10-i

CHAPTER 10: NATIONAL IMPACT ANALYSIS

TABLE OF CONTENTS

10.1 INTRODUCTION ......................................................................................................... 10-1

10.2 FORECASTED EFFICIENCIES FOR BASE AND STANDARDS CASES .............. 10-1

10.2.1 Method and Assumptions .............................................................................................. 10-1

10.3 NATIONAL ENERGY AND WATER SAVINGS ...................................................... 10-4

10.3.1 Definition ....................................................................................................................... 10-4

10.3.2 Inputs.............................................................................................................................. 10-6

10.3.2.1 Shipments.....................................................................................................10-6

10.3.2.2 Equipment Stock..........................................................................................10-6

10.3.2.3 Annual Energy Consumption per Unit ........................................................10-6

10.3.2.4 National Annual Energy and Water Consumption ......................................10-7

10.3.2.5 Site-to-Source Conversion Factors..............................................................10-8

10.4 NET PRESENT VALUE............................................................................................... 10-9

10.4.1 Definition ....................................................................................................................... 10-9

10.4.2 Inputs............................................................................................................................ 10-11

10.4.2.1 Average Annual Product Cost ...................................................................10-11

10.4.2.2 Annual Operating Cost Savings per Unit...................................................10-12

10.4.2.3 Total Annual Increases in Product Cost.....................................................10-13

10.4.2.4 Total Annual Savings in Operating Cost ...................................................10-13

10.4.2.5 Discount Factor..........................................................................................10-13

10.4.2.6 Present Value of Costs...............................................................................10-14

10.4.2.7 Present Value of Savings...........................................................................10-14

10.5 RESULTS OF NES AND NPV CALCULATIONS ................................................... 10-14

10.5.1 Summary of Inputs....................................................................................................... 10-14

10.5.2 Results of National Energy and Water Savings Calculations...................................... 10-15

10.5.3 Results of Net Present Value Calculations .................................................................. 10-17

10.6 ANNUALIZED NATIONAL COSTS AND BENEFITS ........................................... 10-17

10.6.1 Calculation Method...................................................................................................... 10-18

10.6.2 Results for the Adopted Standards............................................................................... 10-19

LIST OF TABLES

Table 10.2.1 Standard Clothes Washers: Base-Case Efficiency Distributions....................... 10-2

Table 10.3.1 Shipment-Weighted Average Annual Energy Consumption in 2015................ 10-7

Table 10.4.1 Shipment-Weighted Average Product Cost in 2015 for Base and Trial 

Standards Levels.............................................................................................. 10-12

Table 10.5.1 Inputs to Calculation of National Energy Savings and Net Present Value...... 10-15

Table 10.5.2 Cumulative (2015-2044) National Energy and Water Savings ....................... 10-16

Table 10.5.3 Discounted Cumulative National Energy Savings........................................... 10-16
10-ii

Table 10.5.4 Discounted Cumulative National Water Savings ............................................ 10-16

Table 10.5.5 Discounted Cumulative Net Present Values.................................................... 10-17

LIST OF FIGURES

Figure 10.2.1 Projected Shipment-Weighted Integrated Modified Energy Factors as a 

Function of Standard Level for Front-Loading Clothes Washers...................... 10-4

Figure 10.3.1 Marginal Site-to-Source Conversion Factors for Electricity ............................. 10-9
10-1

CHAPTER 10. NATIONAL IMPACT ANALYSIS

10.1 INTRODUCTION

This chapter describes the method the U.S. Department of Energy (DOE) used to 

estimate the national impacts of trail standard levels (TSLs) for two product classes of clothes 

washers: front-loading and top-loading standard. DOE evaluated the following impacts: (1) 

national energy and water savings (NES) attributable to each possible standard, (2) monetary 

value of those energy savings to consumers of the considered products, (3) increased total 

installed cost of the products because of standards, and (4) net present value (NPV) of energy 

and water savings (the difference between the operational savings and increased total installed 

cost).

DOE determined both the NES and NPV for all the efficiency levels considered for new 

standards for residential clothes washers. DOE performed all calculations for each considered 

product using a Microsoft Excel spreadsheet model, which is accessible on the Internet.

<www.eere.energy.gov/buildings/appliance_standards/> The spreadsheets, which implement the 

National Impact Analysis (NIA) model, combine the calculations for determining the NES and 

NPV for each considered product with input from the appropriate shipments model. Details and 

instructions for using the NIA model are provided in appendix 10-A. 

Chapter 9 provides a detailed description of the shipments models that DOE used to 

forecast future purchases of the considered products. Chapter 9 includes detailed descriptions of 

consumers’ sensitivities to total installed cost, operating cost, and income, and how DOE 

captured those sensitivities within the model. 

To estimate the national impacts of new standards for all the product classes considered 

in this rulemaking, DOE allocated the product cost and annual energy consumption of each

representative product class to all product classes within its category. 

10.2 FORECASTED EFFICIENCIES FOR BASE AND STANDARDS CASES

This section describes the method DOE used to forecast the energy efficiencies of 

considered products under the base case and each of the potential standards cases. It provides 

efficiency distributions for both product classes of clothes washers.

