RESULTS AND METHODOLOGY OF THE LIFE-CYCLE COST ANALYSIS FOR

RESIDENTIAL WATER HEATER EFFICIENCY STANDARDS

Submitted to the

U.S. Department of Energy

Office of Codes and Standards (OCS)

November 3, 1998

EE-RM-97-900 COMMENT 38UU
TABLE OF CONTENTS

List of Acronyms ................................................... ... -viiRequest for Stakeholder Comments .............................................. -1-

1 Purpose of Life-Cycle Cost Analysis ...................................... . -1-

2 Connection to Remainder of Water Heater Standards Analysis .................. -1-

2.1 From Engineering Analysis ................................ -2-

2.1.1 Order and Combinations of Design Options .................... -2-

2.1.2 Estimates of Factory Costs of Baseline Models and Design Options .. -2-

2.1.3 Estimates of Factory Cost of All Standard Size Baseline Models and

Design Options ..................................... ...... -2-

2.1.4 Energy Parameters of Baseline Models and Design Options ......... -2-

2.2 LBNL Water Heater Cost Database ............................. -2-

2.2.1 Prices of Baseline Models ................................... -3-

2.2.2 Installation Costs .......................................... -3-

2.3 Input to Selection of Trial Standard Levels ...................... -3-

2.4 Output to National Energy Savings Forecast .... .................. -3-

3 Summary of Results .......................... .......................... -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 of LCC 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 of Design Options from Engineering Analysis ........ -9-

5.1.3 Five Major Modules ....................................... -10-

5.1.4 Flowchart ............................................... -10-

5.1.5 Description of Outputs ..................................... -10-

5.2 Life-Cycle Cost M odule .......................................... -12-

5.2.1 Introduction ............................................. -12-

5.2.2 Equations and General Descriptions for LCC and Payback ........ -12-

5.2.3 General Description of Sources of Data ....................... -16-

5.2.4 Life-Cycle Cost and Payback Results ......................... -17-

-iiEE-RM-97-900 COMMENT 38UU
5.3 Equipment Cost Module ............... ....................... -25-

5.3.1 Introduction to Equipment Cost ........................... ... -25-

5.3.2 Equation for Equipment Cost ................................ -25-

5.3.3 General Description of Key Variables ......................... -26-

5.3.4 General Description of Sources of Data ....................... -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 Cost Module ......................... -55-

5.4.3 General Description of Key Variables ......................... -57-

5.4.4 General Description of Data Sources and Calculations in Spreadsheets

.. . . . . .. .. . . .. . . .. .. .. . .. .. . .. .. . .. .. . . . .. . .. . . . .. . . .. . -59 -

5.4.5 Operating Cost Results .................................... -61-

5.5 Energy Analysis Module ........................................ -65-

5.5.1 Introduction to Energy Use ................................. -65-

5.5.2 Equations for Energy Use .................................. -65-

5.5.3 General Description of Key Variables ......................... -66-

5.5.4 General Description of Sources of Data ....................... -67-

Introduction ............................................. -67-

Determining RE, UA, and Pon .............................. -67-

Other Standard-Size Water Heaters ........................... -68-

Determination of the 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 for Hot Water Use ................................ -81-

5.6.5 Results of Hot Water Use Calculations ........................ -84-

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

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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 Cost Data .................. -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 Water Heater 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 for Electric 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-

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FIGURES

Figure 5.1.1 Flowchart of LCC Analysis Spreadsheet ......... .................... -11-

Figure 5.2.1 Distribution of Consumer 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 Cost by Design Option for Gas-Fired Water Heaters -21-

Figure 5.2.5 Payback Period by Design Option for Gas-Fired Water Heaters ........... -22-

Figure 5.2.6 Sensitivity Analysis for Difference in Life-Cycle Cost of 2.5" Jacket

Insulation on Electric Water Heater ................................. -23-

Figure 5.2.7 Sensitivity Analysis for Difference in Life-Cycle Cost of 2" 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 of Incremental Manufacturing Cost for Separate Design

Options for Electric Water Heaters ................................. -39-

Figure 5.3.12 Distribution of Incremental Manufacturing Costs for Separate Design

Options for Gas-Fired Water Heaters ............................... -41-

Figure 5.3.13 Difference in Total Installed Cost by Design Option for Electric Water

H eaters ....................................................... -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 for Electric 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 of EF for Electric Water Heaters .......................... -72-

Figure 5.5.2 Variations of EF for Gas-fired Water Heaters ......................... -72-

Figure 5.5.3 Map of Climate Zones ...... ..... ...................... ..... -73-

Figure 5.5.4 Comparison of Setpoint and Inlet Water Temperatures .................. -75-

Figure 5.5.5 Differences in Energy Consumption by Design Option .................. -78-

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Figure 5.5.6 Differences in Energy Consumption by Design Option - Gas-fired Water

H eaters ...................................................... -80-

Figure 5.6.1 Frequency Chart of Hot Water Use - Households with Electric Water

H eaters ...................................................... -85-

Figure 5.6.2 Frequency Chart for Hot Water Use - Households with Gas-Fired Water

H eaters ....................................................... -85-

-viEE-RM-97-900 COMMENT 38UU
List of Acronyms

AEO Annual Energy Outlook

CEC California Energy Commission

CPI Consumer Price Index

DOE U.S. Department of Energy

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 of cubic feet

NES National Energy Savings

NOAA National Oceanic & Atmospheric Administration

RECS Residential Energy Consumption Survey

WHAM Water Heater Analysis Model

-viiEE-RM-97-900 COMMENT 38UU
RESULTS AND METHODOLOGY OF THE LIFE-CYCLE COST ANALYSIS FOR

RESIDENTIAL WATER HEATER EFFICIENCY STANDARDS

The Energy Policy and Conservation Act, as amended, provides energy conservation

standards for water heaters among other products and authorizes the Secretary of Energy to

prescribe amended or new energy standards for each type of covered product. This is a

preliminary Life-Cycle Cost Analysis; it is part of the 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, retail prices, 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

* hot water draw model

Note: This edition of the 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 for electric water heaters

produced a slight change in their life-cycle costs. Second, a correction in the 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 of Life-Cycle Cost Analysis

This report describes the analysis of economic 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 by performing the calculation for a

large sample of individual households. Variables within the household that cannot be

characterized or are uncertain are represented by a range of values. The results are expressed as

the fraction of households being impacted at particular magnitudes. Life-cycle cost (LCC)

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EE-RM-97-900 COMMENT 38UU
captures the total sum of purchase price and future operating expenses for water heaters. Another

measure of economic impact, payback period, is also calculated.

2 Connection to Remainder of Water Heater Standards Analysis

The LCC Analysis is one step in the analysis of water heater efficiency standards. Much

of the input for this analysis comes from the Engineering Analysis'. The other major input is

from a database of water heater specifications and costs2. The results of the LCC Analysis will

be used by the Department to select the trial standard levels used in the later stages of analysis

and decision making. The outputs will also be used by the National Energy Savings forecast and

the Utility and Environmental analyses.

2.1 From Engineering Analysis

2.1.1 Order and Combinations of Design Options

The combinations of design options are taken directly from the Engineering Analysis.

They are presented in order of ascending cumulative payback period using the DOE test

procedure conditions and the 1998 national average energy price.

2.1.2 Estimates of Factory Costs of Baseline Models and Design Options

The estimates of factory cost for the baseline models and the incremental cost of design

options are from data supplied by the Gas Appliance Manufacturers Association (GAMA). For a

few design options, GAMA was unable to supply estimates of manufacturer costs. In these

cases, consultants familiar with the water heater industry were hired to supply this data.

2.1.3 Estimates of Factory Cost of All Standard Size Baseline Models and Design Options

GAMA supplied estimates of factory cost for the typical size tanks only. The range of

factory costs were estimated for water heaters with different size tanks by adding or subtracting

the material costs for different amounts of steel, for both jacket and tank, and of foam insulation.

2.1.4 Energy Parameters of Baseline 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

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EE-RM-97-900 COMMENT 38UU
LBNL has developed a database of specifications 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 of certified efficiency ratings. 4 Retail 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 of Baseline Models

For this analysis, the price of baseline models was taken from the LBNL Water Heater

Cost Database. The baseline models were defined as those 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 to the actual costs of installing water heaters, delivery, removal, and permit fees are also

included. Typical costs for miscellaneous parts used in installing a water heater, such as pipe

fittings, were also added.

2.3 Input to Selection of Trial 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 not been screened out at this stage of the

analysis and considers each fuel type separately. The trial standard levels will be a subset of the

design options considered in the LCC Analysis and will cover all three fuel types simultaneously.

The Department will consider the results presented here to help decide which design options to

assign to 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 of water

heaters. The LCC Analysis includes the range of energy consumption and installed cost of water

heaters for all the design options. The average of these ranges will be used in the national energy

savings calculations.

3 Summary of Results

This analysis estimates the portion of the population that will benefit from different

design options in terms of reduced life-cycle cost. The average life-cycle cost reduction is also

estimated. The results of this study are summarized in the following table.

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EE-RM-97-900 COMMENT 38UU
Electric Water Heaters

Design Option Fraction of Population 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 5 9.3 22.51

Gas-fired Water Heaters

Design Option Fraction of Population 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 of Population Average LCC

Benefitting Savings

._____________________ __ _ (%) ($)

1 Heat Traps .

2 1 + 2" Jacket Insulation

3 2 + Improved Flue Baffle

4 3 + Interrupted Ignition -- -

The results from the analysis of the oil-fired water heaters will be included in a later

version of this report.

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4 Methodology and Definitions

Analysis of an energy efficiency standard involves calculations of impacts; for example,

the impact of a standard on consumer life-cycle cost. In order to perform the calculation, the

analyst must first: 1) specify the equation or model that will be used; 2) define the quantities in

the equation; and 3) provide numerical values for each quantity. In the simplest case, the

equation is unambiguous (contains all relevant quantities and no others), each quantity has 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 the model 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

of uncertainty and variability is intended to provide more complete information to the decisionmaking process.

4.1 Uncertainty and Variability

To account for the uncertainty and variability, the LCC model was developed using

Microsoft Excel combined with Crystal Ball (a commercially 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 then takes thousands of random

samples from the probability distribution for each input within the model to calculate the outputs.

The distribution of the values calculated for the model outcome therefore reflects the probability

of the values that would occur. This technique provides solutions to a broad range of questions

and helps provide an insight into the likelihood of various possible outcomes.

An importance analysis is also produced which shows the relative contribution of each of

the inputs to the total range of outputs.

A variety of graphic displays are used to illustrate the implications of the analysis results.

These include: a) a cumulative probability distribution showing the percentage of US households

which would have a net life-cycle saving by owning a more energy-efficient water heater or b) a

chart that depicts variation of the life-cycle cost for each design option considered.

