~~~~=. fogre show .htaleetiiypiepo._tin share a elnn aten hlh price projections for gas and LPG are more varied~~~~~~~~. a. Oil prices remainrelatively.f.at
After adjusting for ,= 'nfltio and' enrg :rc chngs enrg prcs frtewith it. Future annual operating costs are estimated as annual energy use multiplied by the annual energy price series for each ofthe four scenarios. Section 5.4.4 gives a detailed description ofhowthe calculation is implemented inthe spreadsheet models. When a consumer saves electricity, thebill savings depend upon the marginal energy charge as reflected in the utilityrate schedule (cents per kilowatt-hour), which may be higher or lower than the average rate. An exact accounting would require knowing foreach household: the quantity and timing ofenergy used with and without the saved energy, and the rate schedule (rate per kilowatt-hour as afunction ofthe quantity ofkilowatt-hours used, including seasonal and/or time-of-day pricing). In general, such detailed information isnot known. Three approaches are considered: I) average rates, calculated as the ratio ofhousehold expenditures for electricity (including fixed charges) tokWh consumed; 2) partial adjustment ofknown inaccuracies by subtracting the average fraction corresponding to fixed charges from average rates; and 3) estimating the actual consumer marginal energy rate. We review the advantages and disadvantages ofeach ofthese approaches below: a) Average rates. Advantage: Simple. Available in published historical data and forecasts. Disadvantage: May over- or under-estimate the consumer marginal energy rate. b) Subtract average fixed charge everywhere. Advantage:Approximately accounts for fixed charges. Edison Electric Institute (EEI) has assembled information on fixed charges foraverage general service residential rates for a large number ofutilities that show fixed charges on average represent about 7.5% ofaverage rates).'7 Disadvantage: Byreducing the value ofenergy savings in all cases, including those where the marginal rate is higher than the average price including fixed charges, thismethod under-estimates the actual consumermarginal energy rate in some cases. c) Estimate distribution ofconsumer marginal energy rates. Advantage:Theoretically most accurate. Disadvantage:Practical difficulties: The rate schedules for households in the RECS survey are not known. Assignment to utility service territories and to rate schedules would need to be imputed. Month by month electrical consumption wouldbe needed to determine the monthly marginal rate. Rate schedule data does not exist for all utilities and, when available, is usually limited to general service residential customers. Average rates are assumed in this analysis even though it isrecognized thatthe use of marginal energy rates would improve the accuracy ofthe analysis. At this time, however, the data needed to determine marginal rates is not readily available. Moreover, inasmuch as it is unknown at this point ifremoving fixed costs ismore or less reflective ofmarginal rates, this intermediate -53-step is nottaken in this analysis. In order to develop consumer marginal energy rates, the Department proposes to collect data on currentrate schedules and energy consumption. Those rates will be assigned to a national sample ofbuildings and households, weighted to represent the total U.S. population of buildings and households. The result will be a weighted distribution ofconsumption by marginal rates. This approach will be applied to residential and commercial customers. DOE proposes to obtain a sample ofresidential buildings from existing surveys, such as the RECS or from acommercially available database. RECS data hasthe advantage ofbeing in the public domain. In contrast, acommercially available database is likelyto be more expensive, but mayhave significant added value interms ofassigning thebuildings to states or to utilities, including abroader sample ofthe population, and permitting stratification ofthis larger sample to distinguish among some sub-populations. Each building will be assigned to a geographic region (e.g., state or utility service territory). Energy consumption bymonth will be included in the database foreach building, in order to treat seasonal changes in consumption andrates. Peak demand will be included forcommercial buildings. Recent Federal surveys (RECS, Commercial Building Energy Consumption Survey (CBECS)) gather information byfuel on annual energy consumption and total expenditures. Total expenditures included customer and other fixed charges, energy rates, demand charges, taxes, etc., but these were not tabulated separately from each other. These surveys gathered customer billsbut did not extract information onrate schedules, fixed charges, or marginal rates. The Department proposes to explore the feasibility ofextracting historical information on rate schedules, including the relationship between fixed charges and marginal rates to average prices. This effort, ifsuccessful, will provide information about the extent to which marginal rates differ from average prices, or from average prices less fixed charges. Given restructuring ofpartsofthe energy supply sector, customers may have more than one bill (e.g., one from the distribution company, and one or more from generators or suppliers). To capture complete information, future surveys are expected to gather energy-pricing information directly from customers, rather than from utilities or local distribution companies. The most efficient means to collect energy-pricing information inthe future involves changing the current processing ofthe billing information so as to gather more detail from the bills, to include consumption bymonth andpricing information. The pricing information would include for each customer, the rate schedule, marginal rates, fixed charges, demand charges for commercial and industrial customers, or time-of-use rates where applicable. The Department will express the need for these data in discussions with EIA about the design offuture surveys. Residential electricity rate schedules will be collected from Federal databases where available, state regulatory agencies ordirectly from utilities. The information obtained foreach rate schedule will include any fixed charges (customer charges, etc.), block structure, and rate per kilowatt-hour by block. Information from utilities or local distribution companies will be examined to determine: confirmation ofthe setofrate schedules, the number ofcustomers by -54-

### state using each rate schedule, the total electricity sales by state by rate schedule, and (ifpossible) monthly electricity sales by state byrate schedule. Inthe database ofbuildings, such characteristics as energyconsumption and expenditures andnumber ofcustomers by state orutilitywill be used to map a rate schedule onto each ofthe buildings inthe national sample. The marginal rate foreach building will bethe block from the rate schedule corresponding tothatbuilding's monthly energy consumption. For life-cycle savings calculations, the monthly energy savings will be estimated for each building. Those monthly energy savings for eachbuilding willthen be evaluated for each building atthe monthly marginal rate, using the rate schedule assigned to each building. 5.4.2 Equations for Operating Cost Module A generalized equation that describes the operating costs ofall three types ofwater heaters-- electric, gas-fired, and oil-fired -- canbe expressed as follows:

OprCost . - AnnuaIQa,-,T,,rPd.f x FutrPrice e + MaintCost year,optons Energv7Tpe-elecgas.oilAn Ener peopn P +Main



### Foreach particular type ofwaterheater, the generic formula shows different specific forms. A. Equations for Electric Water Heater Operating CostModule

OprCostyear.oio n = AnnualQin 0 oo n x FutrElecPriceye 

### and

FutrElecPriceyear= ElecPrice 9g x EleclncrRatio yea 

### and

ElecPrice 9 8 = ElecRate x Inflator93 x ElecScaler 

### where: -55-AnnualQin = average annual electricity consumption (kWh/year) FutrElecPrice = future price ofelectricity in 1998$ (0/kWh) ElecPrice98 = revised RECS house electricity price in 1998$ (0/kWh) ElecIncrRatio = ratio offuture electricity price to 1998 price ElecRate = RECS-reported electricity price in 1993$ (¢/kWh) Inflator93 = an inflation factor to convert 1993$ to 1998$ ElecScaler = a conversion factor for electricity price change that is different from inflation. It is the ratio ofthe average real electricity price in 1998 to that in 1993 in constant dollars.