10.2.1 Method and Assumptions

A key factor in estimating NES and NPV is the trend in energy efficiency forecasted for 

the base case (without new standards) and each of the standards cases. In calculating the NES, 

per-unit annual energy consumption is a direct function of product efficiency. For the NPV, two 
10-2

inputs, the per-unit total installed cost and the per-unit annual operating cost, depend on 

efficiency. The first input, the per-unit total installed cost, is a direct function of efficiency. The 

per-unit annual operating cost, because it is a function of the per-unit annual consumption, is 

indirectly dependent on product efficiency. 

Chapter 8 described how DOE developed a base-case energy efficiency distribution 

(which yields a shipment-weighted average efficiency) for each of the considered product classes 

for the first year of the forecast period. To project the trend in efficiency over the entire forecast 

period, DOE considered recent trends and the potential effect of programs such as ENERGY 

STAR. As discussed in chapter 8, DOE did not find a basis for projecting an increase in the 

average efficiency of front-loading clothes washers. For top-loading clothes washers, DOE 

assumed that the growth in share of the medium- and high-efficiency levels would level off at 

around 20 percent. Although there is room for the shares of the higher efficiency levels to grow, 

DOE believes that the growth will be constrained by the likelihood that consumers with a strong 

interest in energy efficiency will purchase front-loading clothes washers instead of top-loading 

clothes washers.

Table 10.2.1 provides the base-case efficiency distributions for the three years in 

which AHAM provided data (2006-2008) as well as the years 2015 (the assumed effective date 

of new standards) and 2022. The year 2022 is identified because it is seven years after 2015, the 

time period between the year 2008 (the last year in which data was made available by AHAM) 

and 2015.

Table 10.2.1 Standard Clothes Washers: Base-Case Efficiency Distributions

Front Loading Top Loading

Standard

2006 2007 2008

Base Case

2006 2007 2008

Base Case

Level 2015 2022 2015 2022

Baseline 10.60% 3.80% 0.10% 0.0% 0.0% 46.9% 45.7% 43.6% 40.4% 40.0%

1 10.97% 2.77% 1.4% 0.0% 0.0% 46.9% 45.7% 43.6% 40.4% 40.0%

2 10.97% 2.77% 1.4% 0.0% 0.0% 0.55% 0.6% 1.9% 2.8% 2.9%

3 10.97% 2.77% 1.4% 4.3% 4.3% 0.18% 0.2% 0.6% 0.9% 1.0%

4 51.10% 19.70% 24% 24.0% 24.0% 0.18% 0.2% 0.6% 0.9% 1.0%

5 2.7% 37.90% 48.90% 48.9% 48.9% 0.18% 0.2% 0.6% 0.9% 1.0%

6 1.3% 15.20% 11.40% 11.4% 11.4% 2.60% 3.7% 4.6% 9.1% 9.5%

7 1.3% 15.20% 11.40% 11.4% 11.4% 2.60% 3.7% 4.6% 4.6% 4.7%

8 0% 0% 0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%

SWMEF 1.91 2.20 2.20 2.20 2.20 1.38 1.39 1.42 1.46 1.46

SWIMEF 1.57 1.84 1.84 1.85 1.85 0.95 0.97 1.00 1.03 1.04

SWIWF 8.37 7.41 7.48 5.11 5.11 9.69 9.59 9.48 9.28 9.69

SWMEF Shipment weighted modified energy factor

SWIMEF Shipment weighted integrated modified energy factor

SWIWF Shipment weighted integrated water factor

To determine efficiency distributions for cases in which a candidate standard applies, 

DOE used a “roll-up” scenario for 2015, the year that compliance with any revised standards 
10-3

would be required. DOE assumed that product efficiencies in the base case that did not meet the 

standard under consideration would roll up to meet the new standard in 2015. However, because 

ENERY STAR criteria in 2011 consist of an MEF ≥ 2.00 and a WF ≤ 6.0, DOE also assumed 

that the ENERGY STAR program would not affect the front-loader or top-loader market for any 

new standards set at efficiency levels below the future ENERGY STAR requirements. As a 

result, for top-loader efficiency levels 1 through 5 and front-loader efficiency levels 1 through 3, 

DOE estimated that efficiency distributions would remain unchanged from 2015 through 2044 

(the end of the analysis period). For any new standards set at efficiency levels above the 2011 

ENERGY requirements, DOE assumed that the market share of efficiency levels beyond the 

standard increased. The level of increase was set equal to the market share change from 2006 to 

2008 for the efficiency level directly preceding the standard. Using the above criteria, DOE 

assumed that from 2015 to 2022 the shipment weighted integrated modified energy factor 

(SWIMEF) market share would grow linearly. As noted earlier in the discussion of base-case 

efficiency distributions, DOE chose a year of 2022 because it is it is seven years after 2015, the 

time period between the year 2008 (the last year in which data was made available by AHAM) 

and 2015. Because of the difficulty in forecasting changes in the market beyond 2022, DOE

refrained from speculation and simply assumed that after 2022 the market would remain 

unchanged through 2044.

Figure 10.2.1 is a graphical representation of DOE’s approach. The figure shows a plot of 

the shipment-weighted integrated modified energy factor for Front-Loaders for the base case and 

each candidate standard level. Similar figure could be created for Top-Loading units as well.
10-4

Figure 10.2.1 Projected Shipment-Weighted Integrated Modified Energy 

Factors as a Function of Standard Level for Front-Loading 

Clothes Washers

10.3 NATIONAL ENERGY AND WATER SAVINGS

DOE calculated the national energy and water savings associated with the difference 

between the base case and the case associated with each potential standard for clothes washers. 