One major assumption has been made throughout the analysis. One of two probability

distributions, Triangular or Normal, will be used where a specific form of uncertainty or

variability is totally or partially unknown. The Triangular distribution is one of the simplest

forms of probability distributions. It uses three simple parameters, minimum, most-likely, and

maximum, to describe the probability distribution for a given set of data. It is commonly used in

cases where the knowledge about the factor of interest 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 of them is

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dominant. When nothing but a mean and variance about a random variable is known, the

Department will use the Normal distribution to describe the variable.

4.1.1 Uncertainty

When making observations of past events or speculating about the future, imperfect

knowledge is the rule rather than the exception. For example, the energy actually consumed by a

particular appliance type (such as the average U.S. water heater) has not been directly recorded

very often. Rather, energy consumption is usually estimated based upon available information.

Even direct laboratory measurements have some margin of error. 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 for a quantity. Specifying an exact value for a quantity may be difficult because the value

depends on something else. For example, the amount of hot water used per day by a household

depends upon the specific circumstances and behaviors of the 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 of the entire

population. Surveys can be helpful here, and analysis of surveys can relate the variable of

interest (e.g., gallons of hot 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:

Scenario analysis uses a single numerical value for a quantity in the calculation, then

changes the numerical values and repeats the calculation. A number of calculations are done,

which provide some indication of the extent to which the result depends upon the assumptions.

For example, the life-cycle cost of an appliance could be calculated for electricity prices of 2, 8,

and 14 cents per kWh.

The advantages of scenario analysis are that the calculation is simple; a range of estimates

is used; and crossover points can be identified. When examining a given design option, a

crossover point occurs when the energy price rises to a point at which the savings in operating

cost compensate for the increased purchase expense of the design option. The disadvantage of

scenario analysis is that there is no information about the likelihood of each scenario.

In this analysis of water 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.

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Probability analysis considers the probabilities within a range of values. For quantities

with variability (e.g., electricity prices in different households), surveys can be used to generate a

frequency distribution of numerical values (e.g., the number of households with electricity prices

at particular levels) to estimate the probability of each value. For quantities with uncertainty,

statistical or subjective measures such as a triangular probability distribution can be used to

provide probabilities (e.g., manufacturing cost to improve energy efficiency to some level may be

estimated to be $10 +/- $3).

The advantage is that the probability approach provides the greatest information about the

outcome of the calculations, that is, the probability that the outcome will be in any particular

range is provided. The major disadvantage of the probability approach is that it requires more

information, namely information about the shapes and magnitudes of the variability and

uncertainty of each quantity.

Scenario and probability analysis provide some indication of the robustness of the policy

given the uncertainties and variability. A policy is robust when the impacts are acceptable over a

wide range of possible conditions.

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5 Details of LCC 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 of design options to improve the efficiency of residential water

heaters. To account for all the variability and uncertainty among consumers, the analysis is done

for thousands of households from a weighted sampling from DOE/EIA's 1993 Residential

Energy Consumption Survey (RECS) 7. In addition to the variety of consumers, wherever

possible, other inputs for the analysis are also represented as samples drawn from a range of

values. In this way, the analysis accounts for the full range of characteristics related to residential

hot water use.

All design options for water heaters are analyzed as if they were in production levels

equivalent to the typical existing baseline models, i.e., possessing similar economies of scale.

The term "typical existing" baseline is used in this analysis to refer to current water heater

models that use HCFC-141b as a blowing agent for foam insulation and are of the 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 of the baseline models is provided in the

Engineering Report.

Manufacturers' data from GAMA's consumers directory revealed 25 different volume

sizes for electric water heaters, 19 for gas, and 4 for oil. Within each volume size, there are

varying numbers of models. Some sizes have over 1,000 different models. For the purposes of

this study, the assumption was made that a size with more models indicated that more of that size

was shipped and, therefore, purchased. The sizes with the greatest number of models were

checked against GAMA shipment data for the 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 as representative of current market conditions.

Table 5.1.1 presents a list of all of the standard-size water heaters (based on rated tank volume)

considered in the LCC analysis.

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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 8 0 300

Gas-fired 30 110

Gas-fired (typical) 40 150

Gas-fired 50 190

Gas-fired 7 5 280

Oil-fired (typical) 32 120

Oil-fired 5 0 19 0

* rounded to the nearest 10 liters

The Montreal Protocol bans use of HCFC-141b as a blowing agent for polyurethane

foam insulation after 2003. For this analysis, HFC-245fa is assumed to be the substitute blowing

agent. Polyurethane foam made with HFC-245fa may be slightly less effective as an insulation.

Costs may be slightly higher as well. Additionally, the U.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 effect by the time any new efficiency standard becomes effective. The

future baseline models, which will incorporate these two changes, are referred to as the

"analytic" baseline models in this 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 or fuel switching. These issues are addressed in the

National Energy Savings analysis.

5.1.2 Combinations of Design 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 of cumulative payback as determined in the

Engineering Analysis. Hot water use and energy costs in this analysis reflect the range of values

among consumers, unlike the Engineering Analysis, which is based on the DOE Energy Factor

test procedure and average national energy prices.

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5.1.3 Five Major Modules

A spreadsheet model with five major modules is the basis of the 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 of these modules have accompanying data tables that are used for reference. Each

module has its own inputs and outputs, with some modules using as inputs the outputs of other

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 a Monte Carlo run by sampling all of the inputs 10,000

times. There is a separate spreadsheet available for each type of water 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 the risks 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>. If you have any

questions or are unable to access the web site, please contact Ms. Brenda Edwards-Jones at (202)

586-2945 or by fax at (202) 586-4617.

5.1.4 Flowchart

To provide a general overview, a flowchart showing the major sections of the spreadsheet

and the data flow between the modules is shown in Figure 5.1.1.

5.1.5 Description of Outputs

The main outputs of each 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 of hot water

use is not affected by water heater efficiency, so it is not calculated separately for each design

option.

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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 Discount DELTA LCC & Water

PAYBACK Heater Rate / \ CALCULATIONS / Lifetime

-LCC Comparisons,

Payback, and

Importance Charts

Figure 5.1.1 Flowchart of LCC Analysis Spreadsheet

The summary tables list the average value for each output and the percent of households

that would benefit by using that design option. For example, in the LCC and Payback module,

the values reported in the tables are LCC and Payback. In other modules, other outputs are

reported as appropriate.

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The impact of individual design options are shown in combined histogram and

cumulative frequency charts. These charts show the output (LCC or payback) by percent of the

population in order of ascending value. The bars of the histograms show the relative frequency

of different 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 of the

results for each value. The higher the absolute value of the correlation, the more influence the

input has on the output. A negative correlation indicates a decrease in output in response to an

increase in the input. For example, in Figure 5.2.6, the higher the discount rate, the larger the

difference in LCC.

The final type of chart is a tornado chart, which shows the impact of the inputs of each

module on the output in question. The sensitivity is measured as the rank order correlation

between each input and the output of interest. The higher the correlation the more influence that

input has on the output.

5.2 Life-Cycle Cost Module

5.2.1 Introduction

The life-cycle cost is defined as the total consumer expense over the lifetime of a water

heater, including purchase price and operating expenses (which includes energy expenditures).

Future operating expenses are discounted to the time of purchase, and summed over the lifetime

of the water heater.

5.2.2 Equations and General Descriptions for LCC and Payback

Life-cycle cost is defined by the following equation:

LCCoption = EquipCostoption + NPV(Drate, OprCostoption, Lifetime)

where:

EquipCost = cost of buying and installing a water heater ($)

= (equipment cost) + (sales tax) + (installation cost)

options = one of 5 design options for electric, 5 for gas, and 4 for oil-fired

NPV = Net present value ($) is defined by the following equation:

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Lifetime OrCost

NPV= I - -lar

year=I (1+ Drate)

Dte = Discount rate (real) (%)

OprCost = cost of operating a water heater ($/year)

= (energy usage) x (energy rate) + (maintenance cost)

Lifetime = Lifetime of water heater (years)

EquipCost is defined as the costs associated with buying and installing a water heater. This

includes the cost of a water heater plus sales tax, installation charges, and, if the water heater is

being replaced, charges for the removal of the old water heater.

NPV (Net Present Value ) is the present value today of a future stream of expenditures.

Dae is defined as the rate at which future expenditures are discounted to establish their present

value. A distribution of discount rates was derived to represent the variability in financing

methods consumers use in purchasing appliances. The resulting distribution of discount rates

will be used to calculate a distribution of life-cycle costs for water heaters.

Consumers purchase appliances in new homes and as retail purchases. The retail

purchases are paid by cash, credit cards, or retailer loans. A comment 8 (Whirlpool, 1990)

indicated that for white goods about 40% of retail purchases are paid in cash, 35% use credit

cards, and 25% use retailer loans. The same comment indicates 25% of appliance purchases are

for new homes. (For water heaters, it is estimated that purchases for new homes are now about

20%.) The method of purchase used by consumers is assumed to be indicative of the source of

the funds and the type of financing used by these consumers.

A range of interest rates that may reasonably be expected to apply in the future to

different types of consumer savings or financing were estimated.

For new housing, the estimated nominal mortgage rate ranges from 5-8%, the derived

after-tax rate is based on a tax of 28%, and an inflation rate of 2% is subtracted from the total.

The result is a range of real 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 by the 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 of 3% was selected as indicative of the maximum.

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The interest rates for retailer 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 6 months), the rate becomes much

higher. Maximum rates are over 20% nominal. However, if the purchase is paid for initially by

a credit card and the consumer pays off the balance in less than the life of the water heater, then

the effective interest rate is lower than the nominal credit card rate. The current assumption is a

range of 6-15% real.

DOE recognizes that other factors might be considered in the estimation of real consumer

discount rates, such as the actual impacts of appliance purchases on consumer savings,

indebtedness or consumption, and expressed or imputed consumer preferences. While such data,

if it were to become available, might provide a stronger analytical basis for DOE's choice of

discount rates, it is considered unlikely that such data would have a significant effect on the

range of values considered in the current analysis.

Figure 5.2.1 shows the distribution of real discount rates, ranging from 0 to 15%, with a

mean of 6%.

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 of Consumer Discount Rates

OprCost is defined as the expenditures necessary to keep the water heater operating. It has 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 is the period of time the water heater will provide service. Table 5.2.1 shows lifetimes

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for water heaters by fuel type. Oil-fired water heaters are assumed to have the same distribution

of lifetimes as gas-fired water heaters.

Table 5.2.1 Water Heaters and Lifetime by Fuel 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 of time needed to recover 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 of 5 design options for electric, 5 for gas-fired, and 4 for oil-fired

water heaters

base = the typical analytic baseline design

Numerically, the simple payback period is the ratio of the increase in purchase (and

installation) price to the decrease in annual operating expenditures (including maintenance) from

replacing the analytic baseline water heater with a water heater incorporating another design

option. Payback periods are expressed in years. A payback period of three years means that the

increased purchase price is equal to three times the value of reduced operating expenses in the

year of purchase, or that the increased purchase price is recovered in approximately three years

because of lower operating expenses. Payback periods greater than the life of the product mean

that the increased purchase price is never recovered in reduced operating expenses.

