I Houses without a Washer I
Purchase washer? Yes No

Remain without a Washer
Buy New Washer Buy Used Washer
Figure 9.6 Decision Tree for Housing Without a Washer We assume an annual probability of purchase (relatively small) which varies according to the economic probability of purchase model. We also use the ratio of new vs. used purchase probability which is calibrated with market conditions in 1997 to be consistent with AHAM data. The relatively simple dynamics of the decision by a non-owner household deciding to buy a washer is described by one equation:
CWNoWasherToWasher(year) = Eq. 9-11 ProbNowasherTowasher(year) . CWNoWasherStock(year)

where: CW No Washer to Washer (year) = The number of non-owner households that purchase clothes washers in a given year. Prob No Washer to Washer (year) = The probability that a non-owner household will purchase a clothes washer in a given year. CW No Washer Stock (year) = The number of non-owner households in a given year. And the number of non-owner households is calculated from the existing housing stock and the number of clothes washer owners as described in the following equation:

9-16CWNowasherstock(year) (HousingStock)(year)

- [CWStock1(year) Eq. 9-12

9.2.4.3 Current Assumptions The main assumption is that the probability of purchase from a non-owner household is veiy small. Secondly it is assumed that the new vs. used decision probability is the same as it is with the regular washer - owners. And finally we assume that the different probabilities are independent; i.e., the probability of two decisions or events is the product of the individual event /decision probabilities. 9.2.5 Households with Extended-Life Washers 9.2.5.1 Definition These households have clothes washers that received more repairs than was normal in the reference year of 1996. It is therefore assumed that the lifetime of these clothes washers has been extended by these extra repairs. 9.2.5.2 Approach The input of this particular stock of washers comes from regular washer households that have made extra repairs on their washing machines. Once an extra repair has been made, it is assumed that no more repairs will be made after the next machine breakdown. I Houses with Extended Life Washer I Are there problem Yes, Replace Washer No New, Used, ' Keep Existing or None? 2 Washer

I Buy Used Buy New V Washer Washer Don't Buy

Any Washer Figure 9.7 Decision Tree for Housing with Extended-Life Clothes Washers

9-17Figure 9.7 illustrates the decision tree for the stock of extended-life clothes washers. Note that

these washers are already quite old because they are regular washers that have received extra repairs near breakdown (between 11 and 17 years of age). The main event in this decision tree is whether or not the machine has problems. This probability function is a shifted version of the survival probability function for regular washers; it is illustrated in Figure 9.8. Besides the survival probability function, the decision of whether a machine is replaced with a new washer, a used washer, or no washer is the same as that for regular washers. In terms of equations, the dynamics of the extended-life clothes washers can be described as follows: First the retirement of the clothes washers is calculated simply with the retirement (replacement) probability function (shown in Figure 9.8).

CW

- XRRetired(year,age) = ProbxRltfr(age)*

## cw Eqn. 9-13 -XRstoek(year, age) Then the stock accounting is done such that the change in stock is the number of regular clothes washers that get extra repairs minus the stock that is returned: where:

CW- XRstoek(year, age) = CW- XRStock(year - 1,age - 1)

- CW- XRRetired(year - 1,age -1) + CWxtraRepaixs(year -1,age - 1) Eq. 9-14

CWXR Retired (year, age) = The number of extended-life clothes washers of a particular age retired in a given year. Prob xRRetire(age) = The probability that an extended-life washer of a given age will be replaced or retired. CW-XR stock(year, age) = The number of extended-life washers of a given age in a given year. CW Xtra Repairs (year, age) = The number of regular washers of a particular age that received extra repairs in a given year.

9-18Survival Probability Function 

# ::

___

0 5 10 15 20 25 Washer Age
Figure 9.8 Survival Probabifity Function for Extended Lifetime Washers 9.2.5.3 Current Assumptions There are several assumption of the extended-life clothes washer modeling. These assumptions include: 1. Extended life washers are never repaired again. 2. The extended-life washers have a lifetime that is 6 years greater than that of the regular washers. 3. The new vs. used vs. no replacement decision has the same relative probabilities as in the regular washer case. 4. The different probabilities are independent, that is the probability of two events or decisions is the product of the individual probabilities. 5. The retirement probability function is independent of time. 9.2.6 Accounting Equations For making the shipment forecasts, we specifj a series of equations that defme the dynamics and accounting of the different types of clothes washer stocks. For net new housing the equation describing the stock of new housing is straight forward. The stock of new housing is the difference between the current year housing stock and the previous year's housing stock. Meanwhile the most complicated accounting equation is that which describes the accounting of the existing stock of regular washers. For the stock of regular washers we have two equations which describe the accounting of the population. The first equation says that the number of one-year old clothes washers is equal the number of new clothes washers purchased the previous year:

CWStock(year,age = 1) = CWNew( year- 1) Eq. 9-15 9-19Meanwhile the next equation describes the accounting for washers of the different, older age categories:

CWstock(year, age) = CWstock(year

- 1,age- 1)

- CWRetired(year- 1, age

- 1)-

CWEarly(year- 1, age

- 1)- CWxtraRepairs(year- 1,age

- 1) + Eq. 9-16 (CWused(year

- i)/ [CWEarlyI

# )* CWEarly(year

- 1, age

- 1)
where year = The year that the stock is being estimated. CW Stock (year, age) = The population of regular clothes washers in existing housing of a particular age. CWN (year) = The number of new washer purchases in a particular year. CWRefired(year, age) = The number of regular washers from a particular age category that were replaced in a given year because of problems that had occured. CW Early (year, age) = The number of regular washers that are replaced early from a particular age category in a given year for discretionary reasons. CW used(year) = The total number of used purchases in a given year. [C WEarlyl (year) = The total number of early replacements (of all age categories) of regular washers in a given year. CW Xtra Repairs (year, age) = The number of regular washers that have received lifetimeextending repairs. These washing machines get transferred to the extended lifetime stock.
Equation 16 indicates that the number of clothes washers in a particular age category is equal to the number of clothes washers in the younger age category of the previous year minus the number of clothes washers retired or replaced early and plus the number of used clothes washers of that age category that have been purchased in the previous year. The age distribution of used clothes washers is assumed to be the same as the age distribution of clothes washers that are replaced early (since such early replacements are assumed to provide much of the used clothes washer supply). Then for the stock accounting for the extended life machines (those that have received extra repairs), we have the following:
CW- XRStock(year, age) = CW- XRstock(year-1,age

- 1) CW XRRetired(year-i, age -1) + CWxtraRepaiis(year

- 1,age

- 1) Eq.9-17

9-20where

CW-XR Stock (year, age) = The number of clothes washers in a given year of a given age group that belong to the stock of machines that have received extra repairs. These extra repairs have extended the life of the machine. CW-XR Retired(Y1, age)
= The number ofmachinesof a particular age that are retired from the extra repair stock in a given year. CW Xtra Repairs (year, age)
= The number of regular washers of a particular age in a given year that receive repairs that extend the machine life in a given year. Equation 17 says that the stock of extended life clothes washers comes from regular washers which receive extra repairs when they break down. This stock then ages, and is removed as it is retired due to additional repair problems. For the stock of households with no washer we have the following equation:
CWNo WasherStock(year) = (HousingStock)(year)

- [cWstoci] (year)

- Eq. 9-18 [CW- XRStock] (year)
where CW No Washer S50k(year) = The stock of households who do not ownclothes washers (Housing Stock) (year)
=The total stock of housing in a given year [CW S0k](year) = The total stock of houses with regular clothes washers of any age category. [CW-XR S0k](year)
=The total stock of houses with extended life washers of any age category. Equation 18 says that number of non-owner households is the number of households minus the number of regular washer owners minus the number of extended life washer owners. The new and used washer purchase are related to changes in the different clothes washer stocks as follows:

9-21CWRetired(year,age) + 

# J1
TNew(year) = ProbNewvs.used(year)* XRRetired(year, age) + 

### I I I+ CWEarly(year, age) + Eq. 9-19 CWNowasherTowasher(year) CWNew New Homes( year)

(CWRetired(year,age) + 0.98*1 

### I + CWused(year) = (i

- ProbNew( year)

