•7--·**·-~·**

### •

. QUANTITIES AND CURRENT ASSUMPTIONS FOR CALCULATING LlFE CYCLE COSTS OF CLOTHES WASHERS

James E. McMahon, Ph.D. Ernest Orlando Lawrence BerkeleyNatio.nal Laboratory. March 11, 1998

IPURCHASE EXPENSE Definition: ConsuJner expense for purchasing

### ~ appliance Approach: Consumer.purchase expense includes the retail price ofthe appliance plus sales tax. The baseline · purchase expense is the retail price plus sales tax. The purchase expense for each efficiency level is calculated as the sum ofbaseline purchase expense plus the incremental purchase expense for the
. · efficiency level. The incremental purchase expense is the product ofincremental manufacturing cost,

manufacturer variable markup, and retail variable markup, plus the sales tax. Location: File: · LCC WASHER.XLS Sheet: "Engineering" EXAMPLE FOR CLOTHES WASHERS: (all values in this description are rounded to the nearest dollar): Baseline retail price= $400. · Sales tax (U.S. average)= 5.2% Baseline purchase expense = $421 AHAM provided incremental manufacturing costs for 9 efficiency levels. For example, the. incremental manufacturing cost (shipment-weighted average) for a 35% energy reduction from baseline is $128, with a custom distribution provided by AHAM. The most likely manufacturer variable markup is 1.175 (range ofLO to 1.35, triangular distribution), retail markup is 1.40, and sales tax adds 5.2% ofthe retail price. The SWA incremental purchase expense is: $128 x 1.175 x 1.40 x 1.052 = $222. The purchase expense for the unit having a 35% energy reduction is the baseline purchase expense plus the incremental purchase expense= $421 

### + 222 = $643. CurrentAssumptions: AHAMdata for manufacturing costs. ADL report for markupsandsales tax.

2

### LIFETIME Definition: The period oftimethe clothes washer will provide service. Approach: The lifetime is estimated by comparing historical shipments to percent ofhouseholds currently owning· the appliance (MTSC, 1980). Location: File: LCC WASHER.XLS



### - Sheet: "Lifetime" CurrentAssumption: For clothes washers, lifetimes range from 12 to 17years, with an average of14years.



### 3

### CYCLES PERYEAR 

### Definition: loads oflaundry washed per household per year 

### Approach: The DOEtestprocedure assumes 392 cycles per year. In actuality, the number ofloads oflaundry washed per household peryear depends upon the number ofpersons in the household; and probably on otherfactors. A survey ofU.S. households indicates a relationship between family size and cycles peryear. (John T. Erikson, personal communication, 1995) · Using the sample ofhouseholds having both a clothes washer and a.clothes dryer from the Energy Information Administration,1993 Residential Energy Consumption Survey, we assigned these cycles peryearto each household according to the persons per household. The weighted average result is 379 cycles peryear for the U.S. mix ofhouseholds. This is in good agreement (within 4%) with the DOE test procedure: To the extentthat the groups ofhouseholds using different fuels for water heater and clothes dryers differ, the cycles per year also differ among those groups. CurrentAssumption:

_ For simulatinga sample of househ.olds, each householdisassignedcyclesperyear basedupon the following table (scaledso the average agreeswith th(! testprocedure assumption). Figure 1 shows the weighting for the number of washer cyclesperyear. Per$onsper household 1 2 3-4 5+ Cyclesperyear (RECS) 

### 200 310 454 624 Cyclesperyear (scaled) 

### 210 321 469 645 

### Number ofWasherCycles perYear 40% 35.1% 36.5% 30%**~** 

### ..... .c 20% Oil 

## ·as**~** 10% 0% 207 321 469 645 

### WasherCycles Figure 1 Weighting ofthe number ofwasher cycles per year 4ENERGY PER CYCLE ·. ,; 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. Location: 

### File: LCC WASHER.XLS Sheet: "Engineering" 

### CurrentAssumptions: Each of these components of energy consumedper cycle. is obtained from the data submittedby AHAM,for baseline and for each of the efficiency levels. Figure 2 shows the energy usepercycle vs.MEF

3.5 

### c:;- 3-.0**~ ~**  

# -= 2.5

# ~
- 2.0

0.5 

### 0.0 

### 0.82 0.86 0.91 0.96 1.02 1.09 1.26 1.36 1.49 1.63 MEF Figure 2 

### Energy Use per cycle vs. MEF

5

### ELECTRICITY PRICE 

### Definition: · · The value to a residential customer of saving electricity, expressed as cents per

killowatt-hour. 