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5.2.3 General Description of Sources of Data

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 of data 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 from the

records of fuel suppliers. Also included are weather data (in the form of heating and cooling

degree days) and a weighting variable. The 1993 RECS survey consists of a total of 7,111 sample

households from across the contiguous U.S.

Most, but not all, of RECS household records are used in the analysis and are assumed,

with their weighted averages, to be representative of housing on a national scale. The households

that are included in the analysis have three defining features:

1. Running hot water

2. An individual water heater

3. One of four fuels: electricity, oil, gas, or LPG

Households without these features are not used in the analysis.

RECS sometimes reports ranges, rather than precise numbers, for variables, and there are

also certain omissions of crucial information for variables needed for this analysis. In order to

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 of interest, 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) of the U.S. Department

of Commerce, operates the National Climatic Data Center, which is the world's largest active

archive of weather 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 in the 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.

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Manufacturer Product Literature

Most manufacturers of water heaters provide dealers (and consumers) with literature

describing their models, including their efficiency ratings.

5.2.4 Life-Cycle Cost and Payback Results

Electric Water Heaters

Table 5.2.2 lists the portion of the population benefitting from each design option, in

terms of reduced 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

* median

Figure 5.2.2 shows the cumulative frequency of differences in LCC by design option for

electric water heaters. The percent of the population benefitting and being disadvantaged are

also shown on the graphs. Note that a negative difference in life-cycle cost for a given design

option indicates a savings. The width of the plot shows the spread of savings in the population.

In general, the design options with higher efficiencies tend to show a wider spread in the

population.

Figure 5.2.3 shows cumulative frequency of payback period by design option. The

percent of population which would have a payback of less 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.

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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 150

0 -IAl 60% Z

40% 1 00

000 0% 5

00 - 2 0% :.:-: - _._1N _ ,I N No20% . I -5 0

0 0% 0 -l0%

Delta LCC(S) Delta LCC($)

Delta Life Cycle Cost of 2.5' 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 1 - 80% tc -'°°° j ; : - 1 60% X 60%

; 1 000 S N s40% e

Delta LCC($) Delta LCC($)

I 40% , 40%

i Delta Life Cycle Cost of Tank Bottom Insulation

[ compared to Analytic Baseline (19985)

59% Benefit 41% Disadvantage

1500 20 2100%

iS~ 1000) jfti 60% 1 80%

. 500 , _n lN 40%

Delta LCC($)

.. Frequency -mCumulative %

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

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Payback Period of Heat Trap compared to Payback Period of 2" Jacket Insulation compared

Analytic Baseline (Years) to Analytic Baseline (Years)

82% payback = 3 years 42% payback <= 3 years

6000 . . ... 100% 2500 100%

4000 5 4^000 *80% e >,2000 80% o

400000 e 3000k r60% _ ' 1500 11 - 60% 

2000 -40V% SE 1000 - 40%

U.- 1000 - 20% 3 IU 500 20% o

0 l 0% 0 JlilH| a lsiB-i-.-..-.--- 0%

Years Years

Payback Period of 2.5" Jacket Insulation Payback Period of Plastic Tank compared to

compared to Analytic Baseline (Years) Analytic Baseline (Years)

32% payback <= 3 years 12% payback <= 3 years

2000 ---- 100% 2000 -- 100%

1500 2 80% 1500 80%

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

Uu cO N 0 _ ( ) N. 00 I In U . u< o %e 150 0 100%

- Ln I I8% 

Years YrYears

Payback Period of Tank Bottom Insulation

to Anlytic -compared Baseline (Years) ij ~8% payback ' 3 years

1500 - 100%

80% e i y 10 0 0 lir 60%

2 5 00 L -1 hn i nnn 40% a5 ~. _ _ n20% . 5

- n O N IU) 00

Years

ryA Frequency Cumulative %

Figure 5.2.3 Payback Period by Design Option for Electric Water Heaters

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Gas-fired Water Heaters

Table 5.2.3 lists the portion of the population benefitting from each design option, in

terms of reduced 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 Heat Traps 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 of differences in LCC by design option for

gas-fired water heaters. The percent of the population benefitting and being disadvantaged are

also show on the graphs. Figure 5.2.5 shows cumulative frequency of payback period by design

option. The percent of population which would have a payback of less than or equal to three

years is indicated.

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Delta Life Cycle Cost of Heat Trap compared to Delta Life Cycle Cost 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. .s 80% _ 1 86000 8o0%

6000l +60% i 40 60% |

400o% r_ 4000 40% E 40%

. 2000 20% 000 20% v

0 '0% OQOQOQOQQQ I O% -0 _ _ _ -0% &

Delta LCC($) Deta LCC($)

Delta Life Cycle Cost of 2.5" Jacket Insulation Delta Life Cycle Cost of Slde-Arm Design (w/

compared to Analytic Baseline (19985) Metal Tank) compared to 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 Cost of Improved Flue Baffle

compared to Analytic Baseline (1998$)

4022% Benefit 78% Dsadvantage

8000 2 -* 00 100% 

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 8- rD - - U? 

Doe LCC($)Delta LCC(C($)

Figure Difference 5.2.4 in Life-Cycle Cost by Design Option FluWater for Gas-Fired Heaters

compa -21d to Analytic Baselin (

22% Benefit 78% Disadvantage

4000

40%

Delta LCC($)

[~ ~-lFrequency = Cumulative %

Figure 5.2.4 Difference in Life-Cycle Cost by Design Option for Gas-Fired Water Heaters

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Payback Period of Heat Trap compared to Payback Period of 2' Jacket Insulation compared

Analytic Baseline (Years) to Analytic Baseline (Years)

95% payback <= 3 years 83% payback <= 3 years

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 2

0%

I 0% I - 0%

Years Years

Payback Period of 2.5' Jacket Insulation Payback Period of Side-Arm Design (w/ Metal

compared to Analytic Baseline (Years) Tank) compared to Analytic Baseline (Years)

59% payback <= 3 years 3% payback = 3 years

4000 - ---- '----'-_ 100% 2000 ...-.-. 100%

3000 80% * S 1500- o HB» - 80% *

1 2000 60% 1000 60 OaR 40%j i 40% 

20% 51000 20%

0 'a ..- .!--rlU ,:_ ; Ii;!0% o 0 : SL_: 1, II'a, : -- 0%

Years Years

Payback Period of Improved Flue Baffle

compared to Analytic Baseline (Years)

0% payback < 3 years

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

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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 the rank order correlation

of input 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.

Sensitivity Analysis - Electric Water Heaters

Delta Life Cycle Cost of 2.5' Jacket Insulation compared to Analytic Baseline (19985)

Discount rate 8

Water Heater Lifetime (years) -0.31

Total Cost to Buy and Install a 2.5'

Jacket insulation Water Heater 0

(19985$).:. 02

Annual Operating Cost in 2003 of

Analytic Baseline Water Heater -0.19

(19985)

Annual Operating Cost in 2003 of

2.5' Jacket Insulation Water Heater -0.16

(1998,$)

Total Cost to Buy and Install an 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 of 2.5" Jacket Insulation on

Electric Water Heater

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Sensitivity Analysis - Gas-fired Water Heaters

Delta Life Cycle Cost of 2' Jacket Insulation compared to Analytic Baseline (1998$)

Water Heater Lifetime (years) -0.50 -

Discount Rate 0.45

Annual Operating Cost in 2003 of

Analytic Baseline Water Heater -.27

(1998$)

Annual Operating Cost in 2003 of 2'

Jacket Insulation Water Heater -0.25

Total Cost to Buy and Install a 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 of 2" Jacket Insulation on

Gas-fired Water Heater

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5.3 Equipment Cost Module

5.3.1 Introduction to Equipment Cost

The equipment cost represents the sum of the retail price, sales tax, and installation costs.

The retail price is calculated from the manufacturer's cost multiplied by an overall markup.

The first half of this discussion addresses the typical existing baseline model; the analytic

baseline model is the basis for the later description of the design options.

5.3.2 Equation for Equipment Cost

The water heater cost (equipment cost only) is calculated using the equation:

EquipCostopion, si:e = MfrCoStopton. sie, x Markupsie x (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 of installation of water heater ($)

The markup is calculated using the following ratio:

Markups,,e = RetlPrice se / MfCost ,,s

where:

RetlPrice = water heater price at the retail outlet, all standard-size existing

baseline models ($)

Total installation cost is based on:

TotInstCostop,,o. = InstCost + AddInstCostP,,On

where:

InstCost = cost to install baseline water heater ($)

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AddlnstCost = additional cost(s) to install fuel-fired water heater with certain

design options ($)

The additional installation cost is calculated as follows:

AddInstCostp,,, = AddElecCostop,,o, + AddVentCosto,, o 0 + AddTubeCostopo.

where:

AddElecCost = additional cost of installing a new electric circuit for gas-fired

water heaters with design options that require electricity ($)

AddVentCost = additional cost of upgrading the venting system for gas-fired water

heaters with designs that increase recovery efficiency ($)

AddTubeCost = additional cost to install a burner tube extension for oil-fired water

heaters with certain design options ($)

5.3.3 General Description of Key Variables

MfrCost is the manufacturing cost to produce a water heater. This cost is the sum of the variable

and the fixed costs. The variable costs are composed of the direct costs to the manufacturer,

which are defined as the sum of the material, labor, and overhead costs. The variable

manufacturer cost is also called a full production cost. The fixed costs, the costs to convert to the

production of a new water heater design, are the sum of the capital cost and the product design

cost. The fixed manufacturer cost is sometimes called a conversion cost.

Markup is defined as the ratio between the retail price to the manufacturer's cost. This is an

overall markup; it may include several intermediate markups applied by a wholesaler or other

intermediate sellers.

SalesTax is the local, state or county tax applied to the water heater at the point of sale.

RetlPrice is defined as the retail outlet price of the water heater paid directly by the customer.

This price does not include the installation cost or any other miscellaneous fees such as delivery

fee, removal fee, permit fee, and parts fee.

TotInstCost is the total installation cost of the water heater. It is the price paid directly by the

customer to have the water heater installed including the additional cost of adding a new

electrical circuit and/or upgrading the venting system in the case of some gas-fired water heater

design options.

InstCost is the installation cost of the baseline water heater. It is the price paid directly by the

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customer to have the water heater installed, including any miscellaneous fees such as delivery

fee, removal fee, permit fee, and parts fee. It does not include the cost of adding a new electrical

circuit and/or upgrading the venting system in the case of gas-fired water heaters with design

options that may require these.

AddInstCost is the additional installation cost to install an electric circuit and/or to upgrade the

venting system of a gas-fired water heater, or to install a burner tube extension for oil-fired water

heater.

AddElecCost is the additional cost of installing an electric circuit for the gas-fired water heater

when the design option includes an intermittent ignition device and/or an electromechanical flue

damper and there is no pre-existing electrical outlet near the water heater.