### )* CW- XRRetired(year,age)) Eq. 9-20 CWNowasherrowasher(year)
where: CW New (year)
= The number of new washer purchases in a given year. Prob New (year)
= The probability that a purchase is a new washer CW No Washer to Washer (year)
= The number of washers purchased by non-owners in a given year. CW Used (year)
= The number of used washer purchases in a given year. In the rest of this report we will describe in more detail how this accounting approach is implemented to forecast clothes washer shipments. a 9.3 MODEL In order to estimate the impact of standards-induced price and features changes it is necessary to have a model which describes consumer decisions and is consistent with historical experience. In this forecasting effort we took the following approach: First we used the clothes washer consumer analysis to provide the framework for the modeling approach and the probability of purchase model. We then used market discount rates to adjust the relative size of the price and operating savings coefficients for the logit purchase probability model. Finally, we used industry statistics on historical clothes washer shipments to perform the final calibration of the model parameters.

aNote that in Equations 19 and 20, the 98% replacement rate for retired machines was obtained from the Clothes Washer Consumer Analysis •2 9-22This procedure for developing the economic decision model is illustrated in the following process

flow diagram:

Sample of Consumers

Data on Market Discount Rates
RECS Survey and Historical Shipments Data

Figure 9.9 Model Development 9.3.1 Logit Probabifity of Purchase Model 9.3.1.1 Logit Equation Conjoint Analysis
Logit Probability of Purchase Model

Initial Model Assessment

-- Does Not Match

Revised Probability of Purchase Model

Model Calibration
Calibrated Probability of Purchase Model

The mathematical building block for the modeling of consumer decision probabilities is the logit probability of purchase model. In this model, the probability of purchase depends on the utility of the clothes washer, U, which depends on the attributes of the appliance. This purchase probability is constrained to be between 0 and 1, and relative changes in the probability of purchase are proportional to changes in the utility of the appliance. These theoretical requirements for the decision probability function can be satisfied by requiring that the probability of purchase function satisfies the following equation:

dProb/Prob = dU*(1

- Prob) Eq. 9-21

9-23where Prob = decision probability, and dU is the differential change in utility which is a linear function of

the clothes washer attribute variables. The factor of (1 -Prob) on the right hand side of the equation enforces the condition that the probability of purchase never exceeds 1. We can solve the above equation for the probability function assuming a particular functional form of the utility in terms of the attribute variables:
dU = b d(Price) + c d(Operating Savings) + d d(Feature Index) Eq. 9-22
where the differential change in utility is equal to a linear function of differential changes in price, operating savings and features changes. Different versions of the probability of purchase model can use different sets of attributes depending on which economic attributes are assumed to be the primary drivers for the purchase decision. Given the equation for the differential utility, we obtain the following for the probability of purchase: In(Prob/(1

- Prob)) = a +b

.(Price) +c. (Operating Savings) +d (Feature Index)
or Eq. 9-23 Prob = i/(i + exp(_(a +b

. (Price) + c. (Operating Savings) + d• (Feature Index)))) where a is a constant of integration determined by the values of the probability at initial market conditions. This can also be written as:
Prob = exp(U)/(1 + exp(U)) Eq. 9-24
where U = a + fr(Price)+c(Operating Savings)+d(Feature Index) is the utility, and where this equation will change if for different sets of attribute variables. When additional explanatory variables are included in the economic decision model, they are added as additional linear terms in the utility function with their own coefficients. The above equations thus defines the logit probability of purchase model. Note that the price used in the logit decision model is the NET price of the decision. This means that when we evaluate the decision of a used vs. a new purchase this is less than the price is less than the purchase price of a new machine. Similarly for the decision of a new purchase vs. a repair. For both the
9-24repair and the used purchase, we assume that the cost is a fraction of the cost of a new machine.

Specifically, we assume that the purchase price of a used machine is 34% of the price of a new clothes washer, and the price of a repair is 24% of the price of a new washer. 9.3.1.2 Utility Coefficients and Elasticity Once the form of the purchase probability function is defined, the next task is to estimate the coefficients of the model from the available data. In this regard there are four main sources of purchase behavior and ownership data that we utilized: (1) Industry statistics on historical clothes washer shipments,'°' 11, 12 (2) Results from a marketing study of clothes washer consumer preferences, the Clothes Washer Consumer Analysis,2 (3) AHAM survey results,' and (4) EIA/RECS survey results.'3 For model calibration, we used the conjoint analysis from the Clothes Washer Consumer Analysis was used to verify elements of the model assumptions and set the approximate relative amplitudes of the features and price coefficients. For the next step, we formulated the savings coefficient relative to the price coefficient using intercept survey data on consumer price/savings trade-offs. For the final step, we used historical data to calibrate of the utility coefficient amplitudes, after assuming a given attribute as the primary driver of consumer decisions. Price was selected as the most likely primary driver of consumer purchase decisions, but price/income, income, and interest rate were also examined as possible drivers. We used AHAM and EIA/RECS survey results to set sizes for the initial market segments. In discussions of price sensitivity of the clothes washer market, much of the technical literature discusses variations in demand in terms of the price elasticity. For a logit probability of purchase model, purchase price elasticity for a market segment depends on two main parameters: (1) the initial probability of purchase, or likelihood of purchase, of that market segment, and (2) the coefficient for price in the utility function. Specifically:
elasticity = (dProb/dPrice)/( Prob/Price) = d(ln( Prob))/d(ln( Price))

= b*( 1- Prob)* Price Eq. 9-25

The elasticity therefore decreases with increasing purchase probability, and is proportional to the utility coefficient. Note that elasticity describes changes in purchase behavior for small changes about existing market conditions. For large changes in prices and market conditions, elasticity will not be constant. The fact that elasticity decreases with increasing purchase probability also helps explain the observation in the long-term sales forecasting literature that elasticities for necessities decrease towards zero as the durable reaches acceptance and market saturation.
9-25In the shipments model, we model price impacts on consumer behavior in terms of the probability

function rather than in terms of a simple elasticity value. We use a probability function model so that the impact of large price changes can be properly estimated. When price changes, the purchase probability changes, and so does the elasticity. A full non-linear description of purchase probability variations is a more accurate approach for modeling economic decisions. 9.3.2 Clothes Washer Consumer Analysis DOE initiated a clothes washer consumer study in order to aid in the description and modeling of consumer preferences and purchase behavior. This study used two approaches to identifying and characterizing consumer preferences: (1) Focus Groups and (2) Conjoint Analysis. This study is described in detail elsewhere,2 but we summarize the salient features here. The focus group study was used to determine what features of clothes washers were of importance to consumers. For the focus group study, the participants indicated which clothes washer features are important to them. The study showed that the ten most important clothes washer features in order of priority are: (1) price, (2) capacity, (3) energy and water costs, (4) load size options, (5) durability, (6) water temperature options, (7) door placement, (8) quiet operation, (9) wash time, and (10) warranty. In addition to the focus groups, a conjoint analysis was performed to quantify the relative importance of six different features and their impact on purchase probabilities. The conjoint study asked respondents which clothes washers would they consider purchasing today given a range of clothes washer attributes. The prices considered ranged from $400 to $650. Meanwhile the amount of energy and water savings considered ranged from $0 to $50. In addition, features such as door placement, capacity , water temperature options, and load size adjustment were considered in the analysis as binaiy variables which could be either 0 or 1. For the shipments model spreadsheet, we included the top four features that may be affected by clothes washer standards. These features, include in order of priority, are: (1) price, (2) energy and water savings, (3) water temperature options, and (4) door placement. (Note: load size options were rated more important than door placement, but this feature would not be affected by a standard). 9.3.3 Stated vs. Revealed Preferences Consumers preferences can be measured or indicated in several possible ways. Stated consumer preferences are those which are obtained through surveys such as the conjoint analysis used in the DOE study. Revealed preferences are those which are demonstrated through actual purchase behavior. The situation in which consumers find themselves when they actually make a clothes washer purchase can be significantly different than the presumed purchase context of a stated preference study. The difference between stated and revealed consumer preferences is noted in textbooks that discuss the application of
9-26conjoint analysis:

Market share estimates obtained from conjoint analysis differ from actual shares due to marketing activities such as advertising and distribution, which affect awareness and availability. Appropriate adjustments are therefore needed to account for the effect of these marketing actions.'4 Therefore the results of stated preference studies and revealed preference studies can often be significantly different. Especially when considering application to a post-standards situation where the standard affects the availability of lower-efficiency lower-priced models. Typically a consumer will find himself or herself in a more constrained circumstance during an actual clothes washer purchase. For example, over half of clothes washer purchases are due to the breakdown of an existing clothes washer. Under constrained purchase circumstances consumers will find themselves with fewer choices, and the influence of price, savings, and other clothes washer atiributes will diminish. If one tries to construct a shipments forecast model using stated consumer preferences, it does not fit the historical data. This is due to differences between what consumers say they will buy (stated preferences) and their actual purchase behavior (revealed preferences). This means that while the conjoint study can be used for selected features of the probability of purchase model, most model parameters will need to be calibrated vis a vis historical data. This ensures that the probability of purchase model is consistent with revealed rather than stated preferences. 9.3.4 Determination of Decision Sensitivities Most of the historical variations in clothes washers sales is explained by stock accounting constraints and variations in housing purchases and moves. Over the long term, there is a general increase in the saturation of clothes washers that can be mathematically correlated with any of several economic parameters which may be experiencing a trend over the calibration period. In performing the historical calibration of the consumer decision model, a technical judgement must be made regarding which economic parameter is the primary historical driving force behind consumer decisions. In this analysis we assumed that appliance price is the primary driver historical trends in consumer decisions based on the importance of price indicated in the Clothes Washer Consumer Analysis and other consumer surveys. In addition, other models with different primary drivers for consumer decisions were examined as sensitivities.

9-27Price vs. Savings

$700.00

- $600.00

- $500.00

- $400.00 $300.00

- $200.00

- $100.00 $0.00

- $0.00 $10.00 $20.00 $30.00 $40.00 Savings $50.00 $60.00 Price Poly. (Price)

Figure 9.10 Estimated Price vs. Savings Relation for Current Market Conditions 9.3.4.1 Savings/Operating Cost Sensitivity We estimated the approximate current size of the savings/operating cost sensitivity relative to price using two methods. One method assumes that the current market is in equilibrium, and estimates AP/AS for the current market. The second method analyzes results from a Northwest Energy Efficiency Alliance consumer intercept survey that specifically asks clothes washer shoppers how much of a price increase they would trade off for savings. Both methods give comparable results. Figure 9.10 illustrates the approximate relationship between price and operating cost savings that is implied by the engineering analysis of the costs of higher efficiency washing machines. Since most purchases are near the baseline model, this data implies a typical market payback time between one and two years, though the precise value in this range cannot be specified with statistical certainty. Some stake-holders have presented theoretical arguments against the use of market equilibrium analysis to determine the effective market discount rate for consumers. They argue that such an analysis assumes perfect markets (i.e. no lack of knowledge, indivisibility, uncertainty), and that if markets were perfect then standards would not be necessary. This argument neglects the cost of information and its role y = 0.0772x + 1.2361x + 419.31

9-28in market equilibrium. For individuals making a clothes washer purchase it may be relatively expensive and

uncertain to discover the actual savings as a function of the diversity of clothes washer choices. Standards perform a collective calculation of optimum cost/benefit trade-offs for improved clothes washer efficiency and therefore drastically reduce the cost of information per clothes washer sale through economies of scale in information production and analysis. Though we may not know the exact cause of high market discount rates for consumer decisions, uncertainty on whether savings will be actually achieved at a personal level provides a plausible explanation for revealed preference market discount rates that are higher than stated preference market discount rates. Similarly, the intercept interview performed during the Pacific Energy Associates for the Northwest Energy Efficiency Alliance 15 indicated a market discount rate of one to two years for clothes washer shoppers--depending on the details of how the responses are quantitatively interpreted. Given these two indicators, we selected 75% as a market discount rate halfway between a one-year (100% discount) and two-year (50%) payback. The 75%market discount rate corresponds to a price-to-savings ratio of 1.33 for the current market behavior. The data from the Clothes Washer Consumer Analysis implied a consumer discount rate of 19%, but because of how the choices were structured to allow for a limited set of market discount rate choices, we consider the other methodologies to be more reliable. Specifically, if we divide the average savings on the product choice cards by the average price increment, we obtain a discount rate of 23%. This means that for a set of completely random card selections this will be the average discount rate. In addition, participants in the conjoint survey may have received more information about savings and energy efficiency than average consumers shopping for a clothes washer. In contrast the intercept survey performed by Pacific Energy Associates provided a range of potential trade-offs, and with equal weighting to each of the different choices, and did not provide extra information on energy savings. We therefore consider the intercept survey a more reliable measure of the market discount rate that describes actual consumer behavior in a market with imperfect energy efficiency and savings information. 9.3.4.2 Features Sensitivity An issue with the higher standards levels (trial standard levels 3-6) is whether the higher efficiency standards will force manufacturers to produce only horizontal axis machines. And if only horizontal axis clothes washers are available, this change in available clothes washer features may impact sales. Among stakeholders, there is no consensus with regards to which standard level might require horizontal axis machines. Another issue is that the market dynamics of the adoption of new technologies can be extremely complex. Initially, there may be some resistance to a new technology, but as new technologies become more familiar, this market resistance often diminishes. The Bern study of high efficiency clothes washers indicated that consumers can adapt to the technology of front-loading washers, 16 though the implications of the Bern study results for predicting shipments impacts is uncertain.
9-29The conjoint study indicated that there was a rather dramatic change in consumer sensitivity to door

placement depending on the level of familianty with front-loading washing machines, and geographic location. Those consumers who were familiar with front-loading machines have a sensitivity to front loaders that is 30% less than the sensitivity of the entire sample. In the shipments model, we assumed that if the efficiency of the machine is at the MEF=l .257level or above is implemented, the dominant machines will be front-loaders. But we also assumed that all consumers would become familiar with front-loading washers and that there would be further acceptance of the new technology. Therefore the size of the top/front loading coefficient in the purchase price model was set at V2 the size of the coefficient for the conjoint sub-sample of those familiar with horizontal axis machines. This value presumes that all consumers will be familiar with horizontal axis machines if they come to dominate the market, and that there will be some adaptation to the new technology, though acceptance will not be complete. 9.3.5 Calibration of Shipments Model The clothes washer shipments model was calibrated with historical shipments data. For the calibration of the model that used price as the primary driver of consumer decisions, we fixed the relative size of the price, savings, and front-loading feature coefficients to values determined from evaluation of the Clothes Washer Consumer Analysis, and market discount rates. By fmding a market discount rate of75%, and by estimating the relative size of the front loading elasticity to be about V2of the sensitivity of the consumers familiar with front loaders, the ratios of the coefficients are fixed as follows: c/b = -1.33 d/b = -39.7 Eq. 9-28

The coefficient b was then adjusted until a best fit of historical data was obtained as measured by the (RMS) deviation between historical shipments and model shipments between 1970 to 1996 inclusive. For the fully calibrated model, the RIvIS deviation between the model and the industry data on historical shipments is 0.2 million shipments per year. We also examined the feasibility of explaining historical data with other explanatory parameters as requested by some stakeholders. The results of this analysis are presented in Figure 9.11. The figure shows the optimized historical shipments model predictions utilizing different explanatory economic variables including interest rate, income, price/income, and price. What can be seen in the figure is that while interest rate may have some deficiencies in explaining the historical clothes washer sales, income, price/income, and price can explain the historical sales equally well. It is therefore necessary to use information besides the historical record to determine which of these three economic variables are the most
9-30appropriate variable for the shipments forecast.