DOE calculated cumulative energy savings throughout the forecast period, which extends from

2015 to 2044. The equations shown calculate energy savings; DOE used similar equations to 

calculate water savings. 

10.3.1 Definition 

The following equation shows that DOE calculated annual national energy and water 

savings (NEWS) as the difference between two projections: a base case (without new standards) 

and a standards case. Positive values of NEWS represent energy savings (that is, national annual 

energy consumption (AEC) under a standard is less than in the base case).

1.70

1.80

1.90

2.00

2.10

2.20

2.30

2.40

2.50

2005 2010 2015 2020 2025 2030 2035 2040

SWIMEF

Base TSL 1 TSL 2

TSL 3 TSL 4 TSL 5
10-5

STD

_

BASE NESy = AEC AEC

Cumulative energy and water savings are the sum of annual national energy and water 

savings throughout the forecast period, which extends from the assumed effective date of new 

standards to 30 years after that date. The calculation is represented by the following equations for 

energy and water.

NEScumulative NESy

NWScumulative  NWSy

DOE calculated the national annual energy and water consumption by multiplying the 

number or stock of each product class (by vintage) by its unit energy and water consumption 

(UEC or UWC; also by vintage). The calculation of national annual energy consumption is 

represented by the following equation.

AECySTOCKV UECV

DOE defined the quantities for the above expressions as follows.

AEC = national annual energy consumption each year in quadrillion British thermal units 

(quads), summed over vintages of the product stock, STOCKV;

STOCKV = stock of product (millions of units) of vintage V that survive in the year for which 

DOE calculated annual energy consumption;

UECV = annual energy consumption per product in kilowatt hours (kWh) [electricity 

consumption is converted from site energy to source energy (quads) by applying a 

time-dependent conversion factor];

V = year in which the product was purchased as a new unit; and 

y = year in the forecast.

The stock of a product depends on annual shipments and the lifetime of the product. As 

described in chapter 9, DOE projected product shipments under the base case and standards 

cases. DOE projected that shipments under the standards cases would be slightly lower than 

under the base case, because of the higher purchase cost of more efficient products. In other 

words, DOE believes that the higher purchase cost would cause some consumers to forego 

purchasing new products. 

To avoid including savings attributable to shipments displaced because of standards, 

DOE used the projected standards-case shipments and, in turn, the standards-case stock, to 

calculate the annual energy consumption for the base case. 
10-6

10.3.2 Inputs 

The inputs to the calculation of national energy savings (NES) are:

• Shipments;

• product stock (STOCKV);

• annual energy consumption per unit (UEC);

• national annual energy consumption (AEC); and

• site-to-source conversion factor (src_conv).

10.3.2.1 Shipments

DOE forecasted shipments of each product class under the base case and all standards 

cases. Several factors affect forecasted shipments, including purchase cost, operating cost, and 

household income. As noted earlier, the increased cost of more efficient products causes some 

consumers to forego buying the products. Consequently, shipments forecasted under the 

standards cases are lower than under the base case. The method DOE used to calculate and 

generate the shipments forecasts for each considered product class is described in detail in 

Chapter 9, Shipments Analysis.

10.3.2.2 Equipment Stock

The equipment stock in a given year is the number of products shipped from earlier years 

that survive in that year. The NIA model tracks the number of the number of units shipped each 

year. DOE assumes that products have an increasing probability of retiring as they age. The 

probability of survival as a function of years since purchase is the survival function. Chapter 9

provides additional details on the survival functions that DOE used for each product class.

10.3.2.3 Annual Energy Consumption per Unit

DOE used the shipment-weighted integrated modified energy factors (SWIMEFs) 

presented in section 10.2 for the base case and standards cases, along with the data on annual 

energy consumption presented in chapters 7 and 8, to estimate the shipment-weighted average 

annual per-unit energy consumption under the base and standards cases. The average annual perunit energy consumption projected for 2015 for each product category is shown in Table 10.3.1.
10-7

Table 10.3.1 Shipment-Weighted Average Annual Energy Consumption in 2015

Base 

Case

Trial Standards Levels

1 2 3 4 5

Front-Loading Standard

 SWIMEF 1.85 1.85 1.85 1.91 2.20 2.46

 Avg. Elec Use 246 246 246 241 234 214

 Avg. Gas Use 1.20 1.20 1.19 1.17 1.09 0.97

 Avg. Oil Use 0.04 0.04 0.04 0.04 0.04 0.04

Top-Loading Standard

 SWIMEF 1.03 1.35 1.41 1.35 1.83 2.04

 Avg. Elec Use 431 335 322 335 264 261

 Avg. Gas Use 2.21 1.69 1.90 1.69 1.49 1.46

 Avg. Oil Use 0.08 0.06 0.06 0.06 0.05 0.05

Front-Loading Compact

 SWIMEF 1.03 1.13 1.13 1.13 1.13 1.13

 Avg. Elec Use 199 173 173 173 173 173

 Avg. Gas Use 0.90 0.85 0.85 0.85 0.85 0.85

 Avg. Oil Use 0.04 0.03 0.03 0.03 0.03 0.03

Top-Loading Compact

 SWIMEF 0.59 0.86 0.86 0.86 1.15 1.15

 Avg. Elec Use 346 233 233 233 190 190

 Avg. Gas Use 1.62 1.23 1.23 1.23 0.86 0.86

 Avg. Oil Use 0.06 0.04 0.04 0.04 0.03 0.03

10.3.2.4 National Annual Energy and Water Consumption

The national annual energy and water consumption (AEC) is the product of the annual 

energy and water consumption per unit and the number of units of each vintage. This method of 

calculation accounts for differences in unit energy consumption from year to year. The equation 

for determining the annual energy consumption, which was presented in section 10.3.1, is

repeated here. As stated previously, the equations for water consumption are the same as the 

equations for energy consumption.