AddVentCost is the additional cost to install an upgraded venting system or upgrade an existing

venting system to eliminate condensate problems in gas-fired water heaters with design options

that increase recovery efficiency. As discussed in the Engineering Report, the flue loss efficiency

has been limited to 80.0%. Consequently the only upgrades considered are the installation of

Type-B vent connectors between the water heater and the existing vent system.

AddTubeCost is the additional installation cost to install a burner tube extension for an oil-fired

water heater with thicker insulation than the baseline unit.

5.3.4 General Description of Sources of Data

Introduction

To determine the equipment cost, manufacturing cost, retail price, installation cost, and

sales tax information are needed. GAMA provided estimates of water heater manufacturing costs

for typical existing baseline models". LBNL contracted with a consultant' 2 recommended by

GAMA for additional data. (Fixed manufacturing costs, because they apply only to costs

associated with converting to new water heater designs, are discussed later in this section in

conjunction with the analytic baseline.)

The source of the retail price, the sales tax, and the installation cost is the LBNL Water

Heater Cost Database which contains data collected from large retail chains and various

wholesale distributors. The following variables from the database are used to identify the retail

price data:

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RatedVolume Volume of the water heater tank

WHModel Model name

YearsWarranty Number of years covered in the model's warranty

WHFuel Type of fuel 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 for all 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 other than typical existing baseline water heaters, i.e., all other standard

sizes, are based on the manufacturing cost for the typical water heater plus (or minus)

incremental costs for extra (or less) foam insulation and sheet metal.

Manufacturing Cost

Variable Manufacturing Cost. The variable component of the manufacturing cost for the typical

existing model is the sum of direct material, direct labor, overhead, and transportation 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 a part of the 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.

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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 water heaters are based on the

manufacturing cost for the typical existing baseline water heater plus (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 Water Heaters -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

The retail price is defined as the retail outlet price of the 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 is based on the LBNL Water Heater Cost Database 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 of retailer responses on which the retail cost data is based. Figure

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EE-RM-97-900 COMMENT 38UU
5.3.3 presents the sample sizes for gas-fired water heaters. For example, the retail price for the

50-gal electric water heater is based on a sample of 50 responses regarding the retail price of

existing baseline water heaters and the retail price for the 40-gal gas-fired water heater is based

on a sample of 52 responses. The size of the data samples generally reflects that of the 1996

GAMA-reported shipment share of each water heater size (rated volume)' 3. The comparisons of

GAMA water heater shipments vs. water heater sample size by rated 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 Cost Sample 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

30 gal 40 gal 50 gal 6 5 80gal 30 gal 40 gal 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 vs Sample Sizes

Retail Cost Sample 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

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EE-RM-97-900 COMMENT 38UU
show the minimum and maximum values for the retail price ranges obtained through the survey.

For example, the mean 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. In the case of gasfired water heaters, the mean retail price for the 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

Bectric Water Heaters Gas-fired Water Heaters

$600 $600 s600 5$56 .23

$500 _5 $ . 5.5007_-___--sl'____ |

'S400 .____ 1~~~~~~~~~$~~~5- _ _ _ _ _4 _) _ -U400 $ 29a 9 n 0 400 _-- __ _--_ -------- _.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 _

30 g 40 ga 50l 65l 80 gal- g

Figure_______ 5__RtilPics-_lcti30 gal 40 gal 50 gal 75 gal

Figure 5.3.5 Retail Prices - Electric Water Figure 5.3.6 Retail Prices - Gas-fired Water

Heaters Heaters

Installation Cost

The installation cost of the 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 for the

development of the 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 for electric water heaters, showing the number of

retailer responses on which 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 of 41 responses about installation costs for the existing baseline

water heaters and the installation cost for the 40-gal gas-fired water heater is based on a sample

of 48 responses.

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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 for gas-fired water heaters. The mean

values represent the average reported installation cost for each water heater size. The figures also

show the minimum and maximum values for installation costs obtained through the survey. For

example, the mean installation cost for the 50-gal electric water heater is $160.73, with the

minimum reported to be as little as $65.00 and the maximum as high as $258.00. The relatively

narrow installation cost range for 65-gal electric water heaters is primarily due to the small

installation cost sample size for this particular tank size (see Fig. 5.3.7). In the case of gas-fired

water heaters, the average installation cost for the 40-gal size water heater is $159.52, with a

minimum of $65.00 and a maximum of $258.00.

4tallatfin~CaI-st Installation Cost

BectriVterHeaters [ ts-fired Water Heaters

$350 t $300

$300 _____________$25ao $25__ o_ 25

o 0 o ___0 _____5 00 2 1

0 $200 - _ 0 16262 . $159.52 $156.52 15&71

° $150 - __ 

16£ 6 $1 ! 6 a 5 6 0 $1 73J 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

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Manufacturer-to-Retail Markup

The manufacturer-to-retail markup is defined as the ratio of the retail price to the

manufacturer cost. The retail prices reflect those of water heaters sold in 1998. Since the retail

price and the estimated manufacturer cost differ for each 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.

The markup includes the average national value for taxes of 5.20% (A.D.L., 1998). Note that the

retail prices are calculated using an exact value for the 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

Analytic Baseline

As explained in the Engineering Report, the HCFC-141b blowing agent currently in use

will be replaced by 2003. This report assumes that the 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 for the insulation components for both blowing agents are

shown in Table 5.3.5. The total cost per pound of foam with the new blowing agent is $1.32 as

compared to $1.00 for foam 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 of flammable vapors. The new analytic baseline model for gas-fired water heaters

includes the cost of design changes to prevent ignition of flammable vapors.

All of the following discussions are based on the analytic baseline models. The rated tank

volumes of the analytic baseline models are the same as the tank volumes of the existing baseline

models.

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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 not provide data for 2.5 " Jacket Insulation for electric water heaters, 2.5"

Jacket Insulation, Plastic Tank, and Side Arm Heater for gas-fired, nor any of the design options

for oil-fired water heaters. The missing data was supplemented by information obtained from

consultants M. Minnear and E. West' 5. LBNL recalculated the costs of the insulation and the

sheet metal to reflect the characteristics of the HFC-245fa blowing agent.

Design Option Combinations. As shown in Appendix F of the Engineering Report, many

combinations of design options were initially analyzed. Most of the selected designs consist of

combinations of basic design options. The Engineering Report gives a detailed explanation of the

selection of design option combinations and the payback calculations. Energy costs for ordering

and combining design options for all three fuel types were based on AEO's national average

energy prices for the year 2003. A list of design 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

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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 of each design component. The uncertainty ranges of the incremental

total costs for most of the design options were provided by GAMA. Some of the variations (2.5"

Jacket Insulation, Plastic Tank, and Side Arm Heaters) were developed using the ranges provided

by M. Minniear and E. West. Since the uncertainty values were provided for the existing models,

the next step was to recalculate the data to be applicable for the design options based on the

analytical model.

Incremental Manufacturing Costs

The LCC analysis uses individual design options that are then grouped together in

combinations of design options according to the results of the Engineering Analysis. This

analytic procedure requires incremental manufacturing costs of individual design options.

The distributions of the manufacturing costs for most 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 data is used as a basis 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 of the methodology used in the development. A

detailed explanation of the procedure is presented in Appendix B of this report.

The general methodology is as follows: 1) GAMA distributions of the manufacturing cost

for each design option (aside from the existing baseline) are adjusted for HFC-245fa foam by

adding or subtracting the cost of the foam. 2) The GAMA distributions of the manufacturing

cost for the other standard sizes are adjusted by adding or subtracting the cost of extra foam and

extra sheet metal. No size adjustments for costs of the Plastic Tank or Insulated Tank Bottom

design options were made. 3) The distributions of the manufacturing cost for the design options

not provided by GAMA are based on distribution ranges provided by LBNL consultants.

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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

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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 is included as a separate design option in this table, it is only used in conjunction with a Side Arm Heater.

Note: GAMA levels for gas-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)

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Table 5.3.10 lists the incremental costs for the 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 of the incremental manufacturing costs of separate

design options for the 50-gal electric water heater.

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Incremental Manufacturer Cost of Heat Traps Incremental Manufacturer Cost of 2" Jacket

Insulation

5000

4000 e 4000 5000 . l

30003000

C 2000 2000 . |

I 1000 1000 -

00008~88~~8 0000000000

$ $

Incremental Manufacturer Cost of 2.5 Jacket Incremental Manctrer Cost of Plastic 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 Cost of Insulated

Tank Bottom

4000

3000

2000

I 1000

Figure 5.3.11 Distribution of Incremental Manufacturing Cost for Separate Design Options for

Electric Water Heaters

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EE-RM-97-900 COMMENT 38UU
Table 5.3.11 lists the incremental costs for the 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 of the incremental manufacturing cost of separate

design options for the 40-gal gas-fired water heater.

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EE-RM-97-900 COMMENT 38UU
Incremental Manufacturer Cost of Heat Traps Incremental Manufacturer Cost of 2' Jacket

Insulation

10000

S" & 18° 600_0 ! ] 5000 6000

8 600 0 |8 l 4004000

o 4000 3000

u 2000 . 2000

00000000000 00000000000

$ $

Incremental Manufacturer Cost of 2.5" Jacket Incremental Manufacturer Cost of 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 of Incremental Manufacturing Costs for Separate Design Options for

Gas-Fired Water Heaters

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Variable Manufacturing Cost. The variable manufacturing cost for each design option is

calculated as the sum of the analytic baseline manufacturing cost plus the associated incremental

variable manufacturing cost for that design option. The incremental variable manufacturing cost

is the sum of the incremental material, labor, and overhead cost to produce the design option.

The typical analytic baseline variable manufacturing costs and the incremental variable

costs for design options used in the analysis for electric water heaters are presented in Table

5.3.12 and for the gas-fired water heaters in Table 5.3.13. These costs come from the Engineering

Report.

As mentioned earlier, for health and safety reasons, future gas-fired water heaters must

resist flammable vapor ignition. Because of this, the variable manufacturing cost for the analytic

baseline model includes a cost of $15 for a design to prevent ignition of flammable vapors.

Since the added variable cost is included in the typical analytic baseline design, it does not

impact the cost-effectiveness of any design improvement. Note that the incremental insulation

costs for the baseline electric water heater tank (50-gal) are lower than for gas-fired (40-gal),

because the insulation for the 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.

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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

Fixed Manufacturing Cost. The fixed component of the manufacturing cost is the cost to convert

the production line to manufacture a new water heater design. Some of the fixed costs used in

the analysis were submitted by GAMA; the consultants provided the rest of the fixed costs. The

fixed cost is the sum of the capital cost and the product design cost. Production volume has a

significant impact on the per unit conversion cost, particularly on the capital cost. GAMA did

not provide the range of production volume used to calculate the fixed costs, because of the need

to protect specific manufacturer responses.

The fixed manufacturing cost for each design option is the sum of the incremental capital

cost and the incremental product design cost to produce the design option. The incremental fixed

manufacturing cost data used in the analysis for electric water heaters is presented in Table

5.3.14 and for the gas-fired water heaters in Table 5.3.15.