7.00 New Clothes Washer Shipments

6.50 C) 6.00

0 . 5.50 8

- 5.00 

### a 4.50 Historical 'Price Model Income Price/Income Interest
4.007
3.50
3.001970 1975 1980 1985 1990 1995 2000 Year Figure 9.11 Inter-comparison of Models with Different Primary Economic Decision

Variables We use two additional criteria to select the most appropriate primary economic decision variable. The first criteria is whether or not the chosen explanatory variable is consistent with the focus group responses obtained during the Clothes Washer Consumer Analysis, and the second is whether the chosen explanatory variable represents the full range of reasonable forecasted standards impacts. In the focus group results, participants consistently rated price as the most important clothes washer attribute with capacity being a close second. Therefore, a model which includes only income as an explanatory variable would attach no importance to price and would be inconsistent with the persistent importance of price indicated in the Consumer Analysis. The next question is whether or not income is a factor in such consumer decision-making. While it is probably true that income was a factor when clothes washer price was relatively large compared to household income, its importance in the recent past when the purchase price of a clothes washer is less than 1% of average aimual household income is less clear. The Consumer Analysis found no significant correlation between income and price sensitivity. There is therefore some chance that price is the only
9-31primary driver to clothes washer sales. This would be the case if consumers measured the relative benefits

of a new clothes washer compared to other consumer purchases they could make, but felt little, if any, income constraints on the purchase. The price-only shipments model uses price relative to other possible purchases by scaling the price relative to the consumer price index for all items. There is also some chance that price/income is the primary driver to clothes washer sales even though some data supports the price-only model. But if one assumes that price/income is the primary driver one obtains a narrower range of possible standard-induced sales impacts when one does a statistical error analysis. Given the probability that price is (or may be) the primary driver, we therefore conclude that the price-only model and its statistical error analysis more accurately represents the full range of possible impacts and the complete range of uncertainty in the forecasted results. 9.3.6 Range of Shipments Model Forecasts Given the price-only shipments forecast model we can use statistical analyses to estimate an approximate confidence interval for the calibration of the price sensitivity and consequent uncertainty in the standard-induced shipment impacts. The statistical analysis method that we use is a chi-square analysis. In this analysis, one uses changes in the size of the chi-square metric as a function of the fitted parameter to determine the probability that the actual parameter value is different from the best-fit parameter value. If we assume that the errors in the data are uncorrelated and normally distributed, and that the minimum root mean square (RMS) deviation between the model and the data is a measure of the standard deviation of the noise in the data, then we can use the chi-square distribution to estimate the size of the confidence interval for the calibration scaling coefficient parameter. The coefficient scaling parameter obtains its minimum value at 0.125. For the 1970-1996 period the number of degrees of freedom is taken as 26, then the chi-square for the 99% confidence interval with 26 degrees of freedom is 55.5. This means that the increase in RMS at the 99% confidence limit is (45.6/26)1/2 = 1.3 times the minimum RMS. For the 1970-1996 fit, the RMS deviation increases to 1.3 times its minimum value at approximately 0.25, and it remains below this value for a coefficient scaling parameter of 0. This implies that the 99% confidence interval for the coefficient scaling parameter in the price-only model ranges from 0 to approximately 0.25. The uncertainty interval is probably slightly larger than this because auto-correlations in the random variations would decrease the degrees of freedom in the chi-square analysis. We therefore round up slightly to 0.30 to represent the likely upper range. To represent the range of possible coefficient scaling parameter values, we chose a coefficient scaling parameter for the price-only model that ranges from 0 to 0.30, with 0.15 as the median value. Given the data available for development of the shipments forecast model at this time, this range should be close to the technically best representation of the possible standards-induced impacts. Given an uncertain range of forecasted results, the most representative forecast is a matter of judgement. Such judgements depend on the relative importance that one places on different risks and
9-32economic factors. For the clothes washer shipments forecast, the high range represents impacts that would

be most relevant to those who place much value on the risks of possible sales impacts, while the low end of the range represents impacts that are relevant to those who have confidence in the market's ability to innovate and meet consumer demand. For impartial regulatory applications the median of these two partial views is likely the most representative judgement.
9.4 RESULTS Once the model is calibrated with historical data, it provides a rather detailed estimate of the possible impacts of standards on purchases, replacement, and repair of clothes washers. In this section we detail the forecasted impacts of the model on different aspects of clothes washer shipments, sales, and retention. Additional charts showing the shipment forecast results for different price elasticities scenarios are presented in Appendix M.
New Clothes Washer Shipments
10.00 9.00 8.00

._ 7.00 (I, a 6.00 B

. 5.00 a 4.00
3.00
2.00
1.00
0.00 - 1970 X Historical

- Base Case Trial Level 2 •*Trial Level 3 'Trial Levels 4/5 Trial Level 6

1980 1990 2000 2010 2020 2030 Year Figure 9.12 Clothes Washer Shipments Forecasts
The results presented in Figure 9.12 represent our best estimate of possible standards impacts on shipments as a function of the trial standard levels. Trial standard level 1 has a less than 1% difference with
9-33the base case shipments so it is not illustrated. The illustrated impacts are the ones that would accrue

assuming that price is the primary long-term economic driver for changes after the effects of housing, replacements and changes of residence are considered. There is some uncertainty in the forecasted impacts, and the 99% confidence interval for potential impacts ranges from no decrease in sales to a potential decrease in shipments that is approximately twice that shown. These results are those that are implied by the costs given by the engineering analysis which gives the incremental cost for each efficiency level improvement. The forecast assumes no future innovation in decreasing manufacturing costs from current estimates, no progress in improved marketing of clothes washers based on operating savings or increases in consumer income levels. But the model does assume some increasing adaptation by consumers to front-loading machines for those standard levels that my induce changes in the clothes washer configuration (efficiencies above MEF=l .257are assumed to be front-loading machines).



### Esthnated StandardsImpacts Shipments and SalesofNewWashers
60% 50% 40% 30% 20% 10% 0% -10% New Shipments (04-30) XNew Shipments ((2004) NewSales($,04-30) New Sales($, @2004)

#1 #2 #3 #4 #5 #6

TrialStandard Level
Figure 9.13 Estimated Standards Impacts on New Clothes Washer Shipments and Sales

9-349.4.1 Sales Impacts of Standards-induced Price Changes

9.4.1.1 New Clothes Washers Figure9.13 shows the forecasted clothes washer sales impact of the different proposed standard levels. As shown in the figure, sales and shipment impacts of the trial standard levels 1 and 2 are within 3% of base case. Larger sales impacts are forecast for standard levels above trail standard level 2. For the negotiated agreement (trial standard level 3), the impacts at 2004 are close to trail standard level 1, while the longer-term forecasts are similar to trial standard levels 4 and 5. For trial standard levels 4 through 6, the volume of new clothes washers shipments is forecast to decrease significantly, while total dollar volume of sales is forecast to increase. Both the impacts at the year of the standard and the average impacts over the forecast period, 2004 to 2030, are illustrated. The biggest factor that influences the size of the potential standards-induced changes is the actual retail price increase that is induced by the standard. If price increases are large, the shipments volume decreases almost proportional to the price increase, but because the price elasticity is less than one, price increases result in increased gross sales dollar volume. The net financial impact of these opposing effects is examined in more detail in the manufacturing impact analysis.