AEC STOCKV UECV

In determining national annual energy consumption, DOE first calculated annual energy 

consumption at the site, then applied a conversion factor, described below, to calculate primary 

energy consumption. Annual water consumption is calculated at the site only. No conversion 

factor was applied to water consumption.
10-8

10.3.2.5 Site-to-Source Conversion Factors

In determining national annual energy consumption, DOE initially calculated the annual 

energy consumption at the site (for electricity, the energy in kWh consumed at the household or 

establishment). It then used site energy consumption to calculate primary (source) energy 

consumption by applying a conversion factor to account for losses associated with the 

generation, transmission, and distribution of electricity. The site-to-source conversion factor is a 

multiplicative factor used to convert site energy consumption into primary or source energy 

consumption, expressed in quads (quadrillion Btus). DOE used annual site-to-source conversion 

factors based on the version of the National Energy Modeling System (NEMS)athat corresponds 

to EIA’s Annual Energy Outlook 2010 (AEO 2010).1The factors are marginal values, which 

represent the response of the system to an incremental decrease in consumption. For electricity, 

the conversion factors change over time in response to projected changes in generation sources 

(i.e., the types of power plants projected to provide electricity to the Nation). Figure 10.3.1

shows the site-to-source conversion factors from 2005 to the end of the forecast period. DOE 

assumed that conversion factors remain at 2030 values throughout the rest of the forecast.

 

a

For more information on NEMS, please refer to the U.S. Department of Energy, Energy Information 

Administration documentation. A useful summary is National Energy Modeling System: An Overview 2000, 

DOE/EIA-0581(2000), March 2000. EIA approves use of the name NEMS to describe only an official version of 

the model without any modification to code or data. Because this analysis entails some minor code modifications 

and the model is run under various policy scenarios that are variations on EIA assumptions, DOE refers to the model 

by the name NEMS-BT (BT is DOE’s Building Technologies Program, under whose aegis this work has been 

performed). NEMS-BT was previously called NEMS-BRS.
10-9

Figure 10.3.1 Marginal Site-to-Source Conversion Factors for Electricity

10.4 NET PRESENT VALUE

DOE calculated the net present value (NPV) of the increased product cost and reduced 

operating cost associated with the difference between the base case and each potential standards 

case for the considered residential clothes washer product classes. 

10.4.1 Definition

The NPV is the value in the present of a time-series of costs and savings. The NPV is 

described by the equation:

NPV PVS PVC _=

Where:

PVS = present value of savings in operating cost, and 

PVC = present value of increased total product cost to consumers. 

0

2000

4000

6000

8000

10000

12000

14000

2000 2005 2010 2015 2020 2025 2030 2035 2040 2045 2050

Year

Marginal Site-to-Source Conversion Factor for 

Electricty (Btu/kWh)
10-10

DOE determined the PVS and PVC according to the following expressions.

PVS ∑OCSy  DFy

PVC ∑TICy  DFy

Where:

OCS = total annual savings in operating cost each year summed over vintages of the product 

stock, STOCKV;

TIC = total annual increases in product cost each year summed over years of the product 

shipments, SHIPy;

DF = discount factor in each year; and 

y = year in the forecast.

DOE calculated the total annual consumer savings in operating cost by multiplying the 

number or stock of a given product class (by vintage) by its per-unit operating cost savings (also 

by vintage). DOE calculated the total annual increases in consumer product cost by multiplying 

the number or shipments of the given product class (by vintage) by its per-unit increase in 

consumer product cost (also by vintage). The calculation of total annual operating cost savings 

and total annual product cost increases is represented by the following equations.

OCSy∑STOCKV UOCSV

TICy∑SHIPyUTICy

Where:

STOCKV = stock of products of vintage V that survive in the year for which DOE calculated 

annual energy consumption;

UOCSV = annual per-unit savings in operating cost;

V = year in which the product was purchased as a new unit;

SHIPy = shipments of products in year y; and

UTICy = annual per-unit increase in installed product cost in year y.

DOE determined the total increased product cost for each year from the effective date of 

a potential standard to 2044. DOE determined the present value of operating cost savings for 

each year from the effective date of the standard to the year when all units purchased by 2044

have been retired. DOE calculated costs and savings as the difference between a standards case 

and a base case without new standards. 
10-11

DOE developed a discount factor from the national discount rate and the number of years 

between the present (i.e., year to which the sum is being discounted) and the year in which the

costs and savings occur. The NPV is the sum over time of the discounted net savings.

10.4.2 Inputs

The inputs to calculation of the net present value (NPV) are:

• Average annual product cost;

• average annual savings in operating cost;

• total annual increases in product cost;

• total annual savings in operating cost; 

• discount factor;

• present value of costs; and

• present value of savings.