B. Equations for Gas and LPG Water Heater Operating Cost Module. OprCost,,.,a = AnnualQelecc,.x FutureElecPricer+ AnnualQgaso.xFutrFuelPricee,.,,, +MaintCosto,, and

FutrElecPriceyea, =ElecPrice 9 8 x EleclncrRatioyear FutrFuelPriceEnergyTypeyear= FuelPrice9sx FuellncrRatioEnergyTypeyear and

FuelPrice98 =FuelRate x Inflator93 x GasScaler and

ElecPrice 9 g =FuelRate x Inflator93 x ElecScaler and, ifEnergyType = LPG, then -56-FuelPrice98 = FuelRate x Inflator93 x LPGScaler where additionally: AnnualQelec = annual electricity consumption (kWh/year) AnnualQgas = annual gas consumption (MCF/year') FutrFuelPrice = future price ofwater heating fuel($/MCF) FuelPrice98 = revised water heating fuel price ($/MCF) FuelIncrRatio = ratio offuture water heating fuel price to 1998 price FuelRate = RECS house water heating fuel rate in 1993$ ($/MCF) Inflator96 = an inflation factor to convert AEO and GRI energy prices to 1998$ Inflator93 = an inflation factor to convert RECS house energy price to 1998$ ElecScaler = a conversion factor forreal electricity price change GasScaler = aconversion factor for real gas price change LPGScaler = a conversion factor for real LPG price change 5.4.3 General Description ofKey Variables AnnualQin is the average annual energy consumption, i.e., the total amount ofenergy consumed by the water heater during the process ofheating water and keeping ithot. For electric water heaters this is in kWh/yr. For fuel fired water heaters this is in Btu/yr.

Note: MCF denotes thousands ofcubic feet. Wherever LPG is also applicable, the corresponding unit is gal/year.
-57-AnnualQelec is the annual electricity consumption used by the electronic ignition system and/or the electromechanical flue damper in a gas-fired water heater. AnnualQgas is the annual gas or LPG consumption ofthe water heater (MCF/year) FuelRate is the price ofwater heating fuel for the household as reported in RECS (in 1993$). The fuel price is defined as the average price per unit fuel (MCF) recorded. In the electric water heater spreadsheet model, FuelRate is ElecRate. ElecRate is the price ofelectricity for thehousehold as reported in RECS (in 1993$). The electricity price is defined asthe average priceper unit electricity (kWh) consumed. The analysis averages any seasonal fluctuations in the price ofelectricity. Inflator93 adjusts the RECS household energy price (1993$) to reflect 1998 dollars, using the Consumer Price Index (CPI). The analysis assumes that the average annual rate ofinflation for 1998 will equal the average rate during the first quarter of 1998. CPI1 99 8

- CPI19 = 1.1251 CPI1993 Inflator96is an inflation factor to convert AEO and GRI energy prices to 1998$ CPI199 8

- - = 1.0362 CI 1996 FuellncrRatio isthe ratio offuture national average water heating fuel price to the 1998 price forthe selected scenario. The year 1998 serves as the base year. FutrFuelPriceisthe price ofwater heating fuel ($/MCF) in each future year. It is calculated as a product ofFuelPrice and FuellncrRatio for aparticular fuel type. EleclncrRatio isthe ratio ofnational average electricity price between some future year and 1998 for the selected scenario. The year 1998 serves as the base year. FutrElecPrice isthe projected household electricity price at aparticular sampled house from RECS for the specified scenario in 1998$.

-58-ElecScaler is a conversion factor forreal electricity price change, represented by the ratio of electricity prices in 1998 to the electricity prices in 1993 in constant dollars. NationalAveragePrice998 = 0.9820 NationalAveragePrice, 9 9 3 GasScaler is aconversion factor forreal gas price change in constant dollars NationalAveragePrice 1 9 98 = 1.0601 NationalAveragePrice 1993
LPGScaler isa conversion factorfor real LPG price change in constant dollars National AveragePrice 1 99 8 = 0.6166 National AveragePrice 1 993 FuelPrice, isthe revised gas-fired waterheating fuel price ($/MCF) in 1998. It takesthe RECS household energy price (FuelRate) and multiplies itby Inflator93 and the corresponding scaler for gas or LPG, respectively. ElecPrice, 8 is the revised electricity price. Ittakes the RECS household electricity price (ElecRate) and multiplies it by the Inflator93 and the ElecScaler to change 1993 dollars to 1998 dollars to account forinflation and electricity price change. MaintCost is the price to repairthe water heater when it fails ($/year). In reality, ifany electric or the baseline gas-fired water heater fails, residential consumers tendtoreplace the entire water heater rather than having the water heater serviced. Therefore, the electric and baseline gas-fired water heaters have no associated maintenance costs. Oil-fired water heaters and burners are cleaned and maintained more regularly and therefore do have maintenance costs. The mean value for the maintenance costs associated with all sizes ofbaseline oil-fired models is $97.14 per year. This meanvalue comes from prices for annual maintenance contracts gathered from telephone conversations with seven oil-fired equipment suppliers in the eastern U.S* . Note that the costs are for a separate contract for a water heater only. Costs may go down significantly if multiple oil-fired appliances are onthe same contract in a household. 5.4.4 General Description ofData Sources and Calculations in Spreadsheets

The data fromthe seven oil-fired equipment suppliers can be found in Appendix G ofthe Engineering Report.
-59-The average annual energy consumption is calculated with the Water Heater Analysis Model (see Section 5.5 for a full discussion ofWHAM) and is an input tothe operating cost module. In the electric water heater model, it represents the annual electricity use ofa water heater (AnnualQin). For water heaters that use more than one type offuel, the annual usage of each type offuel is calculated separately. For instance, in some designs ofgas-fired water heaters, AnnualQin is a sum ofthe annual gas (orLPG) (AnnualQgas) and the electricity consumption (AnnualQelec). Fuel rates as reported in the 1993 RECS are used as abase to capture the variability of fuel prices across the nation. Consumer Price Indexes (CPI) fromthe U. S. Bureau ofLabor Statistics are used to calculate Inflator93that accounts for inflation over the period of 1993 to 1998. Similarly, national average energy prices reported in DOE's Energy Information Administration (EIA)AnnualEnergyReview'8 are used to compute scalers (ElecScaler, GasScaler, and LPGScaler) to take into account real energy price changes since the 1993 RECS survey. Multiplying FuelRate by Inflator93 and then by the corresponding scaler yields the 1998 value ofunit fuel price (FuelPrice) in 1998 dollars for each RECS household. DOE/EIA publishes projections offuture energy prices in itsAnnual EnergyOutlook 1998 (AEO). The projections include three cases: reference, high economic growth, and low growth. The Gas Research Institute also publishes a forecast for future fuel rates (electricity, gas, and oil) in its 1998Editionof the GRIBaselineProjection. These projections show a similar pattern (see Figures 5.4.1, 5.4.2, 5.4.3, and 5.4.4), but vary in magnitude. The four scenarios are used in the analysis to help demonstrate how future energy price trends affect the outcome ofthe analysis. Since the four fuel price projections are reported as 1996 dollars per million Btu, they are converted into appropriate units (cent/kWh for electricity, $/MCF for gas, and $/gal for LPG and oil) and into 1998 dollars (multiplied by Inflator96). The incremental ratios ofthe energy price scenarios are derivedby dividing each year's projected priceby the 1998 price (ElecIncrRatio for electricity and FuellncrRatio otherwise) and applied to the FuelPrice ofeach RECS sample house to represent its future energy prices (FutrElecPrice forelectricity and FutrFuelPrice forother fuels) for the selected scenario. The annual operating costs ofthe water heater are then computed based on the equations described in Section 5.4.2. Two implementation details need to be noted here. One, GRI only projects to the year 2015; in this analysis GRI projections (for all fuels) are extended to the subsequent years (2016
- 2020) by extrapolations based on a linear fit to the available time series data ofeach fuel. Two, GRI did not have a projection for LPG future prices in time to be included in this analysis. It was therefore estimated using the average ratio ofhistorical LPG to oil prices.



### -60-5.4.5 Operating Cost Results 

### Electric WaterHeater OperatingCost Table 5.4.1 liststhe average annual operating cost forthe analytic baseline and design options for all sizes ofelectric water heaters, based on 1993 RECS. The average operating cost savings from the baseline are listed for each design option. Table 5.4.1 Operating Costsfor Electric Water Heaters Design Option Average Annual Average Savings Operating Cost from Baseline 

### ($) ($) 0 Analytic Baseline 292.93 1 0+ Heat Traps 285.05 7.88 2 1+ 2" Jacket Insulation 281.22 11.71 3 1+ 2.5" Jacket Insulation 277.55 15.38 4 3 + Plastic Tank 274.01 18.92 5 3 + Insulated Tank Bottom 275.66 17.27 Figure 5.4.5 presents foreach design option, the difference in operating cost compared to baseline.