Estimated Standards Impacts Shipments and Sales of Used Washers 100%

80%

60%

40%

20%

0% Trial Standard Level Used Shipments (04-30) Used Shipments (@2004) 'Used Sales ($, 04-30) ' Used Sales (S. 2004

Figure 9.14 Estimated Standards Impacts on Used Clothes Washer Shipments and Sales

9-35 #1 #2 #3 #4 #5 #6Some of the measures that consumers might take to avoid purchase of a new higher-prices

clothes washer keep them out of the market for only a relatively short period of time. Therefore there is some recovery from the initial shipments drop that might be seen in the year of the standard. 9.4.1.2 Used Clothes Washers Figure 9.14 illustrates the potential impacts of standards on the used clothes washer market. The used market will provide one of the most attractive options for consumers having broken clothes washers and who wish to avoid the expense of a new clothes washer. The model estimates that initially, consumers will keep their clothes washers longer, but eventually they will need to be replaced when they breakdown. This means that the long-term increase in the used clothes washer market is larger than the initial increase at the year of the standard. In estimating the relative impact on used clothes washer sales, we assume that the price of used clothes washers follows the price of new clothes washers and increases proportionally. 9.4.2 Impacts on Mean Age of Washers, Used Market, and Washer Repairs Figure 9.15 illustrates the estimated impacts on the mean age of clothes washers, the mean clothes washer lifetime, and the total volume of clothes washer repairs. These are average impacts over the standard period of 2004 to 2030. These three different measures of clothes washer retention measure different types of consumer reactions to higher potential clothes washer prices. The increase in repair rate measures the impact of consumers who perform an extra repair on their clothes washer rather than retire the machine. Such repairs are few compared to the total volume of clothes washer repairs because of the large volume of minor repairs that occur over the lifetime of a washer. According to Consumer Reports, about 23% of clothes washers have repairs during the first five years of ownership.17 The extended lifetime of clothes washers reflects repairs that consumers might undertake to extend the lifetime of clothes washers. Such extended repairs will have a delayed effect on the average lifetime of a clothes washer, and only a relatively small fraction of machines will receive such extended repairs (some machines may not be repairable, and consumer will also have the choice of purchasing a used washer). An extra repair extends the life of a 14 year old machine by at most six years. At trial standard level 6 less than 10% of machines receive extra repairs that extend the machine life. This implies that the lifetime of washers is increased by at most one half year by the imposition of a standard. The increase in mean age of a clothes washer illustrates both the impacts of extra repairs and a more vigorous used clothes washer market. When more machines are cycled through the used market, then the proportion of older machines increases slightly, and this results in a slight increase in the average age of machines. Again, it takes several years for used shipments to have a significant impact on the clothes
9-36washer age distribution, so the averaged impact over the period is significantly smaller than the peak age

increase which occurs several years after implementation of the standard.

Estimated Standards Impacts Washer Age, Lifetime, & Repairs 6%
5% 4% E 3%

- 2%
1% 0% -1% /

/ // // -x-

----- #1 #2 #3 #4 #5 #6

Trial Standard Level Mean Age •Lifetime Renairs

Figure 9.15 Estimated Standards Impacts on Washer Age, Lifetime, and Number of

Repairs

9.5 CONCLUSIONS In order to provide a more detailed picture of potential standards-induced impacts on the clothes washer market, we have formulated an accounting model for clothes washer purchases. The model keeps separate accounts for the new housing, early replacement, breakdown replacement!repair, and non-owner markets. The method also apportions washer purchases to the new and used clothes washer market segments. The method uses a logit probability of purchase model for purchase decisions made by consumers that accounts for the impacts of price, operating cost, and features on shipments. Model parameters were estimated by using a variety of data sources. The data sources included AHAM data on current market shares for different clothes washer markets, AHAM historical shipments and efficiency data, AHAM engineering data, and results from the Clothes Washer Consumer Analysis. The shipments model estimates potential standards-induced impacts on new and used clothes
9-37washer shipments, gross sales revenue, mean clothes washer ages, lifetimes, and repair rates. Details of

the predicted impacts are illustrated in Figures 9.13 through 9.15.

REFERENCES Association of Home Appliance Manufacturers, Home Appliance Saturation and Length of First Ownership Study, May, 1996. Chicago, IL. Prepared by NFO Research, Inc. <www.aham.org> 2. U.S. Department of Energy - Energy Efficiency & Renewable Energy - Office of Codes and Standards, Clothes Washer Consumer Analysis, April, 1999. Washington, DC. 3. U.S. Department of Energy - Energy Efficiency & Renewable Energy - Office of Codes and Standards, Preliminary Technical Support Document: Energy Efficiency Standards for Consumer Products: Clothes Washers (TSD), October, 1998. Washington, DC. 4. Olney, M. L., Demand for Consumer Durable Goods in 20th Century America. Explorations

in Economic History, 1990. 27: p. 322-349 5. Hanssens, D. M., Order Forecasts, Retail Sales, and the Marketing Mix for Consumer Durables. Journal of Forecasting, 1998. 17: p. 327-346 6. Dipak, J. and R. C. Rao, Effect of Price on the Demand for Durables: Modeling, Estimation and Findings. Journal of Business & Economic Statistics, 1990. 8(2): p. 163-170 7. Golder, P. N. and G. J. Tellis, Beyond Diffusion: An Affordability Model of the Growth of New Consumer Durables. Journal of Forecasting, 1998. 17: p. 259-280 8. Dolan, R. J., Power pricing: how managing price transforms the bottom line, in The Free Press. 1996: New York. 9. Parker, P. M., Price Elasticity Dynamics Over the Adoption Life Cycle. Journal of Marketing Research, 1992. XXIX: p. 358-367 10. Association of Home Appliance Manufacturers, 1997 Major Appliance Industry FactBook. 1998: Chicago, IL. 11. The Share-of-Market Picture. Appliance Magazine, September, various years

9-3812. U.S. Department of Commerce - Bureau of the Census, Statistical Abstract of the United

States, various years. Washington, DC. 13. U.S. Department of Energy - Energy hformation Administration, Residential Energy Consumption Survey: Household Energy Consumption and Expenditures 1993, October, 1995. Washington, DC. Report No. DOE/EJA-0321(93). 14. Lehmann, D. R., S. Gupta, and J. H. Steckel, Marketing Research. 1997, Addison-Wesley: New York, NY. 15. Hewitt, D., J. Pratt, and G. Smith,A Second Wash Wise Market Progress Evaluation Report, July 28, 1998, Prepared for The Northwest Energy Efficiency Alliance. Prepared by Pacific Energy Associates. Report No. E98-012, p. 20. <http://www.nwalliance.org/resources/reports/e98-0 12.pdf> 16. Tomlinson, J. J. andD. T. Rizy,Bern Clothes Washer Study: FinalReport, Marcl 1998,U.S. Department of Energy, Oak Ridge National Laboratory, Energy Division. Oak Ridge, TN. Report No. ORNL/M-6382. 17. Whenitbreaks... asmartguidetogettingthingsfixed. ConsumerReports, 1998. May: p. 12-19

9-39CHAPTER 10. NATIONAL ENERGY IMPACTS AND REGULATORY IMPACT ESTIMATES

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............................ TABLE OF CONTENTS
10.1 INTRODUCTION 10-1 10.1.1 Methodology and Definitions 10-1 10.2 NATIONAL ENERGY/WATER SAVINGS (NES) 10-2 10.2.1 Definition 10-2 10.2.2 NES Inputs 10-3 10.2.2.1 Annual Energy Consumption (AEC) 10-4 10.2.2.2 National Energy Savings (NES) 10-4 10.2.2.3 Source Conversion Factor (src_conv) 10-5 10.2.2.4 Stock of Clothes Washers by Vintage (STOCKV) 10-6 10.2.2.5 Cycles per Year (flcycie) 10-6 10.2.2.6 Energy per Cycle (UEC) 10-6 10.2.2.7 Annual Water Consumption (AWC) 10-9 10.2.2.8 Water per Cycle (UWC) 10-9 10.2.2.8 Clothes Washer Shipments 10-10 10.2.2.10 Voluntary Programs 10-10 10.3 NET PRESENT VALUE (NPV) 10-11 10.3.1 NPV Metric 10-11 10.3.2 NPVlnputs 10-12 10.3.2.1 Discount Factor 10-12 10.3.2.2 Present Value of Costs (PVC) 10-12 10.3.2.3 Present Value of Savings (PVS) 10-13 10.3.2.4 Net Equipment Cost 10-13 10.3.2.5 Total Operating Cost Savings 10-14 10.4 OUTPUT FOR NES & NPV 10-14 10.4.1 Assumptions 10-15 10.4.2 Base Case Shipments 10-15 10.4.3 National Energy Savings and Net Present Value from Possible Standards .. 10-15 10.5 USER INSTRUCTIONS FOR NES/SHIPMENTS SPREADSHEET 10-18 10.5.1 BASIC OPERATING INSTRUCTIONS 10-18

10-iLIST OF TABLES

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......... Table 10.1 National Energy/Water Saving Inputs 10-4 Table 10.2 Example of Average Electric Consumption for the Base Case 10-8 Table 10.3 Percent of Annual Clothes Washer Shipments having Energy Consumption