The increase in total annual product cost is equal to the annual change in the average 

annual product cost (difference between base case and standards case) multiplied by the 

shipments forecasted in the standards case. As with the calculation of the NES, DOE did not 

calculate total annual product costs using base-case shipments. To avoid including savings due to 

displaced shipments (by consumers deciding not to buy higher-cost products), DOE used the 

standards-case projection of shipments and, in turn, the standards-case stock, to calculate product 

costs. 

The total annual savings in operating cost savings are equal to the change in annual 

operating cost (difference between base case and standards case) per unit multiplied by the 

shipments forecasted in the standards case. 

10.4.2.1 Average Annual Product Cost

The average annual product cost is directly dependent on efficiency. DOE therefore used

the SWIMEFs presented in section 10.2 for the base case and each standards case, along with the

product costs at various efficiency levels (presented in chapter 8), to estimate the shipmentweighted average annual product cost under the base and standards cases. Table 10.4.1 shows the 

shipment-weighted average consumer product cost based on the SWIMEFs that correspond to 

the base case and each standards case in 2015.

In the preliminary analysis, DOE followed its past practice and assumed that the 

manufacturer costs and retail prices of products meeting various efficiency levels remain fixed, 

in real terms, after 2010 (the year for which the engineering analysis estimated costs) and 

throughout the period of the analysis. As discussed in chapter 8, examination of historical price 

data for certain appliances and equipment that have been subject to energy conservation 
10-12

standards indicates that the assumption of constant real prices and costs may, in many cases, 

over-estimate long-term appliance and equipment price trends.

For the direct final rule, DOE applied a price trend based on historical PPI data for 

household laundry equipment to forecast the price of clothes washers sold in each year in the 

forecast period (see chapter 8 for derivation and description of the price trend). DOE also 

investigated the impact of different product price forecasts on the consumer net present value 

(NPV) for the considered TSLs for residential clothes washers. DOE considered four product 

price forecast sensitivity cases: (1) a trend based on the experience curve approach;b(2) a trend 

based on the “chained price index--other consumer durable goods except ophthalmic” that was 

forecasted for AEO2010; (3) constant prices at 2010 levels. The approach used to forecast the 

price trends and the results of these sensitivity cases are described in appendix 10-D.

Table 10.4.1 Shipment-Weighted Average Product Cost in 2015 for Base and Trial 

Standards Levels

Base 

Case

Trial Standards Levels

1 2 3 4 5

Front-Loading Standard

SWIMEF 1.85 1.85 1.85 1.91 2.20 2.46

Avg. Product Cost 2010$ $893 $893 $893 $898 $938 $964

Top-Loading Standard

SWIMEF 1.03 1.35 1.41 1.35 1.83 2.04

Avg. Product Cost 2010$ $447 $454 $461 $454 $523 $536

Front-Loading Compact

SWIMEF 1.03 1.03 1.03 1.03 1.03 1.03

Avg. Product Cost 2010$ $861 $865 $865 $865 $865 $865

Top-Loading Compact

SWIMEF 1.03 1.03 1.03 1.03 1.03 1.03

Avg. Product Cost 2010$ $419 $426 $426 $426 $480 $480

10.4.2.2 Annual Operating Cost Savings per Unit

The average annual operating cost includes the costs for energy, repair, and maintenance. 

As described in chapter 8, for all the considered products DOE assumed that potential standards 

would produce no increase in maintenance or repair costs. For both product classes, therefore, 

 

b

In the experience curve method, the real product price (or proxy thereof) is related to the cumulative production or 

“experience” with a product. As experience accumulates, the cost of producing the next unit decreases. The 

percentage reduction in cost that occurs with each doubling of cumulative production is known as the learning or 

experience rate. In typical experience curve formulations, the experience rate parameter is derived using two 

historical data series: price (or cost) and cumulative production, which is a function of shipments during a long time 

span.
10-13

DOE determined the per-unit annual savings in operating cost based only on the savings in 

energy costs attributable to a standard. DOE determined the per-unit annual savings in operating 

cost by multiplying the per-unit annual savings in energy consumption developed for each 

product class by the appropriate energy price. As described in chapter 8, DOE forecasted energy

prices based on EIA’s AEO 2010. 

10.4.2.3 Total Annual Increases in Product Cost 

The total annual increase in product cost for any given standards case is the product of 

the average cost increase per unit due to the standard and the number of units of each vintage

shipped. The equation for determining the total annual increase in product cost for a given 

standards case, which was shown in section 10.4.1, is repeated here.

TICy∑SHIPyUTICy

10.4.2.4 Total Annual Savings in Operating Cost 

The total annual savings in operating cost for any given standards case is the product of 

the annual savings in operating cost per unit attributable to the standard and the number of units 

of each vintage. This method accounts for differences in annual savings in operating cost from 

year to year. The equation for determining the total annual savings in operating cost for a given 

standards case, which was presented in section 10.4.1, is repeated here. 

OCS ∑STOCKV UOCSV

10.4.2.5 Discount Factor

DOE multiplied monetary values in future years by a discount factor to determine the 

present value. The discount factor (DF) is described by the equation:

( y yp )

_

( r )

DF

1+

1

=

Where:

r = discount rate, 

y = year in which the monetary value exists, and 

yP = year in which the present value is being determined.