-61-Delta Operating Cost in 2003 of Heat Trap Delta Operating Cost in 2003 of2" Jacket compared to Analytic Baseline (1998$) Insulation comparedto Analytic Baseline (1998$) 3500 100% 3000 8 3000 100% 80% 250e 5 2500 80%

2000 60% t 2000_ 60% | 1500 40% ., 1 1000 40% 1000E 500 20% ~0 ' 5E o -- 20% 0
. ; II 0 " 0% S/Year SYear

Delta Operating Cost in 2003 of2.5' Jacket DeltaOperating Cost in 2003of Plastic Tank Insulation compared to Analytic Baseline (19988) compared toAnalytic Baseline (198$) 2500
- -- * 100% 2500
. 100% 2000 80%

. 2000 80 1500 5 15 00.
_ 60% 0% IL 5000 00 0% I 0% o0% I '

I 150 0 S/Year S/Year

Delta Operating Cost in2003 of Tank Bottom Insulationcompared to Analytc Baseline (1998)
2500 - -- 100% 2000 80% r 1500 60% Z

1000 40% E ,t 500 20% 0
- .0% S/Year Frequency

- Cumulative % Figure 5.4.5 Difference in Operating Costs by Design Options for Electric Water Heaters

-62-

### Gas-firedWaterHeater OperatingCosts Table 5.4.2 liststhe average annual operating cost for the analytic baseline and for design options ofall standard sizes ofgas-fired water heaters, based on 1993 RECS data. The average operating cost savings from the baseline are listed for each design option. Table 5.4.2 Operating Costs for Gas-Fired Water Heaters Design Option Average Annual Operating Average Annual Cost Savings from Baseline

________________________ __ ($) ($) 0 Analytic Baseline 159.36 1 0+ Heat Traps 155.12 4.24 2 1+ 2" Jacket Insulation 147.00 12.36 3 1+ 2.5" Jacket Insulation 145.28 14.08 4 3 + Side Arm Heater 126.25 33.11 5 2 + Improved Flue Baffle 143.10 16.26 Figure 5.4.6 shows acumulative frequency plot ofthe difference in operating cost compared tobaseline for gas-fired water heaters.

-63-Delta Operating Cost in 2003 ofHeat Trap Delta Operating Cost in2003 of2' Jacket compared to Analytic Baseline (1998$) Insulationcompared toAnalytic Baseline (1998$) 6000 100% 5000 80% 5000 100% 60% _>i |4000-. | ; g.4000 jf -80% 3000 I | 3000 60% § 2000 40 % a2 40% I U. 20% 1000 20% 0 0% 0 - 0% t P Ir $iP° S/Year $/Year

Delta Operating Cost In2003of 2.5' Jacket Delta Operating Cost In 2003 ofSide-Arm Heater Insulationcompared toAnalytic Baseline (1998$) compared to Analytic Baseline (1998) 2500 100% 4000 100% 2000 . - 0 32000 O80 % a O C I 20003 of Imp40d

Baffle compared toAnalytic Baseline (1998$) 4000 -u 100% 4,300 0- y -80% e 3 20000 0 3



# . 1{ ;' 40% I 0 -S I 0% 5oo ~ear WSIear~S/Year

r-q Frequency BCumulatibe % Figure 5.4.6 Difference inta Operating Costs by Design 2003Options for Gas-Fired FluWater Heaters Baffl-64-e compared toAalytc Baseline (99) 4000 100%
2000 60% -6r ~40%4 U. 1000 20%
$/Year

·r' Frequency · Cumulative % Figure 5.4.6 Difference in Operating Costs by Design Options for Gas-Fired Water Heaters

-64-5.5 Energy Analysis Module 5.5.1 Introduction to Energy Use Residential water heater energy usage can be accurately estimated using a simplified energy equation, the Water Heater Analysis Model. WHAM is a simple energy equation that accounts for avariety ofoperating conditions and water heater characteristics when calculating energy consumption. Three parameters - recovery efficiency (RE), standby heat loss coefficient (UA), andrated input power (Pon)
- are usedto describe the efficiency characteristics ofthe water heater. The operating conditions ofthewater heater are indicated byaverage daily hot water draw volume, inlet water temperature, thermostat setting, and airtemperature around the water heater. WHAM was developed as amethod to quickly andreliably estimate residential water heater energy consumption. Because it iswritten as an equation, itcan be implemented in spreadsheets. It does not require the detailed inputs that other water heater simulation models demand. In each ofthe LCC analysis spreadsheets, water heater energy consumption is calculated for 10,000 different households for both baseline water heaters and all design options being considered. The energy analysis module uses the average daily hot water consumption foreach household calculated by the Hot Water Draw Module. Other key characteristics, such as water temperature for each household, are from the RECS database. The LCC analysis uses RE and UA values from computer simulations developed forthe Engineering Analysis and Pon from manufacturers' product literature to describe the energy performance ofwater heaters. 5.5.2 Equations for Energy Use The WHAM equation,which solves for average daily water heaterenergy consumption (Qi,), is expressed as follows: 

### vol den

### -Cp (Ta nk

- 

### Tn) UA (T Tank- 

### Tamb

# ) in..=P+ 

### 24 UA)

# (T ank 1amb) where: Qin = total water heater energy consumption (Btu/day) RE = recovery efficiency

-65-Pon = rated input power (Btu/hr) UA = standby heat loss coefficient (Btu/hr-°F) Ttn = thermostat setpoint temperature (°F) Tin= inlet water temperature (°F) Tamb= temperature ofthe air surrounding the water heater (°F) vol = volume ofhot water drawn in 24hours (gal/day) den = density ofstored water atthe average ofthe setpoint and inlet temperature (Ib/gal) Cp = specific heatofstored water atthe setpoint temperature (Btu/lb-°F) 5.5.3 General Description ofKey Variables Recovery Efficiency (RE). The recovery efficiency (RE) is the ratio ofenergy added to the water compared to the energy input to the water heater. It represents how efficiently energy is transferred to the water when the heating element is on orthe burner isfiring. RE covers the steady-state efficiency only. Itaccounts forthe amount ofenergy lost through the water heater jacket and the flue and fittings while the heater is firing. Rated InputPower (Pon). Rated input power isthe nominal power rating the manufacturer assigns to aparticular design ofwater heater expressed in kW for electric water heaters or Btu/hr for gas-fired or oil-fired water heaters. For gas-fired waterheaters this includes the pilot light. Standby Heat Loss Coefficient (UA). The standby heat loss coefficient (UA) indicates the water heater hourly standby energy losses expressed in Btu/hr-°F. It is reported in terms of energy inputrequired to maintain the water atthe setpoint temperature. This represents the rate at which energy must be added to the water heater when it isnot heating water for delivery. Thermostat Setpoint Temperature (Ttnk). Thethermostat setpoint temperature is the desired delivery temperature ofthe hot water. InletWater Temperature(Tin). The inlet water temperature is the temperature ofthe water supplied to the water heater. Temperatureofthe AirSurroundingtheWaterHeater (Tamb). The temperature surrounding the water heater isthe ambient air temperature ofthe space in which the water heater is located.