### Issues: All households with clothes washers use electricity for the washer, and some households use ·electricity for water heating and clothes drying. Showing the change the customer will see in his/her electricity bill due to increased energy efficiency is complex because: 

### i) electricity price varies from house to house, depending upon the rate schedule charged by th_e utility and the consumption pattern of the particular customer; and2) future prices cannot be known with certainty, especially since the market is currently restructuring·and consumers are expected**~o** be.able to choose among competing utilities. · 

### Approach: The variations in electricity price are handled by separating the problem into three parts: a) variability in energy price among households; b) value·ofsavings; and c) future trends. Each of these parts is discussed and current assumptions described. 

### a) Variability A national survey which gathered information on electricity bills is used to represent the variability from house to house. An advantage ofusing a survey containing information on specific households is the ability io directly capture correlations among quantities.' Such correlations are important for electric and gas prices, for example, or among household. characteristics (e.g., fuel ofthe water heater and clothes dryer, persons per household) that affect energy consumption. · 

### Current Assumption: All those householdsfrom the Energy Information Administration's 1993 ResidentialEnergy Consumption Survey (RECS) survey which.have both a clothes washer anda clothesdryerare being used Energyprices are reportedin the survey results for each household These householdsare assignedweights to represent the U.S. Figure 3 shows residential electricity prices ranging from 2to17cents/kWh. 

### b) Value ofsavings The prices shown in Figure 3 are average prices including fixed charges. When a consumer saves electricity, the bill savings depend upon the marginal energy charge as reflected in the utility rate schedule (cents perkilowatt-hour), which may be higher or lower than the average rate in the Figure above. An exact accounting would require knowing for each household: the quantity and timing of energy used with and without the saved energy, and the rate schedule (price per kilowatt-hour·as a function ofthe quantity ofkilowatt-hours used, including seasonal and/or time ofday pricing). In general, such detailed information is not known. Three approaches are considered: I) average rates, calculated as the ratio ofhousehold expenditures for electricity (including fixed charges) to kWh consumed; 

### 2) partial adjustment 

### of known
. 6inaccuracies by subtracting the average fraction corresponding to fixed charges from average rates; and 3) estimating the actual consumer·marginal energy rate. 

### 1) Average rates. ADVANTAGE: Simple. Available in published historical data and forecasts. DISADVANTAGE: May over- or**under-~stimate** the actual consumer marginal energy rate. 

### 2) Subtract average fixed charge everywhere. ADVANTAGE: Approximately accounts for fixed charges. Edison Electric Institute has assembled information onfixed charges for average general service residential rates for a large number ofutilities that show fixed charges on average represent about 

### 7.5% ofaverage.rates. DISADVANTAGE: By reducing the value ofenergy savings in all cases, including those where the marginal price is higherthan the average price including fixed charges, this method
. under-estimates the actual consumer marginal energy rate in some cases. 

### 3) Estimate distribution ofconsumer marginal energy rates. ADVANTAGE: Theoretically most accurate. DISADVANTAGE: Practical difficulties: a) The rate schedules·for households in the RECS survey are not known. Assignment to utility service territories and to rate schedules would need to be imputed. Month by month electri.cal consumption would be needed to determine the monthly marginal price. Rate schedule data does not exist for 

### all utilities and, when available, is usually limited to general service residential·customers.
- 

### CurrentAssumption (Approach # 2): Subtract afixedpercentage (7.5% from each household's e/ectriciryprice) representing the average fixed charge.

4.0% 

### :;- 3.5%**.~** 3.0%



## -ca 2.5%



## E 

# = 2.0% 

## = 

# - 1.5% 

### "' 

# - .c 1.0% 1:11) •Q;j 0.5%**~** 0.0% 2 Residential Electricity Prices in 1997

4 6 8 10 --with Fixed Charge ·······subtract 7.5%

12 14. 16 18 C ) ce'nts/kWh Time**tren~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~d** Figure 3 Distribution of 1997 Residential Electricity Prices

I , 

### 7Estimating future electricity prices is now more difficult than· ever. In some states, the electricity supply industry is undergoing restructuring. Where previously, each household could be assignedto a particular utility company, and the**rat~s** offered by that utility obtained from surveys, restructuring means that households will be able to purchase electricity from a larger set ofsuppliers. A projected trend in national average prices is applied to each household's energy prices, after accounting for "value ofsavings" (described above). The user can select from the following: 1) Constant energy prices at 1997 values 2) Energy Information Administration Annual Energy Outlook 1998, High Economic Growth 3) Energy Information Administration Annual Energy Outlook 1998, Reference Case 4) Energy Information Administration Annual Energy Outlook 1998, Low Economic Growth 5) Gas Research Instfrute 1998 Baseline Projecti9n Figure 4 shows the trends for the last four ofthose projections. 

### CurrentAssumption: Time trend fromAE098Reference Case.

Location: File: Sheet: 9

# l Electricity Price 

### w/o fixed cost 8**··~.,**

# ..

# . ,."•.: ••-::



# ..**~**



### .......**~** 

# ..**--~** 

## -= 7

.**~.~**••• <..!..:_•--

---- .