Equivalent to Horizontal Axis Washers 10-10 Table 10.4 Net Present Value Inputs 10-12 Table 10.5 Assumptions Used for Generating National Impacts 10-15 Table 10.6 Range of Energy Savings and NPV for Each Standard Level 10-16 Table 10.7 Reference Case - All Parameters Set to Medium or Average 10-16 Table 10.8 NES Results: proposed rule (MEF = 1.04 @ 2004 & MEF=1.26 @2007) 10-17 Table 10.9 Efficiency Level: Energy and Water Savings (proposed rule) 10-17 Table 10.10 National Energy Saving Quantities and their Locations in the National

Energy Savings Spreadsheet 10-19 Table 10.11 Net Present Value Quantities and their Locations in the National Energy

Savings Spreadsheet 10-19

LIST OF FIGURES Figure 10.1 Annual Cost and Savings for the Proposed Clothes Washer Rule 10-17

10-uCHAPTER 10. NATIONAL ENERGY IMPACTS AND REGULATORY IMPACT ESTIMATES
10.1 INTRODUCTION This chapter describes the method for estimating the quantity and value of future national energy savings (NES) from possible standards and other regulatory actions and options. The NES is one of the metrics for evaluating the standard impacts, while the examination of other regulatory options is referred to as the regulatory impact analysis (RIA). The two metrics discussed in this chapter are: • National Energy/Water Savings (section 10.2), and • Net Present Value (NPV) of Energy/Water Savings (section 10.3). All calculations are performed on a series of Microsoft Excel spreadsheets which are accessible over the Internet. Basic outputs from the spreadsheet calculations are discussed in section 10.4. A more detailed set of results is available in Appendix N. Access to and basic instructions for the spreadsheets are discussed in section 10.5. 10.1.1 Methodology and Definitions The methodology applied to the national energy and water savings and the regulatory impact estimates includes detailed calculation of both baseline and regulatory scenarios for sales, energy, water use, and appliance purchase expenses. There are several interrelated factors that can affect appliance purchase expenses, and energy and water savings. These factors include changes in purchase price caused by the promulgation of standards, price-induced changes in consumer purchase behavior, differences in energy and water consumption rates for clothes washers with different efficiencies and the concomitant differences in operating cost. Performance standards and regulatory interventions can change both purchase behavior and the mix of appliance efficiencies that are in the market. These purchase changes then result in changes in the age distribution and mix of efficiencies and resource consumption rates of household appliances. The NES and RIA impact models consist of two main components: The first component is a shipments model that provides the accounting of both sales, and clothes washers stocks for different efficiency and age categories of clothes washers. The shipments model estimates the number of clothes washers of each age and each efficiency category for each year of interest. The second component of the NES and RIA calculations is a net cost/benefit calculation of the relative costs and savings of the standard, regulatory and baseline scenarios. The NES and RIA calculations are presented in an integrated Excel spreadsheet that provides results in both tabular and graphical form along with presentation of the overall evaluation metric for the scenarios. These metrics include the net present value of the energy and water savings, the 10-1benefit/cost ratio of the resource savings, the net cumulative volumetric water savings, and the

energy savings for each fuel typea for each decade. 10.2 NATIONAL ENERGY/WATER SAVINGS (NES) 10.2.1 Definition This section provides the definition of national energy savings. National annual energy savings are calculated as the difference between two projections: a base case (without new standards) and a standards case. Positive values of NES correspond to energy savings, that is, energy consumption with standards is less than energy consumption in the base case.
NEST =AECb -AECstandard Eq. 10-1 Cumulative energy savings are the sum over some period (e.g., 2000-2030) of the annual national energy savings. NES = NES Eq. 10-2 The national annual energy consumption is calculated according to the following equation:



### AEC = 

### STOCKV *

### (UECV * 'cvcie) Eq. 10-3 The national water consumption is calculated according to the following equation:



### AWC>STOCKv*(UWCv*n Eo.10-4 cycle' where the different quantities are defined as follows:
AEC = Annual energy consumption each year (Quads), summed over

aWater heaters or clothes dryers may use one of several fuel types (e.g. electricity, natural gas, LPG (propane), and--for water heaters--distillate oil).
10-2vintages of clothes washer stocks, STOCKV.

AWC = Annual water consumption each year (lOs gallons), summed over

vintages of clothes washer stocks, STOCKV.

11cycle = Cycles per year (e.g., loads of laundry) NES = Annual national energy savings (Quads) STOCKV = Stock of clothes washers (millions of units) of vintage V surviving in the

year for which annual energy consumption is being calculated. Vintages range from 0 (new)- to 23-years old. UECV = Energy consumption per clothes washer per cycle (kWh electricity,

MMBtu gas or oil). (NOTE: electricity consumption is converted from site energy (kWh) to source energy (Quads) by applying a time dependent conversion factor (Btu/kWh). See quantity "src_conv" below in discussion of AEC.) UWC, = Water consumption per clothes washer per cycle (gallons per cycle) V = Year in which the washer was purchased as a new unit. y = year in the forecast (e.g., 2000-2030)
10.2.2 NES Inputs This section provides information about the quantities and assumptions used to calculate national energy/water savings for clothes washer standards. For each quantity, the discussion includes: • definition • approach • current assumption The inputs into the NES analysis are listed in the table below.

10-3Table 10.1 National EnervIWater Savin2 Innuts

National Annual Energy Consumption (AEC) National Annual Energy Savings (NES) Source conversion factor (src_conv) Stock of clothes washers (STOCKV) Cycles per year (ncycie) Energy per Cycle (UEC) Water per Cycle (UWC) Shipments Effect of Voluntary Programs 10.2.2.1 Annual Energy Consumption (AEC) Definition. National energy consumption associated with residential clothes washers and dryers. Approach. National energy consumption is the product of energy consumption per washer times the number of clothes washers of each vintage. This approach accounts for differences in unit energy consumption from year to year. Annual energy consumption per clothes washer is calculated as the product of energy per cycle times number of cycles per year.

AEC = STOCKV *(UEC * "cycie) Eq. 10-5 CurrentAssumptions. Energy consumption is calculated at the site (e.g., electricity in kWh consumed in the household). Primary energy consumption is calculated from site energy consumption by applying a conversion factor to account for losses, such as losses in generation, transmission and distribution of electricity. See Source Conversion Factor, below. 10.2.2.2 National Energy Savings (NES) Definition. Energy savings attributable to the new standards. Approach. Energy savings are calculated as the difference between projected energy consumption in the Base Case (having no new standards) and the projected energy consumption in the Standards Case. CurrentAssumptions. Because the shipments model estimates small changes in the number of households with clothes washers, the base case and the standards case have a different number
10-4of residential clothes washers. To account for this effect, we assume that the households that change

from owning a washer to not owning a clothes washer, are still washing their clothes using a clothes washer with average energy and cost characteristics. The average per unit cost/benefit, and energy characteristics of the clothes washer utilized by the non-owner (who was an owner in the base case scenario) is assumed to be the same as that for user-owned residential clothes washers. We therefore rescale the energy and cost estimates according to the relevant population of users. For the net present value calculation (NPV) we scale the costs and benefits to correspond to the population of residential users who are benefitting directly from the more efficient machines. This means that for NPV, costs are scaled to correspond to the standards case. Meanwhile, for the national energy savings calculation, we assumed that those who are using common area washers or laundromats are using machines with the same efficiency as the residential clothes washers. This means that we scale the savings to correspond to the population of households in the base case. In the most extreme case, the change in the number of households owning clothes washers is less than 4%, but the adjustment in the calculation is necessary for computational accuracy. 10.2.2.3 Source Conversion Factor (src_conv) Definition. For electricity, this is the factor by which site kWh is multiplied to obtain primary (source) Btu. The source conversion factor accounts for losses in generation, transmission and distribution. For natural gas, this is the loss in transmission and distribution. Approach. After calculating energy savings at the site, multiply those site energy savings by a conversion factor to obtain primary energy consumption, usually expressed in Quads (quadrillion Btu). This conversion permits comparison across fuels by taking account of the heat content of different fuels and the efficiency of different energy conversion processes. Current Assumptions. The source conversion factor is applied to site electricity, to convert from site kWh to source Btu. This analysis assumes that the source conversion factor changes over time, and applies annual values. The annual values for each fuel type are the U.S. average conversion factors, calculated from AE099, Table A4.' For the source conversion factors, DOE uses the following method: (1) From the NEMS Annual Energy Outlook reference case, the source energy consumption is extracted. (2) An energy savings scenario is input into NEMS (specifically a deviation from the reference case) to obtain the corresponding source energy consumption. (3) The difference in source energy consumption between the energy savings scenario and the reference case is calculated. (4) The source energy savings in Btu, adjusted for class specific transmission and distribution losses, is divided by the site energy savings in kilowatt-hours to provide the time series of conversion factors in Btu per kilowatt-hour. Since NEMS can not adjust for class specific transmission losses, this information was 10-5obtained from sources outside of NEMS. For residential electricity customers, transmission losses