-66-Volume ofHotWaterDrawn in 24-Hour Period (vol). This isthe estimated daily household use ofhotwater. Density ofWater(den). The density ofhot water at the average ofthe setpoint and inlet temperatures. This is mass perunit volume, expressed as Ib/gal (kg/l). Specific Heat ofWater(Cp). The specific heat ofwater atthe average ofthe setpoint and inlet temperatures. This is the amount ofheat needed to increase or decrease the temperature of 1 pound ofwater by 1°F (1kg/K). 5.5.4 General Description ofSources ofData 

### Derivations of Energy Parameters Introduction The total water heater energy consumption (Q,)is calculated using water heater energy parameters such as the recovery efficiency (RE), the standby heat loss coefficient (UA), and the rated input power (Pon) and the estimated hot water use. The definitions for the water heater energy parameters are provided bythe U.S. DOE EFtest procedure for water heaters'9
. The energy parameters were developed from simulation models, water heater manufacturer and retail contacts, independent sources, and customized calculation tools developed at LBNL. Determining RE, UA, andPon The LCC analysis uses RE and UA values from computer simulations developed for the Engineering Analysis. Two detailed water heating simulation programs
- WATSIM forelectric water heaters and TANK for gas-fired water heaters

- were used to perform the simulations. The WHAM water heater simulation tool was used for oil-fired water heaters. WATSIM is a detailed electric water heater simulation program developed bythe Electric Power Research Institute (EPRI)20
. The use ofWATSIM is explained in the Engineering Report. The output ofWATSIM does not directly provide values forRE andUA. It does, however, provide detailed temperature profiles ofthe water inside the tank during the simulation run. These temperature readings can be used to determine the energy parameters ofthe electric water heater using the standard testprocedure calculations. A spreadsheet tool, described in Appendix A ofthe Engineering Report, was developed to calculate RE and UA. TANK is a detailed gas-fired storage water heater simulation program developed by Battelle for the Gas Research Institute2'. TANK isexplained inthe Engineering Report. The outputs ofTANK include RE and UA.

-67-The simplified water heater analysis model (WHAM) was used forthe analysis ofoilfired water heaters. In the case ofthe oil-fired water heaters, the total daily energy consumption was calculated based on the estimated burner operating hours. Then, arearranged WHAM equation was used to estimate UA. The use ofthe WHAM model for the calculation ofthe energy parameters foroil-fired water heaters isexplained in the Engineering Report. Theprimary source ofdata for ratedinput power (Pon) isthe water heater manufacturers' product literature. In order to generate values for Pon, a large sample ofwater heaters was examined and typical values for each standard size were assigned. Table 5.5.1 is a summary ofall standard water heater sizes studied in this analysis with corresponding values for UA, RE, and Pon forthe three fuel types. Table 5.5.1 Water Heater Design Characteristic Values Rated Volume UA RE Pon (gal) (liter) (Btu/hr-°F) (Btu/hr) Electric 30 (110) 2.92 .972 15354 40 (150) 3.40 .968 15354 50 (190) 3.64 .967 15354 65 (250) 3.98 .966 15354 80 (300) 4.42 .965 15354 Gas 30 (110) 11.56 .758 30000 40 (150) 13.86 .756 40000 50 (190) 16.14 .723 50000 75 (280) 21.80 .672 75000 Oil 32 (120) 14.93 .760 90000 

### 50 (190) 18.26 .760 104000

Other Standard-Size Water Heaters The typical analytic baseline models represent the most common size water heater with an EF at the minimum allowed by current energy efficiency standards. These units have the

-68-largest market share in their product class (50-gal/ 90 liter for electric, 40-ga/1 50 liter for gasfired, and 32-gal/120 liter for oil-fired). Other standard-size water heaters that were also considered in the LCC analysis are listed in Table 5.1.1. All standard-size analytic baseline models were modeled by adjusting the typical analytic baseline models in the WATSIM and TANK simulation tools. Table 5.5.2 shows the values of the electric water heater parameters which have been adjusted in WATSIM in order to model the standard tank sizes. Thetypical tankdiameter for each standard size is determined from a large sample ofwater heaters selected from the product literature. The actual tank volume ofthe electric water heater is 10% less than the rated volume. The values forthe tank diameter and actual tank volume were used tocalculate the tankheight. The rest ofthe geometry parameters, such as the locations ofthe hot water and cold water outlets, the electric heater elements, the thermostats, and the miscellaneous feed through fittings, were determined by scaling them relative to the length ofthe baseline model. In WATSIM all heights are referenced from the bottom ofthe tank support skirt (top ofthe base pad). Table 5.5.2 Electric Water HeaterModeling Parameter Variations 30-gal 40-gal 50-gal 65-gal 80-gal Tank Diameter (ft) 1.17 1.17 1.32 1.50 1.67 Tank Height (ft) 3.48 4.60 4.54 4.55 4.52 Location ofH.W. Inlet (ft) 3.48 4.60 4.54 4.55 4.52 Height ofHeater Element I (ft) 0.48 0.63 0.62 0.62 0.60 Height ofHeater Element 2 (ft) 2.48 3.28 3.24 3.25 3.23 Height ofThermostat 1(ft) 0.70 1.01 1.00 1.00 1.00 Height ofThermostat 2 (ft) 2.79 3.69 3.64 3.65 3.62 Height ofFeed-Through 1(ft) 3.48 4.60 4.54 4.55 4.52 Height ofFeed-Through 2 (ft) 3.48 4.60 4.54 4.55 4.52 Height ofFeed-Through 3 (ft) 0.13 0.13 0.13 0.13 0.13 Height ofFeed-Through 4 (It) 3.48 4.60 4.54 4.55 4.52 Table 5.5.3 shows the values ofthe gas-fired waterheater parameters which have been adjusted in TANK in order to model all the standard tank sizes. All the required TANK input parameters, such asthe tank diameter, theinternal flue diameter, and the firing rate for each standard size, are determined from a large sample ofwater heaters selected fromproduct literature. The actual tankvolume ofthe gas-fired water heater is 5% lessthanthe rated volume. The TANK simulation program calculates most ofthe geometry parameters based on the values for the tank diameter and volume. The location (elevation) ofthe thermostat does not change from size to size and thethermostat is fixed at a height of0.39 feet (11.9 cm). TANK requires an input forthe 'Volume to Thermostat (gal)' parameter, which is determined asthe amount of water that would need to be added to an empty waterheater tank to raise the level ofthe water to the thermostat location. Thisparameter is determined using the specific tank diameter and the thermostat elevation.

-69-Table 5.5.3 Gas-fired Water Heater Modeling Parameter Variations 30-gal 40-gal 50-gal 75-gal Tank Volume (gal) 28.5 38. 47.5 71.25 Firing Rate (Btu/hr) 30000 40000 50000 75000 Tank Diameter (in) 13.84 15.84 17.84 21.84 Internal Flue Diameter (in) 2.84 3.84 3.84 3.84 Volume to Thermostat (gal) 3.1 4.05 6.36 7.70 Detailed computer simulations were performed for each design option and all combinations ofdesign options as they applied to all ofthe standard-size baseline models. Determination of the Uncertainty RangesforEF,RE, UA, andPon The energy factor (EF) is the ratio ofoutput energy in the form ofhot water to the input energy atthe standard testconditions. The WHAM equation is used in the LCC analysis to calculate EF values for all the design options as a function ofRE, UA, and Pon, which are calculated as explained above. The following procedure was developed to calculate the uncertainty ranges for all the energy parameters. An estimate ofthe EF values and the associated uncertainty ranges for all the design options added separately to typical existing baseline electric and gas water heaters were provided by M. Minniear, aconsultant. The EF uncertainty range data forthe typical tank size was used to develop ratios to represent the variations ofthe EF values for all the standard tank sizes. The range ofuncertainty for RE and UA was developed from the range ofuncertainty for EF. This isdone by calculating the variations in RE and UA that would independently cause the desired variation ofEF. The range on the RE and UAterms isreduced by 1/V2. This assumes that the RE and UA distributions have approximately equal impacts on EF. A detailed explanation oftheentire procedure to developthe uncertainties forthewater heater energy parameters is found in Appendix C. Variations in Pon have a much smaller impact on EF within the operating limits ofactual water heaters. Values forthe variations in Pon were developed by determining the Ponrange for each standard size ofwater heaters listed in the GAMA directory. The impact on EF for variations in RE, UA, and Pon are shown in Table 5.5.4 for electric water heaters and in Table 5.5.5 forgas water heaters. Figure 5.5.1 shows the variation ofEF for electric water heaters caused by deviations ofRE, UA, and Pon from typical values ofRE = 98%, UA = 3.3 Btu/hr-°F, and Pon = 4.5 kW. Figure 5.5.2 shows same for a gas-fired water heater for deviations from typical values ofRE = 78%, UA = 14.4 Btu/hr-°F, and Pon = 40,000 Btu/hr.