Although DOE used consumer discount rates to determine the life-cycle cost of clothes 

washers (chapter 8), it used national discount rates to calculate national NPV. DOE estimated 

NPV using both a 3-percent and a 7-percent real discount rate, in accordance with the Office of 

Management and Budget’s guidance to Federal agencies on the development of regulatory 
10-14

analysis, particularly section E therein: Identifying and Measuring Benefits and Costs.

2 DOE 

defined the present year as 2011.

10.4.2.6 Present Value of Costs

The present value of increased product costs is the annual total cost increase in each year 

(the difference between a standards case and the base case), discounted to the present and 

summed throughout the period in which DOE is considering the installation of products (that is,

from the effective date of standards, 2015 to 2044). DOE calculated annual increases in installed 

cost as the difference in total product cost for new appliances purchased each year, multiplied by 

the shipments in the standards case.

10.4.2.7 Present Value of Savings

The present value of savings in operating cost is the annual savings on operating cost (the 

difference between the base case and a standards case), discounted to the present and summed 

from the effective date to the time when the last unit installed by 2044 is retired from service.

Savings are decreases in operating cost associated with the higher energy efficiency of products

purchased in the standards case compared to the base case. Total annual savings in operating cost 

are the savings per unit multiplied by the number of units of each vintage that survive in a 

particular year. 

10.5 RESULTS OF NES AND NPV CALCULATIONS

The National Impact Analysis (NIA) model produces estimates of the NES and NPV 

attributable to a given candidate standard level. The inputs to the NIA model were discussed in 

sections 10.3.2 (inputs to NES) and 10.4.2 (inputs to NPV). DOE generated the NES and NPV 

results using a Microsoft Excel spreadsheet, which is accessible on the Internet 

<www.eere.energy.gov/buildings/appliance_standards/> Details regarding and instructions for 

using the spreadsheet are provided in appendix 10-A.

10.5.1 Summary of Inputs

Table 10.5.1 summarizes the inputs to the NIA model. A brief description of the data is

provided for each input.
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Table 10.5.1 Inputs to Calculation of National Energy Savings and Net Present Value

Input Description

Shipments Annual shipments from shipments model. (See chapter 9.)

Effective date of standard 2015

Base-case forecasted efficiencies See section 10.2.

Standards-case efficiencies See section 10.2.

Annual energy consumption per unit Annual weighted-average values are a function of SWEUF. 

(See section 10.3.2.1.)

Total installed cost per unit Annual weighted-average values are a function of the 

efficiency distribution. (See section 10.4.2.1.)

Energy and water cost per unit Annual weighted-average values are a function of annual 

energy and water consumption per unit and energy prices. 

(See chapter 8 for energy and water prices.)

Repair and maintenance costs per unit No changes in repair and maintenance cost assumed at higherthan-baseline efficiency levels.

Forecast of installed cost per unit Price forecast based on historical PPI data.

Forecast of energy and water prices Energy prices: EIA AEO2010 forecasts (to 2035) and 

extrapolation thereafter. (See chapter 8).

Water prices: Bureau of Labor Statistics 2010 from 1953 and 

extrapolation thereafter. (See chapter 8).

Marginal energy site-to-source 

conversion factor

A time-series conversion factor that includes electric 

generation, transmission, and distribution losses. Conversion, 

which changes yearly, is generated by DOE-EIA’s NEMS* 

program.

Discount rates 3% and 7% real.

Present year Future expenses are discounted to 2011.

* Chapter 14, Utility Impact Analysis, provides more detail on the National Energy Modeling System (NEMS).

10.5.2 Results of National Energy and Water Savings Calculations

The following sections provide NES calculation results for the efficiency levels analyzed 

for the considered products. NES results, which are cumulative from 2015 through 2044, are 

primary energy savings and site water savings. DOE based the inputs to the NIA model on 

weighted-average values, yielding results that are discrete point values, rather than a distribution 

of values as in the life-cycle cost and payback period analyses. Results are presented for each 

TSL which represent specific efficiency level combinations for front- and top-loading clothes 

washers. Efficiency level combinations are necessary to account for the effect of the cross-price 

elasticity of demand observed between the two product classes, i.e., the interplay between price 
10-16

increase and market share between the two product classes. The cross-price elasticity between 

top- and front-loading units is described in greater detail in chapter 9. 

Table 10.5.2 shows the NEWS results for the TSLs analyzed for standard-size front- and 

top-loading clothes washers. Table 10.5.3 shows the magnitude of the national energy savings 

(NES) if the savings are discounted at rates of 3 percent and 7 percent. Table 10.5.4 shows the 

magnitude of the national water savings (NWS) if the savings are similarly discounted.