The fixed manufacturing cost for the gas-fired analytic baseline model includes a capital

cost for a design to prevent ignition of flammable vapors. Since the added fixed cost is included

in the typical analytic baseline design, it does not impact the cost-effectiveness of any design

improvement. The assumed fixed cost of $20.00 for the ignition prevention design for gas-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 a total fixed cost for electric water heaters.

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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 Cost Data

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

Other Standard Sizes - Manufacturing Cost. 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 of this report. The manufacturing costs for all sizes were

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estimated from the variable manufacturing cost for the typical existing baseline water heaters by

adding or subtracting the cost of incremental amounts of insulation and sheet metal. It was

assumed that there would be no differences in the fixed manufacturing costs for other size water

heaters. The variable manufacturing costs for Heat Traps, Plastic Tank, and Insulated Tank

Bottom for electric water heaters, and Side Arm Heater and Improved Flue Baffle for gas-fired

water heaters, were assumed to be the same for all sizes. The variable manufacturing cost data

used in the analysis for electric water heaters are presented in Table 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 of increased jacket insulation are presented as incremental 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: Costs of increased jacket insulation are presented as incremental variable manufacturing costs and are based on the

typical analytic baseline.

As explained in the Engineering Report, multiple design options were developed for each

water heater fuel type.

Markup for Design Options

The manufacturer-to-retail markup was assumed to remain constant for all of the design

options within a standard size model. Thus, the retail price for any design was determined

simply by multiplying its manufacturer cost by the derived markup for the existing baseline water

heater of that size.

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EE-RM-97-900 COMMENT 38UU
5.3.5 Results

Electric Water Heater Equipment 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 of electric water heaters, where total

installed cost is the final total cost to the customer, i.e., the sum of the retail price, sales tax, 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, for each design option and for all standard sizes, the difference in

total installed cost compared to the analytic baseline for electric 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 of the incremental total installed cost.

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EE-RM-97-900 COMMENT 38UU
Delta Total Installed Cost of Heat Trap Water Delta Total Installed Cost of 2" Jacket Insulation

Heater compared to Analytic Baseline (1998$) Water Heater compared to Analytic Baseline

(1998$) 1

0000 - 100%

80D00 80% I 4000 -** * 100%

6000 6 3000 80% 2 I8i 6000 % 1 1 W! l~o: jf 60% _ 0

' 40 4 000 0% E 0% 40%~ 20% ' 2000 20% 5 O 0% E

.- N N N > S N 

$ $

Delta Total Installed Cost of 2.5' Jacket Delta Total Installed Cost of Plastic Tank Water

Insulation Water Heater compared to Analytic Heater compared 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%

500 0 aN0 _ 0% : 

Delta Total Installed Cost of Tank Bottom

Insulation Water Heater compared to Analytic

Baseline (1998S)

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

2 500 20% g

0 0

%

doa _ 11,111 NI ,j

$

Frequency a Cumulative %

Figure 5.3.13 Difference in Total Installed Cost by Design Option for Electric Water Heaters

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EE-RM-97-900 COMMENT 38UU
Gas-fired Water Heater Equipment Costs

Table 5.3.19 lists the average manufacturing and total installed cost for the analytic

baseline and the design option combinations for all sizes of gas-fired water heaters, where total

installed cost is the final total cost to the customer, i.e., retail price, sales tax, and any installation

cost.

Table 5.3.19 Equipment Costs for Gas-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 a wider 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 of the incremental total installed cost.

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EE-RM-97-900 COMMENT 38UU
Delta Total Installed Cost of Heat Trap Water Delta Total Installed Cost of 2' Jacket Insulation

Heater compared to Analytic Baseline (1998$) Water Heater compared to Analytic 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 |. 80% 8 - .. 0% 

$ $

Delta Total Installed Cost of 2.5' Jacket i Delta Total Installed Cost of Side-Arm Heater

Insulation Water Heater compared to Analytic I Water Heater compared to Analytic 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 Cost of 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

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EE-RM-97-900 COMMENT 38UU
5.4 Operating Cost Module

5.4.1 Introduction to Operating Cost Module.

Operating a water heater involves two costs. A residential consumer pays for fuel to

operate the water heater and for maintenance to keep the water heater running properly. Fuel

costs depend on the water heater energy usage and the per unit cost of fuel. Maintenance costs

depend on water heater design.

There are four types of fuel commonly used in residential water heaters--electricity, gas,

liquefied petroleum gas (LPG or propane), and distillate fuel (oil). Depending on the particular

type of water heater, more than one type of fuel may be used in its operation. For instance,

electric water heaters use only electricity, whereas gas-fired water heaters use gas (or LPG) 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 is the existing variability in energy price, which depends on the

rate schedule charged by the utility and the consumption pattern of the particular household. The

other is the uncertainty of future energy prices' 6. The uncertainty in the future trend of prices is

further complicated by the current restructuring of the electricity supply industry.

To deal with the variations in energy prices, the fuel rates reported in energy bills of the

sample in the 1993 RECS are used to represent the variability of energy price from house to

house. To account for future uncertainties, various scenarios of projected future energy prices

(trends by national 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 for each of the four

fuel prices, namely, electricity, gas, LPG, and oil, respectively.

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EE-RM-97-900 COMMENT 38UU
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 W. 'O O45 6J GRI exmIc

4

1995 2000 2005 2010 2015 2020

year

Figure 5.4.2 Gas Price Scenarios

EE-RM-97-900 COMMENT 38UU
U.S. Average Residential LPG Price -

Four Scenarios

1.40,

- -1.00 

.20 i

0.80

0 202 - LowGro1th myear

Figure 5.4.3 LPG Price Scenarios

U.S. Average Residential Oil Price -

Two Scenarios

7-

GRI 1986

_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

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Fiue544Ol8rc cnro

The~~~~~~~~~~~~~~~~~~~=. fogre show .htaleetiiypiepo._tin share a elnn aten hlh

price projections for gas and LPG are more varied~~~~~~~~. Oil prices remainrelatively.f.at a. 

After adjusting for 'nfltio ,= and' enrg :rc chngs enrg prcs frte

EE-RM-97-900 COMMENT 38UU
with it. Future annual operating costs are estimated as annual energy use multiplied by the

annual energy price series for each of the four scenarios. Section 5.4.4 gives a detailed

description of how the calculation is implemented in the spreadsheet models.

When a consumer saves electricity, the bill savings depend upon the marginal energy

charge as reflected in the utility rate schedule (cents per kilowatt-hour), which may be higher or

lower than the average rate. An exact accounting would require knowing for each household: the

quantity and timing of energy used with and without the saved energy, and the rate schedule (rate

per kilowatt-hour as a function of the quantity of kilowatt-hours used, including seasonal and/or

time-of-day pricing). In general, such detailed information is not known.

Three approaches are considered: I) average rates, calculated as the ratio of household

expenditures for electricity (including fixed charges) to kWh consumed; 2) partial

adjustment of known 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 of each of these 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 for average general service

residential rates for a large number of utilities that show fixed charges on average

represent about 7.5% of average rates).'7

Disadvantage: By reducing the value of energy savings in all cases, including

those where the marginal rate is higher than the average price including fixed

charges, this method under-estimates the actual consumer marginal energy rate in

some cases.

c) Estimate distribution of consumer 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

would be 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 is recognized that the use of

marginal energy rates would improve the accuracy of the 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 if removing fixed costs is more or less reflective of marginal rates, this intermediate

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EE-RM-97-900 COMMENT 38UU
step is not taken in this analysis.

In order to develop consumer marginal energy rates, the Department proposes to collect

data on current rate schedules and energy consumption. Those rates will be assigned to a

national sample of buildings and households, weighted to represent the total U.S. population of

buildings and households. The result will be a weighted distribution of consumption by marginal

rates. This approach will be applied to residential and commercial customers.

DOE proposes to obtain a sample of residential buildings from existing surveys, such as

the RECS or from a commercially available database. RECS data has the advantage of being in

the public domain. In contrast, a commercially available database is likely to be more expensive,

but may have significant added value in terms of assigning the buildings to states or to utilities,

including a broader sample of the population, and permitting stratification of this 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 by month will be included in

the database for each building, in order to treat seasonal changes in consumption and rates. Peak

demand will be included for commercial buildings.

Recent Federal surveys (RECS, Commercial Building Energy Consumption Survey

(CBECS)) gather information by fuel 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 bills but did not extract information on rate schedules, fixed charges, or marginal rates.

The Department proposes to explore the feasibility of extracting historical information on rate

schedules, including the relationship between fixed charges and marginal rates to average prices.

This effort, if successful, will provide information about the extent to which marginal rates differ

from average prices, or from average prices less fixed charges.

Given restructuring of parts of the 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 in the future involves changing

the current processing of the billing information so as to gather more detail from the bills, to

include consumption by month and pricing 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 of future surveys.

Residential electricity rate schedules will be collected from Federal databases where

available, state regulatory agencies or directly from utilities. The information obtained for each

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 of the set of rate schedules, the number of customers by

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EE-RM-97-900 COMMENT 38UU
state using each rate schedule, the total electricity sales by state by rate schedule, and (if possible)

monthly electricity sales by state by rate schedule.

In the database of buildings, such characteristics as energy consumption and expenditures

and number of customers by state or utility will be used to map a rate schedule onto each of the

buildings in the national sample. The marginal rate for each building will be the block from the

rate schedule corresponding to that building's monthly energy consumption.

For life-cycle savings calculations, the monthly energy savings will be estimated for each

building. Those monthly energy savings for each building will then be evaluated for each

building at the 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 of all three types of water

heaters-- electric, gas-fired, and oil-fired -- can be expressed as follows:

OprCost . - AnnuaIQa,-,T,,rPd.f x FutrPrice e + MaintCost

year, optons Energv7Tpe-elecgas.oilAn Ener peopn P + Main

For each particular type of water heater, the generic formula shows different specific

forms.

A. Equations for Electric Water Heater Operating Cost Module

OprCostyear.oion = AnnualQin oo0 n x FutrElecPriceye

and

FutrElecPriceyear = ElecPrice9g x EleclncrRatio yea

and

ElecPrice9 8 = ElecRate x Inflator93 x ElecScaler

where:

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EE-RM-97-900 COMMENT 38UU
AnnualQin = average annual electricity consumption (kWh/year)

FutrElecPrice = future price of electricity in 1998$ (0/kWh)

ElecPrice98 = revised RECS house electricity price in 1998$ (0/kWh)

ElecIncrRatio = ratio of future 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 of the 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. x FutrFuelPricee,.,,, + MaintCosto,,

and

FutrElecPriceyea, = ElecPrice9 8 x EleclncrRatioyear

FutrFuelPriceEnergyTypeyear = FuelPrice9s x FuellncrRatioEnergyTypeyear

and

FuelPrice98 = FuelRate x Inflator93 x GasScaler

and

ElecPrice9g = FuelRate x Inflator93 x ElecScaler

and, if EnergyType = LPG, then

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EE-RM-97-900 COMMENT 38UU
FuelPrice98 = FuelRate x Inflator93 x LPGScaler

where additionally:

AnnualQelec = annual electricity consumption (kWh/year)

AnnualQgas = annual gas consumption (MCF/year')

FutrFuelPrice = future price of water heating fuel($/MCF)

FuelPrice98 = revised water heating fuel price ($/MCF)

FuelIncrRatio = ratio of future 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 for real electricity price change

GasScaler = a conversion factor for real gas price change

LPGScaler = a conversion factor for real LPG price change

5.4.3 General Description of Key Variables

AnnualQin is the average annual energy consumption, i.e., the total amount of energy consumed

by the water heater during the process of heating water and keeping it hot. For electric water

heaters this is in kWh/yr. For fuel fired water heaters this is in Btu/yr.