-70-Table 5.5.4 En Efficiency Characteristics

- Electric Water Heaters (50-gal)_ Design Options EFwham EFmin EFmax RE REmin REmax UA UAmin UAmax PON PONmin PONmax ~_____ _ ______________________________________(Btu/hr-°F) (Btu/hr) Existing Baseline (141b) 0.861 0.837 0.863 0.967 0.945 0.969 3.64 3.59 4.31 15354 12966 18766 0 Analytic Baseline (245fa) 0.861 0.837 0.863 0.967 0.945 0.969 3.64 3.59 4.31 15354 12966 18766 I 0+ lleatTraps 0.879 0.865 0.881 0.970 0.958 0.972 3.06 3.01 3.45 15354 12966 18766 2 I +2" Jacket Insul 0.892 0.859 0.894 0.972 0.943 0.973 2.62 2.57 3.50 15354 12966 18766 3 I +2.5" Jacket Insul 0.903 0.869 0.905 0.973 0.945 0.974 2.29 2.24 3.16 15354 12966 18766 4 3 +Plastic Tank 0.907 0.897 0.917 0.970 0.962 0.978 2.06 1.82 2.31 15354 12966 18766 5 3 +Insul Tank Bottom 0.907 0.873 0.909 0.972 0.944 0.973 2.13 2.08 2.99 15354 12966 18766 Table 5.5.5 Energy Efficiency Characteristics

- Gas-fired Water Heaters (40 gal) Design Options EFwham EFmin EFmax RE REmin REmax UA UAmin UAmax PON PONmin PONmax _________________________________~_ ________(Btu/hr-°F) (Btu/hr) Existing Baseline (141b) 0.544 0.529 0.549 0.755 0.735 0.762 13.82 13.51 14.78 40000 28000 60000 0 Analytic Baseline (245fa) 0.544 0.529 0.549 0.756 0.735 0.762 13.86 13.55 14.82 40000 28000 60000 1 0 +Heat Traps 0.554 0.549 0.564 0.756 0.749 0.769 12.96 12.37 13.27 40000 28000 60000 2 1 + 2" Jacket Insul 0.580 0.564 0.584 0.762 0.742 0.767 11.04 10.82 11.98 40000 28000 60000 3 I +2.5" Jacket Insul 0.599 0.583 0.604 0.780 0.760 0.785 10.37 10.16 11.27 40000 28000 60000 4 3 + Side Arm Heater 0.662 0.644 0.673 0.764 0.743 0.771 5.24 4.75 6.06 40000 28000 60000 5 2 + mpr Flue Baffle 0.675 0.656 0.687 0.784 0.762 0.791 5.36 4.87 6.16 40000 28000 60000

-71-EF Sensitivity Using WHAM at defaultelecticwater heatervalues 0.950

0.900

.o UJ
0.850
I-- effectofRE . .- ffectofUA I

0.800 -15% -10% -5% 0% 5% 10% 15% parnatchange Figure 5.5.1 Variations ofEF forElectric Water Heaters EF Sensitivity UsingWHAM atdefaultgas-red water heater vaues 0.600 -_ i efectofdRE | i-- efectd ofLA ieddffePon / 0.580

0.560
-

0.540

0.520

-

0.500 -15% -10%/ -5% 0% 5% 10% 15% parameterchange Figure 5.5.2 Variations ofEF for Gas-fired Water Heaters

-72-APPENDIX A: SENSITIVITY CHARTS FOR SELECTED DESIGN OPTIONS Sensitivity inthis study is defined as the response ofa forecast to a change in an assumption. It measures how the uncertainty ofeach assumption effects thevariation ofa forecast variable using rank order correlation. The calculation is done by ranking the sampled values ofthe assumptions and theresulting forecast, with the largest value assigned the highest rank and the smallestthe lowest, and then computing the correlations between each ofthe assumptions and the forecast. Rank order correlation is less affected by skewed distributions or extreme values in samples and is more robust than a simple correlation. The correlation coefficient provides a meaningful measure ofhow and to what degree assumptions and forecasts change simultaneously in the simulation process. Positive coefficients indicate that forecasts and assumptions change in the same direction, either increasing or decreasing. Negative coefficients imply thereverse. A correlation coefficient of 1(or -1)means that assumptions and forecasts have the strongest proportional (or adversely proportional) relationship whereas 0means no relationship at all. The sensitivity analysis resultis plotted as a "Tornado Chart" thatprovides aquick and easy view ofthe influence each assumption has on aparticular forecast. The sensitivity chart displays the coefficients as horizontal bars whose lengths are proportional to their magnitude in a descending order. Therefore, the assumption represented bythe bar on the top ofa chart is the most important. Crystal Ball, an add-in toExcel spreadsheets, also allows the correlation coefficients between all pairs offorecasts be calculated while the simulation is running so that the effect ofintermediate forecasts on the another forecast can be evaluated, such as the impact ofhot water use on the energy consumption. This appendix includes sensitivity analysis charts for the change in life-cycle cost for all design options for both electric and gas-fired water heaters. Charts are included for the sensitivity analysis oftotal installed cost, operating cost and daily energy consumption for the 2" Jacket Insulation design option for electric water heaters andthe 2.5" Jacket Insulation design option for gas-fired water heaters. These are the design options with the highest average lifecycle cost savings. Sensitivity analysis charts are also included for hot water use forhouseholds with electric waterheaters and for households with gas-fired water heaters.