might consist of about 3 percent (which basically gets you to a substation) and distribution losses may be about 7 percent (substation to house). For the above case, the conversion factor would be the marginal plant heat rate times 1.10. For natural gas, the transmission and distribution losses amount to about 10% of primary energy, so primary energy is calculated from site energy by dividing site energy by 0.90. The resulting conversion factors change over time, and account for the displacement of generating sources. The National Energy Savings spreadsheet models includes a clearly defined - column of conversion factors, one for each year of the projection. 10.2.2.4 Stock of Clothes Washers by Vintage (STOCKy) Definition. Number of user-owned clothes washers in U.S. households at the beginning of a particular year. The vintage is the age of the washer (1-year old up to 23-year old). Approach. The NES spreadsheet keeps track of the number of clothes washers in U.S. households and the year in which they were purchased. This is done through the shipments model which is a dis-aggregated accounting model that keeps track of number of clothes washers in each age category. Current Assumption. For clothes washers, lifetimes range from 11 to 17 years, with an average of 14.1 years (see section regarding the shipments model and the replacement/survival probability). Under scenarios of large purchase price increases, extended-life washers may have lifetimes as long as 23 years. 10.2.2.5 Cycles per Year (cycie) Definition. Loads of laundry washed per household per year. Approach. The DOE test procedure assumes 392 cycles per year. In actuality, the number of loads of laundry washed per household per year depends upon the number of persons in the household, and probably on other factors. Current Assumption. Assume an average of 392 cycles per year for all years. 10.2.2.6 Energy per Cycle (UEC) Definition. Energy consumed per cycle. Approach. In accordance with the DOE test procedure (for modified energy factor, MEF), energy consumption per cycle includes electricity used by the clothes washer, and energy used by the water heater to provide hot water, and energy used by the clothes dryer to dry the clothing. The base case forecast of unit energy consumption is comprised of a weighted average of
10-6baseline efficiency level (MEF=0.8 17), a 35% energy reduction from baseline, MEF = 1.257 and a

pre-baseline level (MEF = 0.760) that corresponds to machines purchased before the 1994 standard. The relative weight represents the relative market share of pre-1994, baseline and of horizontal axis machines that are expected in a baseline scenario. We assume that the market share of vertical axis machines will decrease by 0.5% each year in the baseline case and use this to project the market share of horizontal axis machines in the baseline case. The spreadsheet model also allows alternate assumptions of a 0.25% and 0.75% H-axis escalation rates. For calculating the energy characteristics of the pre-baseline machine, we note that the minimum energy factor (EF) for clothes washers is 0.95 in 1988 compared to 1.18 for the EF for the baseline machine in this rule making. This implies that the pre-baseline machine uses 24.2% more energy in the motor and water energy component (which is the component of energy that the energy factor measures). Assuming that this energy increase relative to the current baseline is due solely to the increase in hot water energy, this implies that the pre-baseline machines use 0.435 kWh/cycle more hot water energy than the baseline machines. This implies 2.02 kWh of water energy for a pre-baseline machine and a 12% decrease of the MEF. The MEF for a pre-baseline machine is therefor set to 0.720 with engineering specifications set at the same as the baseline machine except for a 0.435 kWhlcycle increase in the hot water energy use component. The unit energy consumption is composed of three components: water heating, machine (clothes washer), and dryer energy. Machine energy is electricity. Water heating energy depends upon the fuel type of the water heater. Dryer energy depends upon the fuel type of the dryer. (The DOE test procedure, Appendix Ji assumes a value based on an electric dryer; adjustments were made to this value for a gas dryer2). The unit energy consumption is first calculated for an all-electric household, UECE. For each component (water heat, dryer, and machine), the weighted average is calculated, given the share of new washers that are horizontal axis. Example: In 1998, 6.25% of new washers are assumed to have an efficiency equivalent to horizontal axis.

10-7Table 10.2 Example of Average Electric Consumption for the Base Case Electricity (kWh/Cycle) Share Water Heater Machine Dryer 93.75% (Baseline) 6.25% (Energy Efficiency equivalent to H-Axis) 1.587 0.462 0.209

0.133 1.430

1.270 Weighted average 1.5 17 0.204 1.420 The average electricity consumption per new clothes washer depends upon the shares of fuels for water heating and for clothes drying. The electricity consumed for water heating (calculated in the example above) is multiplied by the percent of households having electric water heating, then summed together with the product of electricity per unit for dryer times percent of households having electric dryers. Finally the machine energy per unit is added. The result is multiplied by cycles per year. UEC E(k WH*%WHE)+(kWh DR*%DR E)+ki machine Eq. 10-6 Example: Continuing with the example for year 1995,

UECE = (1.5 17 * 0.42) + (1.420 * 0.79) +0.204

= 0.637+1.122+0.204

= 1.963 kWh/cycle Annual energy consumption is the product of number of cycles per year and unit energy consumption per cycle. In the example for year 1998, AECE = neycie * UEC = 392 * 1.963 = 769 kWh/year. Energy consumption for natural gas and for oil are obtained by correcting for the difference in recovery efficiency of the water heater, and by converting units from kWh to MMBtu. For natural gas, energy consumption per cycle for water heating (expressed in MMBtu) is:

(kVVh/ 0.75) * (34l2BtuIkWh)/ (1,000,000 BtuJMMBtu), where the denominator, 0.75, is the recovery efficiency of the gas water heater. For distillate oil and LPG, energy consumption per cycle for water heating (expressed in MMBtu) is: (kWh/ 0.81) * 0.OO3412MMBtu/kWh, where the denominator, 0.81, is the recovery efficiency of the oil water heater. Gas consumption for clothes dryer is: 10-8(kWh1 /0.89)* (341 2BtuIkWh)/( 1,000,000 BtuIIVHVlBtu),

where 0.89 is the efficiency of a gas clothes dryer.3'4 Current Assumptions. Each of the components of energy consumed per cycle is obtained from the data submitted by AHAM, for baseline and for each of the efficiency levels. The percent of households having water heaters of each fuel type and having clothes dryers of each fuel type is fixed at the RECS 1993 levels for the period of the forecast. The fuel-type market shares are used to calculate the annual energy consumption for each fuel type. A weighted average unit energy consumption for new clothes washers (including water heat, clothes drying, and machine energy) is calculated for each year of the projection, according to the historical and forecasted market shares of the different efficiency levels. For standard levels below 1.257 MEF (35% level), it is assumed that the market share of standard level machines is the same as that of baseline machines in the base case scenario. The rest of the machines are assumed to be horizontal axis machines represented by the energy and cost characteristics of the 1.257 MEF level machines. 10.2.2.7 Annual Water Consumption (AWC) Definition. National water consumption associated with residential clothes washers. Approach. National water consumption is the product of water consumption per washer times the number of clothes washers of each vintage. This approach accounts for differences in unit water consumption from year to year. Annual water consumption per clothes washer is calculated as the product of water per cycle times number of cycles per year.