Note: MCF denotes thousands of cubic feet. Wherever LPG is also applicable, the corresponding unit is

gal/year.

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EE-RM-97-900 COMMENT 38UU
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 of the water heater (MCF/year)

FuelRate is the price of water 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 of electricity for the household as reported in RECS (in 1993$). The

electricity price is defined as the average price per unit electricity (kWh) consumed. The analysis

averages any seasonal fluctuations in the price of electricity.

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 of inflation for

1998 will equal the average rate during the first quarter of 1998.

CPI199 8 - CPI

19 = 1.1251

CPI1993

Inflator96 is an inflation factor to convert AEO and GRI energy prices to 1998$

CPI1998 - - = 1.0362

CI 1996

FuellncrRatio is the ratio of future national average water heating fuel price to the 1998 price

for the selected scenario. The year 1998 serves as the base year.

FutrFuelPrice is the price of water heating fuel ($/MCF) in each future year. It is calculated as a

product of FuelPrice and FuellncrRatio for a particular fuel type.

EleclncrRatio is the ratio of national average electricity price between some future year and

1998 for the selected scenario. The year 1998 serves as the base year.

FutrElecPrice is the projected household electricity price at a particular sampled house from

RECS for the specified scenario in 1998$.

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EE-RM-97-900 COMMENT 38UU
ElecScaler is a conversion factor for real electricity price change, represented by the ratio of

electricity prices in 1998 to the electricity prices in 1993 in constant dollars.

NationalAveragePrice 998

= 0.9820

NationalAveragePrice,9 9 3

GasScaler is a conversion factor for real gas price change in constant dollars

NationalAveragePrice1 9 98 = 1.0601

NationalAveragePrice1993

LPGScaler is a conversion factor for real LPG price change in constant dollars

National Average Price1 99 8 = 0.6166

National Average Price1 993

FuelPrice, is the revised gas-fired water heating fuel price ($/MCF) in 1998. It takes the RECS

household energy price (FuelRate) and multiplies it by Inflator93 and the corresponding scaler

for gas or LPG, respectively.

ElecPrice, 8 is the revised electricity price. It takes the RECS household electricity price

(ElecRate) and multiplies it by the Inflator93 and the ElecScaler to change 1993 dollars to

1998 dollars to account for inflation and electricity price change.

MaintCost is the price to repair the water heater when it fails ($/year). In reality, if any electric

or the baseline gas-fired water heater fails, residential consumers tend to replace 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 of baseline oil-fired models is $97.14

per year. This mean value 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 on the same contract in a household.

5.4.4 General Description of Data Sources and Calculations in Spreadsheets

The data from the seven oil-fired equipment suppliers can be found in Appendix G of the Engineering Report.

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EE-RM-97-900 COMMENT 38UU
The average annual energy consumption is calculated with the Water Heater Analysis

Model (see Section 5.5 for a full discussion of WHAM) and is an input to the operating cost

module. In the electric water heater model, it represents the annual electricity use of a water

heater (AnnualQin). For water heaters that use more than one type of fuel, the annual usage of

each type of fuel is calculated separately. For instance, in some designs of gas-fired water

heaters, AnnualQin is a sum of the annual gas (or LPG) (AnnualQgas) and the electricity

consumption (AnnualQelec).

Fuel rates as reported in the 1993 RECS are used as a base to capture the variability of

fuel prices across the nation. Consumer Price Indexes (CPI) from the U. S. Bureau of Labor

Statistics are used to calculate Inflator93 that accounts for inflation over the period of 1993 to

1998.

Similarly, national average energy prices reported in DOE's Energy Information

Administration (EIA) Annual Energy Review'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 of unit fuel price (FuelPrice) in 1998 dollars for each RECS household.

DOE/EIA publishes projections of future energy prices in its Annual Energy Outlook

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 1998 Edition of the GRI Baseline Projection. 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 of the 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 of the energy price scenarios are derived by dividing each year's

projected price by the 1998 price (ElecIncrRatio for electricity and FuellncrRatio otherwise)

and applied to the FuelPrice of each RECS sample house to represent its future energy prices

(FutrElecPrice for electricity and FutrFuelPrice for other fuels) for the selected scenario. The

annual operating costs of the 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 of each 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 of historical LPG to oil prices.

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EE-RM-97-900 COMMENT 38UU
5.4.5 Operating Cost Results

Electric Water Heater Operating Cost

Table 5.4.1 lists the average annual operating cost for the analytic baseline and design

options for all sizes of electric 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 Costs for 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 for each design option, the difference in operating cost compared to

baseline.

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EE-RM-97-900 COMMENT 38UU
Delta Operating Cost in 2003 of Heat Trap Delta Operating Cost in 2003 of 2" Jacket

compared to Analytic Baseline (1998$) Insulation compared to Analytic Baseline (1998$)

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 of 2.5' Jacket Delta Operating Cost in 2003 of Plastic Tank

Insulation compared to Analytic Baseline (19988) compared to Analytic Baseline (198$)

2500 - -- * 100%

2500 . 100% 2000 80%

. 2000 80 1500

15 00. _ 5 60% 0%

IL 5000 00 I 0% 

0% o0%

I ' I 150 0

S/Year S/Year

Delta Operating Cost in 2003 of Tank Bottom

Insulation compared 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

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EE-RM-97-900 COMMENT 38UU
Gas-fired Water Heater Operating Costs

Table 5.4.2 lists the average annual operating cost for the analytic baseline and for design

options of all standard sizes of gas-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 a cumulative frequency plot of the difference in operating cost

compared to baseline for gas-fired water heaters.

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EE-RM-97-900 COMMENT 38UU
Delta Operating Cost in 2003 of Heat Trap Delta Operating Cost in 2003 of 2' Jacket

compared to Analytic Baseline (1998$) Insulation compared to Analytic Baseline (1998$)

6000 100%

5000 80% 5000 100%

60% _>i |4000-. | ; g.4000jf -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 In 2003 of 2.5' Jacket Delta Operating Cost In 2003 of Side-Arm Heater

Insulation compared to Analytic Baseline (1998$) compared to Analytic Baseline (1998)

2500 100%

4000 100% 2000 - . 0 32000 O80 % a

O C I 20003 of Imp40d

Baffle compared to Analytic Baseline (1998$)

4000 -u 100%

4,300 0- y -80% e

3 20000 0 3

. 1{ ;' 40% I

0 -S 0% 5ooI 

~ear WSIear~S/Year

r-q Frequency BCumulatibe %

Figure 5.4.6 Difference inta Operating Costs by Design 2003Options FluWater for Gas-Fired Heaters

Baffl-64-e compared to Aalytc 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

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EE-RM-97-900 COMMENT 38UU
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 a variety of operating conditions and water heater characteristics when calculating

energy consumption. Three parameters - recovery efficiency (RE), standby heat loss coefficient

(UA), and rated input power (Pon) - are used to describe the efficiency characteristics of the

water heater. The operating conditions of the water heater are indicated by average daily hot

water draw volume, inlet water temperature, thermostat setting, and air temperature around the

water heater.

WHAM was developed as a method to quickly and reliably estimate residential water

heater energy consumption. Because it is written as an equation, it can be implemented in

spreadsheets. It does not require the detailed inputs that other water heater simulation models

demand. In each of the 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 for each

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 for the Engineering Analysis and Pon from

manufacturers' product literature to describe the energy performance of water heaters.

5.5.2 Equations for Energy Use

The WHAM equation, which solves for average daily water heater energy consumption

(Qi,), is expressed as follows:

vol den -Cp (Ta - nk Tn) UA (T Tank- Tamb )

in..=P+ 24 UA) (T ank 1 amb)

where:

Qin = total water heater energy consumption (Btu/day)

RE = recovery efficiency

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EE-RM-97-900 COMMENT 38UU
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 of the air surrounding the water heater (°F)

vol = volume of hot water drawn in 24 hours (gal/day)

den = density of stored water at the average of the setpoint and inlet temperature

(Ib/gal)

Cp = specific heat of stored water at the setpoint temperature (Btu/lb-°F)

5.5.3 General Description of Key Variables

Recovery Efficiency (RE). The recovery efficiency (RE) is the ratio of energy 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 or the burner is firing. RE covers the

steady-state efficiency only. It accounts for the amount of energy lost through the water heater

jacket and the flue and fittings while the heater is firing.

Rated Input Power (Pon). Rated input power is the nominal power rating the manufacturer

assigns to a particular design of water heater expressed in kW for electric water heaters or Btu/hr

for gas-fired or oil-fired water heaters. For gas-fired water heaters 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 input required to maintain the water at the setpoint temperature. This represents the rate

at which energy must be added to the water heater when it is not heating water for delivery.

Thermostat Setpoint Temperature (Ttnk). The thermostat setpoint temperature is the desired

delivery temperature of the hot water.

Inlet Water Temperature (Tin). The inlet water temperature is the temperature of the water

supplied to the water heater.

Temperature of the Air Surrounding the Water Heater (Tamb). The temperature surrounding

the water heater is the ambient air temperature of the space in which the water heater is located.

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EE-RM-97-900 COMMENT 38UU
Volume of Hot Water Drawn in 24-Hour Period (vol). This is the estimated daily household

use of hot water.

Density of Water (den). The density of hot water at the average of the setpoint and inlet

temperatures. This is mass per unit volume, expressed as Ib/gal (kg/l).

Specific Heat of Water (Cp). The specific heat of water at the average of the setpoint and inlet

temperatures. This is the amount of heat needed to increase or decrease the temperature of 1

pound of water by 1 °F (1 kg/K).

5.5.4 General Description of Sources of Data

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 by the U.S. DOE EF test 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, and Pon

The LCC analysis uses RE and UA values from computer simulations developed for the

Engineering Analysis. Two detailed water heating simulation programs - WATSIM for electric

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 by the Electric

Power Research Institute (EPRI) 20 . The use of WATSIM is explained in the Engineering Report.

The output of WATSIM does not directly provide values for RE and UA. It does, however,

provide detailed temperature profiles of the water inside the tank during the simulation run.

These temperature readings can be used to determine the energy parameters of the electric water

heater using the standard test procedure calculations. A spreadsheet tool, described in Appendix

A of the 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 is explained in the Engineering Report. The

outputs of TANK include RE and UA.