A-ISensitivityAnalysis - Electric Water Heaters Delta LifeCycle Cost of Heat Traps compared toAnalytic Baseline (1998$)

Discount rate 0.33

Water Heater Lifetime (years) -0.26
Annual Operating Cost in2003 of Analytic Baseline Water Heater -0.22 (1998$) | Annual Operating Cost in2003 of Heat Trap Water Heater (1998$)
Total Cost to Buyand Install a Heat Trap Water Heater(1998$) 0.05 Total Costto Buy and Install an Analytic BaselineWater Heater 0.02 (1998$) -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 SensitivityAnalysis - Electric Water Heaters Delta Life Cycle Cost of2' Jacket Insulation compared toAnalytic Baseline (1998$)
! 5 Discount rate 

### E 0.35

Water Heater Lifetime (years) -0.29
Total Costto Buy and Install a2" Jacket Insulation Water Heater 0.20 (1998$) Annual Operating Cost in 2003of Analytic Baseline Water Heater -0.17 (1998$) I Annual Operating Cost in 2003 of 2

Jacket Insulation Water Heater -0.15 (1998$) ;. Total Cost to Buy and Install an Analytic Baseline Water Heater : o 0.11 (1998$) 

### l
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

A-2Sensitivity Analysis

-Electric Water Heaters Delta Life Cycle Costof 2.5' Jacket Insulation compared to Analytic Baseline (1998S)
Discountrate 

### L ;'JS ' 0.38

Water Heater Lifetime (years) -0.31
Total Cost to Buy and Install a2.5"

Jacket insulation Water Heater 0. (1998$) Annual Operating Cost in2003 of Analytic Baseline Water Heater -. 19 (1998$) Annual Operating Cost in2003 of 2.5"Jacket InsulationWater Heater -0.16 (1998$) Total Costto Buy and Install an Analytic BaselineWater Heater !?, 0.12 (1998$5) e -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 Sensitivity Analysis- Electric Water Heaters Delta Life Cycle Cost of PlasticTankcompared toAnalytic Baseline (1998$)

Discountrate 0
Total Cost to Buy and Installa --i .~" t 0.35 PlasticTank Water Heater (1998$)
Water Heater Lifetime (years) -0.31 Annual Operating Cost in 2003 of Analytic Baseline Water Heater .0.20 (1998$) 

# i^-
Annual OperatingCost in2003of -0.18 l j1 PlasticTank Water Heater (1998$) Total Costto Buy and Install an Analytic Baseline Water Heater 0.17 (1998$) -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

A-3Sensitivity Analysis - ElectricWater Heaters Delta Life Cycle Cost of Tank Bottom Insulation compared to Analytic Baseline (1998$) Total Cost to Buy and Install aTank

Bottom Insulation Water Heater 0.41 (1998$) :< i ;: i 04 Discount rate . 0.35

Water Heater Lifetime (years)29
Annual Operating Cost in2003 of I Analytic BaselineWater Heater -0.19 (1998$) Total Costto Buy and Install an i Analytic BaselineWater Heater -* 0.17 (1998$) Annual Operating Cost in2003 of

Tank Bottom InsulationWater -0.16 Heater (1998$) -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 Sensitivity Analysis- Electric Water Heaters Total Cost to Buy and Installa25' Jacket Insulation Water Heater (1998$)

Total Combined Markup from |56 Manufacturer Cost to Retail Price ' 0

Cost to Installa 2.5" Jacket ', -, ' Insulation Water Heater (1998$) ; -

Costto Manufacture a2.5" Jacket . Insultation Water Heater(1998$) 

# [.

Sales Tax 0.04

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

A-4Sensitivity Analysis -Electric Water Heaters Operating Cost of 2.5" Jacket Insulation Water Heater compared toAnalytic Baseline (19985)

Annual Energy Consumption of2.5" -:; : :'; -'. i Jacket InsulationWater Heater 0.8 8 (kWh/year)

Revised electricity pricein 1998$ ($kWh)

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 SensitivityAnalysis - Electric Water Heaters Daily Energy Consumption of 2.5' Jacket Insulation Water Heater Daily Hot Water Use (Gal/day) : *;. :- ; 0 91 Water heater thermostatsetpoint 0.26
Inletwater temperature -0.26 Standby Heat Loss Coefficent of i :23 2.5" Jacket Insulation

- l 0.23 Ambient airtemperature (around water heater) i Rated Input Power of2.5' Jacket
. 

### r' 1: 2 Insulation : |.j Recovery Efficiency of 2.5' Jacket 7 Insulation Water Heater l -1 0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 08 1

A-5SensitivityAnalysis - Electric Water Heaters Daily Hot Water Use (galiday)
Total number of occupants , 0.82 Number of occupants age 14

-64 years 0.64 Number of occupants age 6 - 13 years j .0.33 Household Does Not Own Clothes Washers -0.28 i.,;,.; ,~ I Adult at home during day 0,'I ' ,,*, 0.27 Number ofoccupants age0

-5 years , -i, 0.22 Nominal size ofwater heater f, 0.22 Coefficent for "air 0.15 Senioronly household in multi-family buildings 0.15

Number of occupantsage 65 years or older -0.14 Coefficient for Tinn" 0.13 Household Does Not Own Dishwashers -0.13 Coefficient for 'Ttank' .y 0.12 Average outdoor air temperature . 0.11 Inlet watetpe temperature 0.11 Water heater thermostast sepoint -011 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

A-6Sensitivity Analysis

-Gas-fired Water Heaters Delta Life Cycle Cost of Heat Traps compared to Analytic Baseline (19985)
Water Heater Lifetime (years) -0.32IT

Discount Rate 0.29
Annual Operating Costin 2003 of Analytic Baseline Water Heater
. (1998$)
Annual Operating Cost in2003 of Heat TrapWater Heater (19985) -0.20

Total Costto Buy and Install an ! Analytic Baseline Water Heater -0.04 (19985) Total Cost to Buy and Install a Heat Trap Water Heater(1998$) -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 SensitivityAnalysis - Gas-fired Water Heaters Delta LifeCycle Costof Two InchJacket Insulatloncompared to AnalyticBaseline (1998$)

Water Heater Lifetime (years) -0.50

Discount Rate 045
Annual Operating Cost in2003 of Analytic Baseline Water Heater -. 27r (19985) Annual Operating Cost in2003 of2"

Jacket Insulation Water Heater .0.25 (1998) Total Costto Buy and Install a2" Jacket Insulation Water Heater r 0.12 (1998$) Ld Total Costto Buy and Install an Analytic Baseline Water Heater 0.10 (1998s) .lI -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

A-7Sensitivity Analysis

-Gas-fired Water Heaters Delta Life Cycle Cost of 2.5' Jacket Insulation compared to Analytic Baseline (1998$)

Water Heater Lifetime (years) ! -0.48... " ; |

Discount Rate 1 '* 0.43
Annual Operating Cost in 2003 of Analytic Baseline Water Heater -0.22 w . (1998$) Total Costto Buy and Install a2.5"

Jacket Insulation Water Heater 0.22 (1998$) Annual Operating Cost in2003 of 2.5 Jacket Insulation Water Heater -0.20 (1998$) Total Costto Buy and Install an Analytic BaselineWater Heater 0.18 (1998$) -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 Sensitivity Analysis

-Gas-fired Water Heaters Delta Life Cycle Cost of Side-Arm Heatercompared toAnalytic Baseline (1998$)
Total Costto Buy and Install a Side 0.49 Arm Heater WaterHeater(1998$)

Water Heater Lifetime (years) -0.42

Discount Rate 0.38
Total Cost to Buy and Install an Analytic Baseline Water Heater 0.27 (1998s) Annual Operating Cost in2003 of Analytic Baseline Water Heater -009 (1998$) Annual Operating Cost in2003 of Side Arm HeaterWater Heater -0.05 (1998$) -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

A-8SensitivityAnalysis -Gas-fired Water Heaters Delta Life Cycle Cost ofImproved Flue Baffle compared to Analytic Baseline (19985)

Water Heater Lifetime (years) -0.50

Discount Rate I. .i, 0.45 Annual Operating Cost in2003 of
. . Analytic Baseline Water Heater -0.42 (1998s) Annual Operating Cost In2003 of Improved Flue Baffle Water Heater -0.40 (1998$) Total Costto Buy and Installan Improved Flue Baffle Water Heater I l 0 10 (1998$) Total Cost to Buy and Install an Analytic Baseline Water Heater 0.08 (1998$) -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 Sensitivity Analysis -Gas-fired Water Heaters TotalCost to Buy and Install a2' Jacket Insulation Water Heater (1998$)

Total Combined Markupfrom Manufacturer Costto Retail Price ,. 