Table 10.5.2 Cumulative (2015-2044) National Energy and Water Savings

TSL

Efficiency Level Combination National 

Energy 

Savings 

(Quads)

National 

Water Savings 

(Trillion 

Gallons)

FrontLoading 

Standard

TopLoading 

Standard

FrontLoading 

Compact

TopLoading 

Compact

1 2 2 1 1 1.56 1.11

2 4 5 1 1 1.46 1.05

3 5 2, 6*1 1, 2*2.04 3.03

4 7 7 1 2 2.87 5.33

5 8 8 1 2 3.32 6.89

*Efficiency Level 2 from 2015 through 2017; Efficiency Level 6 after 2017

Table 10.5.3 Discounted Cumulative National Energy Savings

TSL

Efficiency Level Combination Energy 

Savings 

discounted at 

3% (Quads)

Energy 

Savings 

discounted at 

7% (Quads)

FrontLoading 

Standard

TopLoading 

Standard

FrontLoading 

Compact

TopLoading 

Compact

1 2 2 1 1 0.85 0.42

2 4 5 1 1 0.80 0.39

3 5 2, 6*1 1, 2*1.10 0.54

4 7 7 1 2 1.56 0.77

5 8 8 1 2 1.81 0.89

*Efficiency Level 2 from 2015 through 2017; Efficiency Level 6 after 2017

Table 10.5.4 Discounted Cumulative National Water Savings

TSL

Efficiency Level Combination Water Savings 

discounted at 

3% (Trillion 

Gallons)

Water Savings 

discounted at 

7% (Trillion 

Gallons)

FrontLoading 

Standard

TopLoading 

Standard

FrontLoading 

Compact

TopLoading 

Compact

1 2 2 1 1 0.61 0.30

2 4 5 1 1 0.57 0.27

3 5 2, 6*1 1, 2*1.62 0.77

4 7 7 1 2 2.90 1.42

5 8 8 1 2 3.75 1.84

*Efficiency Level 2 from 2015 through 2017; Efficiency Level 6 after 2017
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10.5.3 Results of Net Present Value Calculations

This section provides net present value (NPV) calculation results for the potential 

efficiency standards for residential clothes washer product classes. Results, which are 

cumulative, are shown as the discounted value of the savings in dollar terms. Results are 

provided for each potential efficiency standard. DOE based the inputs to the NIA model on

weighted-average values, yielding results that are discrete point values, rather than a distribution 

of values as in the life-cycle cost and payback period analysis.

The present value of increased total installed cost is the total annual increase in installed 

cost (the difference between the standards case and base case), discounted to the present and 

summed throughout the period for which DOE evaluated the impact of standards.

Savings are decreases in operating cost associated with the higher energy efficiency of 

products purchased in the standards case compared to the base case. Total savings in operating 

cost are the savings per unit multiplied by the number of units of each vintage (i.e., year of 

manufacture) that survive in a particular year. For units purchased by 2044, the operating cost 

includes energy consumed until the last unit is retired from service.

Table 10.5.5 presents the NPV associated with the considered standards for clothes 

washers. Detailed results showing the breakdown of the NPV into national installed product cost 

and operating cost savings are provided in appendix 10-B. As with the NEWS results, NPV 

results are presented as a function of TSL.

Table 10.5.5 Discounted Cumulative Net Present Values

TSL

Efficiency Level Combination Net Present 

Value, 

@ 3% Discount 

Rate (2010$ B)

Net Present 

Value, 

@ 7% Discount 

Rate (2010$ B)

FrontLoading 

Standard

TopLoading 

Standard

FrontLoading 

Compact

TopLoading 

Compact

1 2 2 1 1 20.18 8.73

2 4 5 1 1 18.47 7.77

3 5 2, 6*1 1, 2*31.29 13.01

4 7 7 1 2 41.60 16.42

5 8 8 1 2 50.48 19.92

*Efficiency Level 2 from 2015 through 2017; Efficiency Level 6 after 2017

10.6 ANNUALIZED NATIONAL COSTS AND BENEFITS

The benefits and costs of standards for residential dishwashers can be expressed in terms 

of annualized values over the analysis period. The annualized monetary values are the sum of (1) 

the annualized national economic value of the benefits from operating products that meet the 

proposed standards (consisting primarily of operating cost savings from using less energy, minus 

increases in equipment purchase costs, which is another way of representing consumer NPV), 
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and (2) the monetary value of the benefits of emission reductions, including CO2 emission 

reductions. The emissions reductions for each TSL are described in chapter 15, and the 

derivation of the monetary value of the benefits of emission reductions is described in chapter 16 

of this TSD. The value of the CO2 reductions, otherwise known as the Social Cost of Carbon 

(SCC), is calculated using a range of values per metric ton of CO2 developed by a recent 

interagency process. The derivation of the time series of SCC values is discussed in Appendix 

16A of this TSD. 

Although combining the values of operating savings and CO2 reductions provides a 

useful perspective, two issues should be considered. First, the national operating savings are 

domestic U.S. consumer monetary savings that occur as a result of market transactions while the 

value of CO2 reductions is based on a global value. Second, the assessments of operating cost 

savings and CO2 savings are performed with different methods that use quite different time 

frames for analysis. The national operating cost savings is measured for the lifetime of products 

shipped in the 30-year analysis period. The SCC values, on the other hand, reflect the present 

value of future climate-related impacts resulting from the emission of one ton of carbon dioxide 

in each year. These impacts go well beyond 2100.

10.6.1 Calculation Method

DOE uses a two-step calculation process to convert each time-series of costs and benefits 

into annualized values. First, DOE calculates a present value in the “present” year used in

discounting the NPV of total consumer costs and savings.cFor this calculation, DOE uses 

discount rates of three and seven percent for all costs and benefits except for the value of CO2

reductions. For the latter, DOE uses the discount rate appropriate for each SCC time-series (see 

chapter 16 for discussion).

 ∑ ( ( ) ( 

)

 

)

 

[1]

Where:

 ( ) = Time-series under evaluation,

 = Present value of the time-series ,

 = First year in the analysis period,

 = Last year in the analysis period,

 = Year to which the NPV of consumers’ costs and savings are being discounted,

 = Discount rate used to discount the annual values of time-series to year .