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The simplified water heater analysis model (WHAM) was used for the analysis of oilfired water heaters. In the case of the oil-fired water heaters, the total daily energy consumption

was calculated based on the estimated burner operating hours. Then, a rearranged WHAM

equation was used to estimate UA. The use of the WHAM model for the calculation of the

energy parameters for oil-fired water heaters is explained in the Engineering Report.

The primary source of data for rated input power (Pon) is the water heater manufacturers'

product literature. In order to generate values for Pon, a large sample of water heaters was

examined and typical values for each standard size were assigned.

Table 5.5.1 is a summary of all standard water heater sizes studied in this analysis with

corresponding values for UA, RE, and Pon for the 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

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EE-RM-97-900 COMMENT 38UU
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. The typical tank diameter for each standard size is determined from a large

sample of water heaters selected from the product literature. The actual tank volume of the

electric water heater is 10% less than the rated volume. The values for the tank diameter and

actual tank volume were used to calculate the tank height. The rest of the geometry parameters,

such as the locations of the 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 of the baseline model. In WATSIM all heights are referenced from the

bottom of the tank support skirt (top of the base pad).

Table 5.5.2 Electric Water Heater Modeling 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 of H.W. Inlet (ft) 3.48 4.60 4.54 4.55 4.52

Height of Heater Element I (ft) 0.48 0.63 0.62 0.62 0.60

Height of Heater Element 2 (ft) 2.48 3.28 3.24 3.25 3.23

Height of Thermostat 1 (ft) 0.70 1.01 1.00 1.00 1.00

Height of Thermostat 2 (ft) 2.79 3.69 3.64 3.65 3.62

Height of Feed-Through 1 (ft) 3.48 4.60 4.54 4.55 4.52

Height of Feed-Through 2 (ft) 3.48 4.60 4.54 4.55 4.52

Height of Feed-Through 3 (ft) 0.13 0.13 0.13 0.13 0.13

Height of Feed-Through 4 (It) 3.48 4.60 4.54 4.55 4.52

Table 5.5.3 shows the values of the gas-fired water heater parameters which have been

adjusted in TANK in order to model all the standard tank sizes. All the required TANK input

parameters, such as the tank diameter, the internal flue diameter, and the firing rate for each

standard size, are determined from a large sample of water heaters selected from product

literature. The actual tank volume of the gas-fired water heater is 5% less than the rated volume.

The TANK simulation program calculates most of the geometry parameters based on the values

for the tank diameter and volume. The location (elevation) of the thermostat does not change

from size to size and the thermostat is fixed at a height of 0.39 feet (11.9 cm). TANK requires an

input for the 'Volume to Thermostat (gal)' parameter, which is determined as the amount of

water that would need to be added to an empty water heater tank to raise the level of the water to

the thermostat location. This parameter is determined using the specific tank diameter and the

thermostat elevation.

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EE-RM-97-900 COMMENT 38UU
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 of design options as they applied to all of the standard-size baseline models.

Determination of the Uncertainty Ranges for EF, RE, UA, and Pon

The energy factor (EF) is the ratio of output energy in the form of hot water to the input

energy at the standard test conditions. The WHAM equation is used in the LCC analysis to

calculate EF values for all the design options as a function of RE, 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 of the 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, a consultant.

The EF uncertainty range data for the typical tank size was used to develop ratios to

represent the variations of the EF values for all the standard tank sizes.

The range of uncertainty for RE and UA was developed from the range of uncertainty for

EF. This is done by calculating the variations in RE and UA that would independently cause the

desired variation of EF. The range on the RE and UA terms is reduced by 1/V2. This assumes

that the RE and UA distributions have approximately equal impacts on EF. A detailed

explanation of the entire procedure to develop the uncertainties for the water heater energy

parameters is found in Appendix C. Variations in Pon have a much smaller impact on EF within

the operating limits of actual water heaters. Values for the variations in Pon were developed by

determining the Pon range for each standard size of water 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 for gas water heaters. Figure 5.5.1 shows the variation of EF for

electric water heaters caused by deviations of RE, UA, and Pon from typical values of RE =

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 of RE = 78%, UA = 14.4 Btu/hr-°F, and Pon = 40,000

Btu/hr.

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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

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EF Sensitivity Using WHAM

at default electic water heater values

0.950

0.900

.o

UJ

0.850

I-- effectofRE .

.- ffect ofUA I

0.800

-15% -10% -5% 0% 5% 10% 15%

parnatchange

Figure 5.5.1 Variations of EF for Electric Water Heaters

EF Sensitivity Using WHAM

at default gas-red water heater vaues

0.600 -_

i efectofdRE |

i-- efectd of LA

ieddffePon /

0.580

0.560 -

0.540

0.520 -

0.500

-15% -10%/ -5% 0% 5% 10% 15%

parameter change

Figure 5.5.2 Variations of EF for Gas-fired Water Heaters

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APPENDIX A: SENSITIVITY CHARTS FOR SELECTED DESIGN OPTIONS

Sensitivity in this study is defined as the response of a forecast to a change in an

assumption. It measures how the uncertainty of each assumption effects the variation of a

forecast variable using rank order correlation. The calculation is done by ranking the sampled

values of the assumptions and the resulting forecast, with the largest value assigned the highest

rank and the smallest the lowest, and then computing the correlations between each of the

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 of how 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 the reverse. A correlation coefficient of 1 (or -1) means

that assumptions and forecasts have the strongest proportional (or adversely proportional)

relationship whereas 0 means no relationship at all.

The sensitivity analysis result is plotted as a "Tornado Chart" that provides a quick and

easy view of the influence each assumption has on a particular 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 by the bar on the top of a chart is the

most important. Crystal Ball, an add-in to Excel spreadsheets, also allows the correlation

coefficients between all pairs of forecasts be calculated while the simulation is running so that

the effect of intermediate forecasts on the another forecast can be evaluated, such as the impact

of hot 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 of total installed cost, operating cost and daily energy consumption for the 2"

Jacket Insulation design option for electric water heaters and the 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 for households

with electric water heaters and for households with gas-fired water heaters.

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EE-RM-97-900 COMMENT 38UU
Sensitivity Analysis - Electric Water Heaters

Delta Life Cycle Cost of Heat Traps compared to Analytic Baseline (1998$)

Discount rate 0.33

Water Heater Lifetime (years) -0.26

Annual Operating Cost in 2003 of

Analytic Baseline Water Heater -0.22

(1998$) |

Annual Operating Cost in 2003 of

Heat Trap Water Heater (1998$)

Total Cost to Buy and Install a Heat

Trap Water Heater (1998$) 0.05

Total Cost to Buy and Install an

Analytic Baseline Water Heater 0.02

(1998$)

-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 2' Jacket Insulation compared to Analytic Baseline (1998$)

! 5

Discount rate E 0.35

Water Heater Lifetime (years) -0.29

Total Cost to Buy and Install a 2"

Jacket Insulation Water Heater 0.20

(1998$)

Annual Operating Cost in 2003 of

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-2

EE-RM-97-900 COMMENT 38UU
Sensitivity Analysis -Electric Water Heaters

Delta Life Cycle Cost of 2.5' Jacket Insulation compared to Analytic Baseline (1998S)

Discount rate L ;'JS ' 0.38

Water Heater Lifetime (years) -0.31

Total Cost to Buy and Install a 2.5"

Jacket insulation Water Heater 0.

(1998$)

Annual Operating Cost in 2003 of

Analytic Baseline Water Heater -. 19

(1998$)

Annual Operating Cost in 2003 of

2.5" Jacket Insulation Water Heater -0.16

(1998$)

Total Cost to Buy and Install an

Analytic Baseline Water 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 Plastic Tank compared to Analytic Baseline (1998$)

Discount rate 0

Total Cost to Buy and Install a -- i t.~" 0.35 Plastic Tank Water Heater (1998$)

Water Heater Lifetime (years) -0.31

Annual Operating Cost in 2003 of

Analytic Baseline Water Heater .0.20

(1998$) i^-

Annual Operating Cost in 2003 of -0.18 l j1 Plastic Tank Water Heater (1998$)

Total Cost to 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-3

EE-RM-97-900 COMMENT 38UU
Sensitivity Analysis - Electric Water Heaters

Delta Life Cycle Cost of Tank Bottom Insulation compared to Analytic Baseline (1998$)

Total Cost to Buy and Install a Tank

Bottom Insulation Water Heater 0.41

(1998$) :< i ; : i 04

Discount rate . 0.35

Water Heater Lifetime (years)29

Annual Operating Cost in 2003 of I

Analytic Baseline Water Heater -0.19

(1998$)

Total Cost to Buy and Install an i

Analytic Baseline Water Heater -* 0.17

(1998$)

Annual Operating Cost in 2003 of

Tank Bottom Insulation Water -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 Install a 25' Jacket Insulation Water Heater (1998$)

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

Cost to Install a 2.5" Jacket ', -, '

Insulation Water Heater (1998$) ; -

Cost to Manufacture a 2.5" 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-4

EE-RM-97-900 COMMENT 38UU
Sensitivity Analysis - Electric Water Heaters

Operating Cost of 2.5" Jacket Insulation Water Heater

compared to Analytic Baseline (19985)

Annual Energy Consumption of 2.5" -'. :'; -:; : i

Jacket Insulation Water Heater 0.8 8

(kWh/year)

Revised electricity price in 1998$

($kWh)

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

Sensitivity Analysis - Electric Water Heaters

Daily Energy Consumption of 2.5' Jacket Insulation Water Heater

Daily Hot Water Use (Gal/day) : *;. ; :- 0 91

Water heater thermostat setpoint 0.26

Inlet water temperature -0.26

Standby Heat Loss Coefficent of i :23

2.5" Jacket Insulation l - 0.23

Ambient air temperature (around

water heater) i

Rated Input Power of 2.5' 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-5

EE-RM-97-900 COMMENT 38UU
Sensitivity Analysis - 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 of occupants age 0 -5 years , -i, 0.22

Nominal size of water heater f, 0.22

Coefficent for "air 0.15

Senior only household in multi-family buildings 0.15

Number of occupants age 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-6

EE-RM-97-900 COMMENT 38UU
Sensitivity Analysis -Gas-fired Water Heaters

Delta Life Cycle Cost of Heat Traps compared to Analytic Baseline (19985)

Water Heater Lifetime (years) -0.32 IT

Discount Rate 0.29

Annual Operating Cost in 2003 of

Analytic Baseline Water Heater .