## I, .68;

Cost to Install a 2"Jacket Insulation . .' ;S.' Water Heater (1998S) .,' ,

Sales Tax I 0.06

Cost to Manufacture a 2 Jacket 0 Insultation Water Heater (1998$) 

## U

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

A-9SensitivityAnalysis - Gas-fired Water Heaters Operating Cost of 2' Jacket Insulation Water Heater compared to AnalyticBaseline (1998$)

Annual Gas or LPG Consumption of *. :, ; S
- 2 Jacket InsulationWater Heater 090i (MCF/year)

Revisedwater heatingfuel pricein 4; 1998$ (SIMCF) 0

-1.00 -0.80 0.60 -0.40 -0.20 0.00 0.20 0.40 0.60 0.80 1.00 SensitivityAnalysis -Gas-fired Water Heaters Daily Energy Consumption of 2" Jacket Insulation Water Heater
Daily Hot Water Use (gal/day) 0. . ; , 92 Standby Heat Loss Coefficient of 2- ' -: 0. Jacket Insulation 0.33 Recovery Efficiency of2" Jacket -0.28 T t Insulation Water Heater L Rated Input Power of 2" Jacket Insulation
Water heater thermostat setpoint 0.18
Inlet water temperature -018
Ambient air temperature (around -1 water heater) -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

A-10SensitivityAnalysis- Gas-fired Water Heaters Daily HotWater Use (gaUday)
Total number ofocupants ,. , --- a .- i 0.70 Number of occupart age 14

-64yearns B*, =i f 0°52 Coefficiart or 'enior_mrr ,j : 0.36

Coeflioit or 'no_pay' E,0.35 Numbr of occupant age 6- 13 years - 'sj, 0.31 Adultthome during day 'i; 0.24 Number of occuparts age 0 -5years 0.20 Nominal aize ofwater heater 0.19 Househod Doe Not Own Dastnwhe -0.16 

### r Average outdoorairtarnparture 0 .14 Inlet watrtmprature 0.14 Water heatera themostalalpoint -0.14 Houahold Does NotOmn Clotes Waers I -0.12 Coeffidaent Tor T Ir ~.0.12 CofiaentforTar Tin' 011 Coeftciant forTtank' 0.11 -1.00 -0.80 -0.60 -0.40 -0.20 0.00 0.20 0.40 0.60 0.80 1.00

A-11APPENDIX B: DISTRIBUTIONS OF WATER HEATER MANUFACTURING COSTS Background and Methodology The LCC analysis uses individual design options that are then grouped together in combinations ofdesign options according to the results ofthe Engineering Analysis. This analytic procedure requires incremental manufacturing costs ofindividual design options. The distributions ofthe manufacturing costs for most design options were provided by the Gas Appliance Manufacturers Association (GAMA) as cumulative curves oftotal cost'. GAMA data only applies to 50-gal electric and 40-gal gas-fired water heaters. This data is used as the basis for the development ofthe incremental manufacturing costs for the other standard sizes and for the analyzed design options. The data summarizes 10,000 samples randomly drawn from ranges oftotal manufacturing cost provided by four major water heater manufacturers. Figure B.1 shows manufacturing costs forthe typical existing baseline gas-fired water heater and the same water heater with heat traps. Manufacturing Costs Gas-Fired Water Heaters 100%
_____ _____-_____________________ 90% -________________________

________ 80% 70%
60% 40% .___ / e LVL 1, (baseline) 30% - ------------ LVL2,(heal traps) 20%
_ _____________ _ 10% - _ _ _ 0% $100.00 $110.00 $120.00 $130.00 $140.00 $150.00 $16000 $170.00 $180.00 Total Manufacturer Costs Figure B.1 Cumulative Manufacturing Costs

B-IThe following method was used to estimate the range ofincremental manufacturing costs for individual design options from this data. It was assumed that themanufacturing costs reported for the typical existing baseline water heater and the water heaterwith heat traps were highly correlated. This assumption allows the difference between these two cumulative curves to be observed. A plot ofthis data shows each segment separately as in Figure B.2. What can be seen in this plot is that some ofthe segments spread across a much larger range ofcosts, so thatthe density ofsamples per dollar is much lower. Also, many ofthe segments overlap in cost. A constant sample densitythroughout each segment is assumed. With this assumption, it is possible to assign a fraction ofthe samples in each segmentto anycost range the segment spans. The segments are then further subdivided atthe points where the cost ranges overlap and the fractions ofsamples are distributed into new smaller cost ranges. The fractions ofthe original segments are combined where they span identical ranges of costs to give an assessment ofthe relative frequency ofsamples within each costrange. This data can be plotted as a histogram ofthe frequency ofthe incremental costs ofthat design option. This is done for heat traps on gas-fired water heaters in Figure B.3.
Manufacturing Costs Gas-Fired Water Heaters Difference between Heat Traps and Baseline $1.81 $2.87 52.80 $3.32 $1.81 $1.94

C~ Si ~$1.51 -$1.94
i S.. "'-ts$1.16 $1.51 1.16 $2.53 3eS~~~~~~
. S~~~~~~$2.53 $2.59 $2.59 ~$2.67 $2.67 $3.39 $3.32 ~$3.39 $0.00 $0.50 $1.00 $1.50 $2.00 $2.50 $3.00 $3.50 $4.00 Dfference ofTotal Manufacturing Costs Figure B.2 Difference Between Cumulative Cost Curves as Separate Segments

B-2Incremental Manufacturing Costs Gas-Fired Water Heaters 30%
_ --- __Heat Traps

25%
$3.39 20%
c g 15%

10%

5% $1.16

0%

$0.00 $0.50 $1.00 $1.50 $2.00 $2.50 $3.00 $3.50 $4.00 Incremental Manufacturer Costs Figure B.3 Incremental Manufacturer Costs Implementation A schematic view ofthe methodology used to develop the incremental manufacturing costs for the design options and all standard sizes ispresented in the main body ofthis report in Table 5.3.8 for electric water heaters and Table 5.3.9 for gas-fired water heaters. A detailed discussion ofthe implementation process is presented below. The general approach is as follows: 1) GAMA distributions ofthe manufacturing cost for each design option, except for the existing baseline, are adjusted for HFC-245fa foam by adding or subtracting the cost ofthe foam. 2) The GAMA distributions ofthe manufacturing cost for the other standard sizes are adjusted by adding or subtracting the cost ofextra foam and extra sheet metal. 3) The distributions ofthe manufacturing cost for the design options not provided by GAMA are based on the distribution ranges provided by an LBNL consultant. 2 Electric Water Heaters Existing Baseline: "GAMA Level 1"data is used directly for the typical existing water heater size (50-gal rated volume). The distributions ofthe manufacturing costs for the 30-gal and 40-gal sizes are calculated by subtracting the cost ofextra foam and extra sheet metal from the cumulative data for 50-gal size. The distributions ofthe manufacturing costs for the 65-gal and 80-gal sizes are calculated by adding the cost ofextra foam and extra sheet metal to the 50-gal
B-3size. Analytical Baseline: The distribution ofthe manufacturing cost forthe 50-gal size is calculated by adding the incremental cost ofthe HFC-245fa foam to the "GAMA Level 1"data. The distributions ofthe manufacturing costs for each ofthe other standard sizes are calculated by adding the incremental cost ofHFC-245fa foam to the "GAMA Level 1"data already calculated for the existing baseline ofthe corresponding size. The added incremental cost ofHFC-245fa blown foam varies from $1.51 (30-gal) to $2.68 (80-gal). Heat Traps: The distribution ofthe manufacturing cost is calculated as an incremental cost difference between "GAMA Level 2" and "GAMA Level 1"data as explained atthe beginning ofthis appendix. The same incremental cost distribution is used for the other size waterheaters. 