 

c

For the value of emissions reductions, DOE uses a time series that corresponds to the time period used in 

calculating the operating cost savings (i.e., through the final year in which products shipped are still operating).
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In the second step, DOE calculates, from the present values, the fixed annual payments 

over a 30-year period, starting in the first year of the analysis period (i.e., the compliance year), 

which yields the same present values with discount rates of three and seven percent. This 

requires projecting the present values in the “present” year ahead to the compliance year. The 

fixed annual payments are the annualized values. 

  ( )

 

 ( )

 

( )

 

[2]

Where:

 = Annualized value of the time-series ,

 = Factor to project a value years aheadd with discount rate,

 = Factor to annualize present values over a 30-year period with discount rate.

Although DOE calculates annualized values, this does not imply that the time-series of 

cost and benefits from which the annualized values were determined would be a steady stream of 

payments.

10.6.2 Results for the Adopted Standards

The direct final rule associated with this TSD states that DOE is adopting amended

energy conservation standards for residential clothes washers that correspond to TSL 3. 

Estimates of annualized benefits and costs for the adopted standards are shown in Table 10.6.1.

The Primary, Low Benefits, and High Benefits Estimates utilize forecasts of energy 

prices and housing starts from the AEO2010 Reference case, Low Economic Growth case, and 

High Economic Growth case, respectively. In addition, incremental product costs reflect a 

declining trend using the default product price trend in the Primary Estimate and the High 

Benefits Estimate, and constant product prices in the Low Benefits Estimate. See Appendix 10C 

for discussion of analyses using alternative economic growth scenarios. And see Appendix 8C 

and Appendix 10C for discussion of the product price trends.

 

d

n is the number of years between the “present” year and the compliance year.
10-20

Table 10.6.1 Annualized Benefits and Costs of Amended Standards for Residential Clothes 

Washers for Products Sold in 2015–2044

Discount Rate

Primary 

Estimate*

Low Net 

Benefits 

Estimate*

High Net 

Benefits 

Estimate*

Monetized (million 2010$/year)

Benefits

Operating Cost Savings

7% 1234 1101 1379

3% 1808 1587 2042

CO2 Reduction at $4.9/t** 5% 34.5 31.7 37.4

CO2 Reduction at $22.3/t** 3% 142 130 154

CO2 Reduction at $36.5/t** 2.5% 226 207 246

CO2 Reduction at $67.6/t** 3% 431 396 469

NOX Reduction at $2,537/t**

7% 5.40 5.03 5.82

3% 8.01 7.39 8.68

Total†

7% plus CO2 range 1274 to 1671 1137 to 1502 1423 to 1854

7% 1381 1236 1539

3% plus CO2 range 1851 to 2248 1626 to 1991 2089 to 2520

3% 1958 1725 2205

Costs

Incremental Product Costs

7% 185 258 200

3% 212 309 230

Total Net Benefits

Total†

7% plus CO2 range 1088 to 1485 880 to 1244 1223 to 1654

7% 1196 978 1339

3% plus CO2 range 1639 to 2036 1317 to 1682 1859 to 2291

3% 1746 1416 1976

* The Primary, Low Benefits, and High Benefits Estimates utilize forecasts of energy prices and housing starts 

(which affect product shipments) from the AEO2010 Reference case, Low Economic Growth case, and High 

Economic Growth case, respectively. In addition, incremental product costs reflect a declining trend using the 

default product price trend in the Primary Estimate and the High Benefits Estimate, and constant product prices in 

the Low Benefits Estimate. Because product prices are constant in the Low Benefits Estimate, the incremental 

product costs are higher than in the other two estimates. Although the price trends in the Primary Estimate and the 

High Benefits Estimate are the same, the incremental product costs are higher in the High Benefits Estimate because 

this case assumes High Economic Growth and thus has more product shipments. The approach used for forecasting 

product prices is explained in section IV.F.1 of the direct final rule. 
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** The CO2 values represent global values (in 2010$) of the social cost of CO2 emissions in 2010 under several 

scenarios. The values of $4.9, $22.3, and $36.5 per ton are the averages of SCC distributions calculated using 5%, 

3%, and 2.5% discount rates, respectively. The value of $67.6 per ton represents the 95th percentile of the SCC 

distribution calculated using a 3% discount rate. The value for NOX (in 2010$) is the average of the low and high 

values used in DOE’s analysis.

† Total Benefits for both the 3% and 7% cases are derived using the SCC value calculated at a 3% discount rate, 

which is $22.3/ton in 2010 (in 2010$). In the rows labeled as “7% plus CO2 range” and “3% plus CO2 range,” the 

operating cost and NOX benefits are calculated using the labeled discount rate, and those values are added to the full 

range of CO2 values.
10-22

REFERENCES

 

1

Energy Information Administration, Annual Energy Outlook 2010 with Projections to 2035, 

2010. Washington, DC. Report No. DOE/EIA-0383(2010). 

<http://www.eia.doe.gov/oiaf/aeo/>

2 Office of Management and Budget. OMB Circular A-4, Regulatory Analysis. 2003. OMB: 

Washington, D.C. September 17, 2003. 

<www.whitehouse.gov/omb/assets/omb/circulars/a004/a-4.pdf>