AWC = STOCKV * (UWC * 'cyc1e) Eq. 10-7
10.2.2.8 Water per Cycle (UWC) Definition. Water consumed per cycle. Approach. Similar to the calculations for the energy use per cycle, the base case forecast of unit water consumption is comprised of a weighted average of baseline water use and water use at the 1.257 MEF (35% reduction in energy use level). Current Assumptions. The water consumed per cycle is obtained from the data submitted by AHAM, for baseline and for each of the efficiency levels (Note: The efficiency characteristics of the baseline machine is a weighted average of vertical axis machines that would be produced without a standard). A weighted average unit water consumption for new clothes washers is calculated for each year of the projectionby taking a weighted average of horizontal-axis and vertical-axis machine characteristics, using the horizontal axis market share projection that is selected by the user.
10-910.2.2.8 Clothes Washer Shipments

Clothes washers shipments are obtained from a dis-aggregated clothes washer sales and stock accounting model that is described separately in chapter 9. The model is fully integrated with the cost and energy use scenarios in the National Energy Savings calculations. This means that when the user selects a scenario that changes the price or operating expenses of the clothes washers, this cost data feeds into the shipment forecast model to estimate changes in the stock and sales of different categories of clothes washers. This provides an estimate of feedback effects (e.g. the increased expense of more efficient clothes washers results in a decrease in sales which decreases the replacement rate of less efficient machines). 10.2.2.10 Voluntary Programs A separate report describes voluntary programs already in place, which are promoting clothes washers with higher energy efficiency (see Appendix J)•5 The impact of these programs has been expressed here as the percent of new clothes washers each year that will have efficiencies corresponding to those of horizontal-axis washers (35% reduction in energy use from the baseline washer design). The current spreadsheet provides the user with the opportunity to specify escalation rate of the market share increase of horizontal axis machines (relative to the base case washer design). This escalation rate is the relative amount that the market share of vertical axis machines will decrease each year. The escalation rate used for the reference base case scenario is 0.5%per year. This means that the relative market share of vertical axis machines is 99.5% of the market share for the previous year, starting with a market share of 6.25%for horizontal axis and 93.75%for vertical axis machines in 1998. This provides for a gradual, exponential decrease in vertical axis market share in the forecast. For illustrative purposes, Table 10.3 shows the values used in the draft spreadsheet. Table 10.3 Percent of Annual Clothes Washer Shipments having Energy Consumption

Equivalent to Horizontal Axis Washers Year Percent of shipments 1998 6.25% 2000 7.19% 2010 11.72% 2020 16.04% 2030 20.14%

10-1010.3 NET PRESENT VALUE (NPV)

10.3.1 NPV Metric NPV is the value in the present time (chosen as 1999 for this analysis) of a time series of costs and savings. Net present value is described by the equation:
NPV=PVS-PVC Eq. 10-12 where: PVS = present value of savings ("Total Fuel & Water Savings")

= TotalOperatingCostSavings *DiscountFactor Eq. 10-13 PVC = present value of costs ("Net equipment Cost")

= TotalEquipmentCosyDiscountFactor Eq. 10-14 y = Years (from start date of the valuation analysis) The net present value is calculated from the projections of national expenditures for appliances, including purchase price and operating costs. Costs and savings are calculated as the difference between a new standards case and a base case without those new standards. Future costs and savings are discounted to the present. A discount factor is calculated from the discount rate and the number of years between the "present" (year to which the sum is being discounted) and the year in which the costs and savings occur. The net present value is the sum over time of the discounted net savings. Current Assumptions. The assumptions are contained in the terms PVC and PVS, which are discussed below. Net present value (NPV) is the value today of a future stream of savings less expenditures. In the NES spreadsheet table labeled "Cost and Net Present Value," "Total Energy and Water Savings" is the present value of the savings. "Net equipment Cost" is the present value of increased purchase prices. "Net Present Benefit" is the difference between "Total Fuel and Water Savings" and "Net equipment Cost." "Benefit/Cost Ratio" is the ratio of "Total Fuel and Water Savings" to "Net equipment Cost."

10-1110.3.2 NPV Inputs

This section provides information about the quantities and assumptions used to calculate net present value for clothes washer standards. For each quantity, the discussion includes: • definition • approach current assumption Table 10.4 summarizes the inputs to the NPV calculation. Table 10.4 Net Present Value Inputs

Input Discount factor Net equipment Cosç, Total Operating Cost Savings

10.3.2.1 Discount Factor Definition. The factor by which to multiply monetary values in one year, in order to determine the present value in a different year. Discount Factor is also described by the equation:

Discount Factor = 11(1 + DiscountRate)aresentY) Eq. 10-15 Approach. For example, to discount monetary values in the year 2001 to the value in year 1999, assuming a discount rate of 7% is 1/(1.07)2 or 0.873. Current Assumptions. The discount rate is assumed to be 7% real.a For purposes of discounting dollar costs and savings, the present year is defined to be 1999. 10.3.2.2 Present Value of Costs (PVC) Definition. Net equipment cost, discounted to the present, and summed over the time period (from start of standards to year 2030). Approach. Costs are typically increases in purchase price associated with the higher energy
aUsed by DOE in previous rulemakingforthe National Impact Analysis. Higher and lower values can be used as sensitivities (i.e., to bound a range of discount rates).

10-12efficiency of appliances purchased in the standards case compared to the base case. Costs are

calculated as the difference in purchase price for new appliances purchased each year multiplied by the shipments in the standards casea ("Net equipment Costs"). Current Assumptions. The chief assumption made in calculating PVC lies in determining the discount factor to be applied. Here the discount rate is taken to be 7% (see also Discount Factor, above). 10.3.2.3 Present Value of Savings (PVS) Definition. Annual operating cost savings (difference between base case and standards case) discounted to the present, and summed. Approach. Savings are typically decreases in operating costs associated with the higher energy efficiency of appliances purchased in the standards case compared to the base case. The total operating cost savings is the product of savings per unit times number of units of each vintage surviving in a particular year. The operating costs savings are counted for only those households that own clothes washers in both the baseline and standards scenario. Appliances consume energy over their entire lifetime; therefore, we include the energy consumption after 2030 for those machines that are purchased new previous to 2030. Net savings each year are calculated as the difference between Total Operating Cost Savings and Net equipment Costs)' The savings are calculated over the life of the appliance, accounting for the energy and water rates each year. Current Assumptions. As with PVC, the chief assumption made in calculating PVS lies in determining the discount rate to be applied. Here the discount rate is taken to be 7% (see also Discount Factor, above). In addition, see Net Equipment Cost and Total Operating Cost Savings, below. 10.3.2.4 Net Equipment Cost Definition. Annual change in purchase price (difference between base case and standards case), multiplied by shipments in the standards case. Approach. Purchase price per clothes washer in the standards case is subtracted from
aCounting the reduction in energy consumption from a reduction in shipments as a savings would be incorrect. If standards cause a decrease in shipments, then using the lower shipments in the standards case reduces the NPV appropriately. To illustrate with an extreme example, if standards cause shipments to be zero, then NPV is zero, no matter what the shipments were in the base case. Using the shipments from the standards case avoids miscounting any reduction in shipments due to standards as a savings. b In the spreadsheet, Net equipment Costs are expressed as a negative number (the difference between the base case and the standards case) then summed with Total Operating Cost Savings (the difference between base case and the standards case).
10-13purchase price per clothes washer in the base case for one year. The result is multiplied by the

projected shipments in that year. Current Assumptions. See appropriate TSD chapter for a discussion of shipments. As noted, a dis-aggregated accounting model is currently assumed to produce the best shipments forecast. 10.3.2.5 Total Operating Cost Savings Definition. Annual national operating cost savings, calculated as the difference between total operating cost in the base case minus total operating cost in the standards case. Approach. Under both the regulatory and baseline scenario the total energy and water use is calculated according to the engineering estimates for each vintage of clothes washer in stock. The average operating cost difference per clothes washer is then applied to the total stock of clothes washers in the standard scenario to calculate the total operating cost savings. Current Assumptions. See Cycles per Year and Energy per Cycle as discussed in Sections 10.2.2.5 and 10.2.2.6, respectively, and the discussion of energy prices in Chapter 7.
10.4 OUTPUT FOR NES & NPV The NES spreadsheets offer a range of possible outputs, all of which depend on the assumptions used in deriving the results. Table 10.5 details the assumptions used in the NES calculations in this analysis.

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