2" Jacket Insulation: The distribution ofthe manufacturing cost for the 50-gal size is calculated as an incremental cost difference between "GAMA Level 3"and "GAMA Level 1" data and adding the incremental cost ofthe HFC-245fa foam. The distribution ofthe manufacturing costs for the other sizes is accomplished in two steps: first, by adding the incremental cost ofthe HFC-245fa foam to the incremental cost difference calculated from "GAMA Level 3"and "GAMA Level 1"and second, by adding or subtracting the cost ofextra foam and extra sheet metal for the appropriate tank size. 2.5" Jacket Insulation: GAMA provided no data forthis design option. In orderto develop the distribution ofmanufacturing costs, amultiplier was calculated for each water heater size based on the ratio ofthe total incremental manufacturing cost ofthe 2.5"jacket insulation to the 2"jacket insulation used in the Engineering Analysis. The multipliers are applied directly to the previously calculated incremental costs for 2"jacket insulation. For example, the incremental manufacturing cost for 2" insulation (50-gal size) is $13.49 and for 2.5" insulation, $23.77. Therefore, themultiplier is 23.77/13.49=1.762. This value is used to multiplythe calculated incremental cost distribution for 2"jacket insulation in order to obtain the distributions for 2.5" jacket insulation. Plastic Tank: GAMA provided no data forthis design option. The incremental cost distribution was provided bythe LBNL consultant. The costrange varies from -5% to +10%. Insulated Tank Bottom: The distribution iscalculated as an incremental cost difference between "GAMA Level 6" and "GAMA Level 1"data. The same incremental cost distribution is used for the other size water heaters. Gas-firedWaterHeaters Existing Baseline: "GAMA Level 1"data is used directly for the typical existing water heater size (40-gal rated volume). The distribution ofthe manufacturing cost for the 30-gal size is B-4calculated by subtracting the cost ofextra foam and extra sheet metal from the cumulative data for the 40-gal size. The distributions ofthe manufacturing costs forthe 50-gal and 75-gal are calculated by adding the cost ofextra foam and extra sheet metal to the 40-gal size. Analytical Baseline: The distribution ofthe manufacturing cost for the40-gal size is calculated by adding the incremental cost ofthe HFC-245fa foam and the cost ofthe flammable vapor ignition device ($35) to the "GAMA Level 1"data. The distributions ofthe manufacturing costs for each ofthe other standard sizes are calculated by adding the incremental cost ofthe HFC-245fa foam and the incremental cost offoam and sheet metal for the other tank sizes tothe "GAMA Level 1"data previously calculated for the appropriate tank size. Heat Traps: The distribution is calculated as an incremental cost difference between "GAMA Level 2" and "GAMA Level I" data. The same incremental cost distribution is used for the other size water heaters. 2" Jacket Insulation: The distribution ofthe manufacturing cost for the40-gal size is developed as an incremental cost difference between "GAMA Level 3" and "GAMA Level 1" data and adding the incremental cost ofthe HFC-245fa foam. The distribution ofthe manufacturing cost for the other sizes is accomplished in two steps: first, by adding the incremental cost ofthe HFC-245fa foam to the incremental cost difference calculated from "GAMA Level 3"and "GAMA Level 1"and second, by adding or subtracting the cost ofextra foam and extra sheet metal for the appropriate tank size. 2.5" Jacket Insulation: GAMA provided no data for this design option. In order to develop distributions, a multiplier was calculated foreach water heater size based on the ratio of the total incremental manufacturing cost ofthe 2.5"jacket insulation to the 2"jacket insulation used in the Engineering Analysis. The multipliers are directly applied to the previously calculated incremental costs for 2"jacket insulation to calculate distributions for 2.5"jacket insulation. Side Arm Heater: GAMA provided no data for this design option. The incremental cost distribution was provided bythe LBNL consultant. The cost range varies from -10% to +20%. Electronic Ignition: The cost distribution is calculated as an incremental cost difference between "GAMA Level 6" and "GAMA Level 1"data. The same incremental cost distribution is used for the other size water heaters. Improved Flue Baffle: The distribution iscalculated as an incremental cost difference between "GAMA Level 5" and "GAMA Level 1"data. The same incremental cost distribution is used for the other size water heaters.

B-5References 1. Stanonik, F., 1998. Manufacturing Cost Data for Residential Gas and Electric Storage Water Heaters. GAMA, Arlington, VA. Letters to DOE, June 19 and July 17. 2. Minniear, M., 1997. ResidentialWaterHeaters:InitialEstimatesof ManufacturingCosts andEnergy Consumption,Task 1ofLBNL Subcontract 6466797. Minniear Corporation, Panama City, FL. November 12.

B-6APPENDIX C: UNCERTAINTY OF ENERGY PARAMETERS EF, RE, UA, AND PON Energy Factor (EF) Estimated uncertainty ranges for the energy factors (EFs) ofdifferent design options were provided forthe typical tank size ofelectric (50-gal) and gas (40-gal) water heaters byan LBNL consultant.' Ratios were developed to represent the minimum and maximum variations in the EF values ofthe typical tank sizes. Since each design option is acombination ofseveral single designs, the ratio ofacombined design option is assigned to be the largest among the single designs involved. Forexample, gas-fired waterheater design option 3 (1 + 2.5" Jacket Insulation) is a combination ofthree single designs, the Analytic Baseline, Heat Traps, and 2.5" Jacket Insulation. The uncertainty range ofdesign option 3is the largest range ofthese three single designs. This ensures that the estimated uncertainty ranges include those ofevery single design. Then,by multiplying theratios ofthe different design options bytheir corresponding EF values, ratios for EF values ofallthe standard tank sizes were calculated. The resulting uncertainty ranges forEF are characterized by the minimum, the most-likely, and the maximum, so that the probability distribution can be described bya simple triangular distribution. The uncertainty ranges are also in compliance with the Code ofFederal Regulation ruling that specifies thatreported EF values must be no higher than the mean value. In both electric and gas waterheaters, the largest range ofthe EFis within 4% ofthe value in our simulation study. The determination oftheranges ofuncertainty forrecovery efficiency (RE), standby heat loss coefficient (UA), and Rated Input (Pon) is made using the Water Heater Analysis Model (WHAM). They are estimated by assessing howbig the ranges ofthese parameters can be to yield the reported ranges ofuncertainty on EFindependently. To achieve this, the partial derivative ofEF to each ofthe three parameters RE, UA, Pon, is computed. The width ofthe range isreduced slightly to account for the effect on EF when two parameters vary simultaneously. It was found that Rated Input (Pon) is far less sensitive to EF than the other two parameters and that, therefore, the range ofuncertainty ofPon should be decided separately.

C-1Recovery Efficiency (RE) The set ofequations to solve RE for a given EF is:
(REE mde X EFmaxx 41094x (UA x 675- Pon) 

### o12 

### Ponx (1620x EFmaxx UA
- 41094)xX

(RE 

### min = RE modeX 

### EFminx 41094 x (UAx 675- Pon) m mode+ 

### Ponx (1620x EFminx UA- 

### 41094) x 

### 2
Standby Heat Loss Coefficient (UA) Similarly, therange ofuncertainty forUA can be determined bythe following set of equations:


### /Ponx(EFmin 

### UAmax =UAmodex 1 -l + 2EF67.5x (RExPonx - 

### 41094
,,(A „ f Ponx (EFmax
- ) UA min = UAmodeX 

### 1
- + 

### 2 -4 

### 67.5x (REx Pon 41094 )xi

Rated Input (Pon) Since the variation in Pon has an negligible effect on the uncertainty ofEF. the determination ofthe uncertainty is independent ofthe EF value. Therefore, the minimum and the maximum numbers from the LBNL water heater database were used, as listed below: C-2_Ponlin Ponlikely Ponax Electric Water Heater (30-gal) 4606 15354 18766 Electric Water Heater (other sizes) 12966 15354 18766 Gas Water Heater (30-gal) 26000 30000 40000 Gas Water Heater (40-gal) 28000 40000 60000 Gas Water Heater (50-gal) 32000 50000 75000 Gas Water Heater (75-gal) 55000 75000 75000

References

1. Minniear, M., 1997. ResidentialWaterHeaters:InitialEstimatesof ManufacturingCosts andEnergyConsumption,Task 1ofLBNL Subcontract 6466797. Minniear Corporation, Panama City, FL. November 12. 2. Title 10, Codeof Federal Regulations,Part 430-Energy Conservation Program for ConsumerProducts,Section430.24(e)(1)(ii). January 1, 1998.

C-3