(1998$)

Annual Operating Cost in 2003 of

Heat Trap Water Heater (19985) -0.20

Total Cost to 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

Sensitivity Analysis - Gas-fired Water Heaters

Delta Life Cycle Cost of Two Inch Jacket Insulatlon compared to Analytic Baseline (1998$)

Water Heater Lifetime (years) -0.50

Discount Rate 045

Annual Operating Cost in 2003 of

Analytic Baseline Water Heater -. 27r

(19985)

Annual Operating Cost in 2003 of 2"

Jacket Insulation Water Heater .0.25

(1998)

Total Cost to Buy and Install a 2"

Jacket Insulation Water Heater r 0.12

(1998$) Ld

Total Cost to 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-7

EE-RM-97-900 COMMENT 38UU
Sensitivity 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 Cost to Buy and Install a 2.5"

Jacket Insulation Water Heater 0.22

(1998$)

Annual Operating Cost in 2003 of

2.5 Jacket Insulation Water Heater -0.20

(1998$)

Total Cost to Buy and Install an

Analytic Baseline Water 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 Heater compared to Analytic Baseline (1998$)

Total Cost to 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 in 2003 of

Analytic Baseline Water Heater -009

(1998$)

Annual Operating Cost in 2003 of

Side Arm Heater Water Heater -0.05

(1998$)

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

A-8

EE-RM-97-900 COMMENT 38UU
Sensitivity Analysis -Gas-fired Water Heaters

Delta Life Cycle Cost of Improved Flue Baffle compared to Analytic Baseline (19985)

Water Heater Lifetime (years) -0.50

Discount Rate I. .i, 0.45

Annual Operating Cost in 2003 of . .

Analytic Baseline Water Heater -0.42

(1998s)

Annual Operating Cost In 2003 of

Improved Flue Baffle Water Heater -0.40

(1998$)

Total Cost to Buy and Install an

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

Total Cost to Buy and Install a 2' Jacket Insulation Water Heater (1998$)

Total Combined Markup from

Manufacturer Cost to 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-9

EE-RM-97-900 COMMENT 38UU
Sensitivity Analysis - Gas-fired Water Heaters

Operating Cost of 2' Jacket Insulation Water Heater

compared to Analytic Baseline (1998$)

Annual Gas or LPG Consumption of *. :, ;

S - 2 Jacket Insulation Water Heater 090i

(MCF/year)

Revised water heating fuel price in 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

Sensitivity Analysis -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 of 2" 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

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Sensitivity Analysis - Gas-fired Water Heaters

Daily Hot Water Use (gaUday)

Total number of ocupants ,. , --- a .- i 0.70

Number of occupart age 14 -64 yearns 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

Adult t home during day 'i; 0.24

Number of occuparts age 0 -5 years 0.20

Nominal aize of water heater 0.19

Househod Doe Not Own Dastnwhe -0.16 r

Average outdoor air tarnparture 0 .14

Inlet watrtmprature 0.14

Water heatera themostal alpoint -0.14

Houahold Does Not Omn Clotes Waers I -0.12

Coeffidaent Tor TIr ~.0.12

CofiaentforTar Tin' 011

Coeftciant for Ttank' 0.11

-1.00 -0.80 -0.60 -0.40 -0.20 0.00 0.20 0.40 0.60 0.80 1.00

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APPENDIX B: DISTRIBUTIONS OF WATER HEATER MANUFACTURING

COSTS

Background and Methodology

The LCC analysis uses individual design options that are then grouped together in

combinations of design options according to the results of the Engineering Analysis. This

analytic procedure requires incremental manufacturing costs of individual design options.

The distributions of the manufacturing costs for most design options were provided by the

Gas Appliance Manufacturers Association (GAMA) as cumulative curves of total 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 of the incremental manufacturing costs for the other standard sizes and

for the analyzed design options.

The data summarizes 10,000 samples randomly drawn from ranges of total

manufacturing cost provided by four major water heater manufacturers. Figure B. 1 shows

manufacturing costs for the 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

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The following method was used to estimate the range of incremental manufacturing costs

for individual design options from this data. It was assumed that the manufacturing costs reported

for the typical existing baseline water heater and the water heater with heat traps were highly

correlated. This assumption allows the difference between these two cumulative curves to be

observed.

A plot of this data shows each segment separately as in Figure B.2. What can be seen in

this plot is that some of the segments spread across a much larger range of costs, so that the

density of samples per dollar is much lower. Also, many of the segments overlap in cost.

A constant sample density throughout each segment is assumed. With this assumption, it

is possible to assign a fraction of the samples in each segment to any cost range the segment

spans. The segments are then further subdivided at the points where the cost ranges overlap and

the fractions of samples are distributed into new smaller cost ranges.

The fractions of the original segments are combined where they span identical ranges of

costs to give an assessment of the relative frequency of samples within each cost range. This

data can be plotted as a histogram of the frequency of the incremental costs of that 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 of Total Manufacturing Costs

Figure B.2 Difference Between Cumulative Cost Curves as Separate Segments

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Incremental 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 of the methodology used to develop the incremental manufacturing

costs for the design options and all standard sizes is presented in the main body of this report in

Table 5.3.8 for electric water heaters and Table 5.3.9 for gas-fired water heaters. A detailed

discussion of the implementation process is presented below.

The general approach is as follows: 1) GAMA distributions of the manufacturing cost for

each design option, except for the existing baseline, are adjusted for HFC-245fa foam by adding

or subtracting the cost of the foam. 2) The GAMA distributions of the manufacturing cost for the

other standard sizes are adjusted by adding or subtracting the cost of extra foam and extra sheet

metal. 3) The distributions of the 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 of the manufacturing costs for the 30-gal and

40-gal sizes are calculated by subtracting the cost of extra foam and extra sheet metal from the

cumulative data for 50-gal size. The distributions of the manufacturing costs for the 65-gal and

80-gal sizes are calculated by adding the cost of extra foam and extra sheet metal to the 50-gal

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size.

Analytical Baseline: The distribution of the manufacturing cost for the 50-gal size is

calculated by adding the incremental cost of the HFC-245fa foam to the "GAMA Level 1" data.

The distributions of the manufacturing costs for each of the other standard sizes are calculated by

adding the incremental cost of HFC-245fa foam to the "GAMA Level 1" data already calculated

for the existing baseline of the corresponding size. The added incremental cost of HFC-245fa

blown foam varies from $1.51 (30-gal) to $2.68 (80-gal).

Heat Traps: The distribution of the manufacturing cost is calculated as an incremental

cost difference between "GAMA Level 2" and "GAMA Level 1" data as explained at the

beginning of this appendix. The same incremental cost distribution is used for the other size

water heaters.

2" Jacket Insulation: The distribution of the 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 of the HFC-245fa foam. The distribution of the

manufacturing costs for the other sizes is accomplished in two steps: first, by adding the

incremental cost of the 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 of extra

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 the distribution of manufacturing costs, a multiplier was calculated for each water heater

size based on the ratio of the total incremental manufacturing cost of the 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, the multiplier is 23.77/13.49=1.762. This value is used to multiply the 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 for this design option. The incremental cost

distribution was provided by the LBNL consultant. The cost range varies from -5% to +10%.

Insulated Tank Bottom: The 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.

Gas-fired Water Heaters

Existing Baseline: "GAMA Level 1" data is used directly for the typical existing water

heater size (40-gal rated volume). The distribution of the manufacturing cost for the 30-gal size is

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calculated by subtracting the cost of extra foam and extra sheet metal from the cumulative data

for the 40-gal size. The distributions of the manufacturing costs for the 50-gal and 75-gal are

calculated by adding the cost of extra foam and extra sheet metal to the 40-gal size.

Analytical Baseline: The distribution of the manufacturing cost for the 40-gal size is

calculated by adding the incremental cost of the HFC-245fa foam and the cost of the flammable

vapor ignition device ($35) to the "GAMA Level 1" data. The distributions of the

manufacturing costs for each of the other standard sizes are calculated by adding the incremental

cost of the HFC-245fa foam and the incremental cost of foam and sheet metal for the other tank

sizes to the "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 of the manufacturing cost for the 40-gal size is

developed as an incremental cost difference between "GAMA Level 3" and "GAMA Level 1"

data and adding the incremental cost of the HFC-245fa foam. The distribution of the

manufacturing cost for the other sizes is accomplished in two steps: first, by adding the

incremental cost of the 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 of extra

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 for each water heater size based on the ratio of

the total incremental manufacturing cost of the 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 by the 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 is calculated 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.

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References

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. Residential Water Heaters: Initial Estimates of Manufacturing Costs

and Energy Consumption, Task 1 of LBNL Subcontract 6466797. Minniear Corporation,

Panama City, FL. November 12.

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APPENDIX C: UNCERTAINTY OF ENERGY PARAMETERS EF, RE, UA,

AND PON

Energy Factor (EF)

Estimated uncertainty ranges for the energy factors (EFs) of different design options were

provided for the typical tank size of electric (50-gal) and gas (40-gal) water heaters by an LBNL

consultant.' Ratios were developed to represent the minimum and maximum variations in the EF

values of the typical tank sizes. Since each design option is a combination of several single

designs, the ratio of a combined design option is assigned to be the largest among the single

designs involved. For example, gas-fired water heater design option 3 (1 + 2.5" Jacket

Insulation) is a combination of three single designs, the Analytic Baseline, Heat Traps, and 2.5"

Jacket Insulation. The uncertainty range of design option 3 is the largest range of these three

single designs. This ensures that the estimated uncertainty ranges include those of every single

design.

Then, by multiplying the ratios of the different design options by their corresponding EF

values, ratios for EF values of all the standard tank sizes were calculated. The resulting

uncertainty ranges for EF are characterized by the minimum, the most-likely, and the maximum,

so that the probability distribution can be described by a simple triangular distribution. The

uncertainty ranges are also in compliance with the Code of Federal Regulation ruling that

specifies that reported EF values must be no higher than the mean value. In both electric and

gas water heaters, the largest range of the EF is within 4% of the value in our simulation study.

The determination of the ranges of uncertainty for recovery 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 how big the ranges of these parameters can be to

yield the reported ranges of uncertainty on EF independently. To achieve this, the partial

derivative of EF to each of the three parameters RE, UA, Pon, is computed. The width of the

range is reduced 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 of uncertainty of Pon should be decided separately.

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Recovery Efficiency (RE)

The set of equations to solve RE for a given EF is:

(REE md e X EFmaxx 41094 x (UA x 675- Pon)

o12 Pon x (1620 x EFmaxx UA - 41094)x X

= RE min mod e X (RE EFminx 41094 x (UAx 675- Pon)

m mode+ Ponx (1620x EFminx UA- 41094) x 2

Standby Heat Loss Coefficient (UA)

Similarly, the range of uncertainty for UA can be determined by the following set of

equations:

/Ponx (EFmin

UAmax = UAmodex 1 -l + 2EF67.5x (RExPonx 41094-

,,(A „ f Ponx (EFmax - )

UA min = UAmodeX 1 - + -4 2 

67.5x (REx Pon 41094 )xi

Rated Input (Pon)

Since the variation in Pon has an negligible effect on the uncertainty of EF. the

determination of the uncertainty is independent of the EF value. Therefore, the minimum and the

maximum numbers from the LBNL water heater database were used, as listed below:

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_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. Residential Water Heaters: Initial Estimates of Manufacturing Costs

and Energy Consumption, Task 1 of LBNL Subcontract 6466797. Minniear Corporation,

Panama City, FL. November 12.

2. Title 10, Code of Federal Regulations, Part 430- Energy Conservation Program for

Consumer Products, Section 430.24(e)(1)(ii). January 1, 1998.

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