## ~··**~** 6**~~** 

# ----- -High Growth

## ~---:. -:..-:. :.-:·: ....,..•-AEO 1998 • • - - - • 5 -GRI 1998 -Low Growth 1995 2000 2005 2010 2015 2020 2025 2030**Fi~ure** 

### 4 Residential Electricity Price Trends LCC WASHER.XLS LCC Button: List Inputs Click on: Energy Price Projection

8

### GAS PRICE Definition: The value to a residential customer ofsaving gas, expressed as dollars per million Btu: 

### Issues: Some households use gas for their water heater or clothes dryer. Showing the change the customer will see in his/her gas bill due to increased energy efficiency i"s complex because: 1) gas price varies from house to house; depending upon the rate schedule charged by the utility and the consumption pattern of the particular customer; and 2) future prices cannot be known with certainty.

. . 

### Approach: The .variations in gas price are handled by separating the problem into three parts: a) variability in energy price among households; b) value ofsavings; and c) future trends. ·Each of these parts is discussed and current assumptions described. 

### a) Variability A national survey which gathered information on gas bills is used to represent the variability from house to house. An advantage ofusing a survey ·containing information.<?n specific households is the 

### ability to directly capture correlation·s among quantities. Such correlations are important for electric and gas prices, for**e~ample,** or among household characteristics (e.g., fuel ofthe water heater and clothes dryer, persons per household) that affect ·energy consumption. 

### Current Assumption: All those householdsfrom the Energy Informdtion Administration's 1993 Residential Energy Consumption Survey (RECS) survey which have both a clothes washer anda clothes dryer are being used. For each household, relevant energyprices are reported. These householdsare assignedweights to represent the U.S. Figure 5 shows residentialgasprices ranging from 3.8to10.9 $/MMBtu. · b) 

### Value ofsavings The prices shown in Figure 5 include average prices including fixed charges. When a consumer saves energy, the bill savings depend upon the marginal energy charge as reflected in the utility rate schedule, which may be higher orlower than the average rate in the Figure above. An exact accounting would require knowing for each household: the quantity and timing ofenergy used with and without the· saved energy, and the rate schedule (price as a function ofthe quantity ofenergy used, including seasonal pricing). In general, such detailed information is not known. Three approaches are considered: 1) average rates, calculated as the ratio ofhousehold expenditures for gas (including fixed charges) to gas consumed; 2) partial adjustment ofknown inaccuracies by subtracting the average fraction corresponding to fixed. charges from average rates; and 3) estimating the actual consumer marginal energy rate. 1) Average rates. ADV ANTAGE: Simple. Available in published historical data and in forecasts.
9DISADVANTAGE: May over- or.under-estimate the actual consumer marginal energy rate. 2) Subtract average fixed charge everywhere. ADV ANTAGE: Approximately accounts for fixed charges. The American Gas Association has assembled information on fixed charges for residential gas customers that ·show fixed charges on average represent about 12% ofaverage rates
.. DISADVANTAGE: By reducing the value ofe!lergy savings in all cases, including those· where the marginal price is higher than the average price including fixed charges, this method under-estimates the actual consumer marginal energy rate in some cases. , , · 3) Estimate distribution ofconsumer marginal energy rates. ADV ANTAGE: Theoretically most accurate. DISADVANTAGE: The rate schedules·for households in the RECS sur\ley are not known.' Assignment to ut_ility service territories and to rate schedules would need to be imputed. ; Monthby month consumption would be needed to determine the monthly marginal price. 

### Rate:

· schedule data does not exist for all utilities and, when available, is .usually limited to general

service residential customers. CurrentAssumption (Approach 

### # 2): Subtract afixedpercentage (12% from each household'sgas price) representing the average.fixedcharge.



### 0.50% 0.40% 

## .:E 0.30% Oil 

# ·-**~** 

### 0.20% 0.10%

3 4 

## Residential Gas Prices 

## in 1997

5 

### 6 7 

### 8 9 

### dollar/MMBtu --withFbed Charge

· · · · - · · subtract 12%



# .J,111**lll1.11~u.** I 

### I I 1 ·I I I 

### 10 11 12 

### Figure 5 Distribution of 1997 Residential Gas Prices

10 I 13I 

### c) Time trend Estimating future electricity prices is· now more difficult than ever: In some states, the electricity supply industry is undergoing restructuring. Where previously, each household could be assigned to a particular utility company, and the rates offered by that. utility obtained from surveys, restructur,ing means**th~t.**households will be able to purchase electricity from a larger set ofsuppliers.
. A projected trend in national average prices is applied to each household's energy prices, after accounting.for "value ofsavings" (described above). The user cari select from the following: 1) Constant energy prices ·at 1997 values
. 

## ?) Energy Information Administration Annual Energy Outlook 1998, High Economic Growth 3) Energy Information Administration Annual Energy Outlook 1998, Reference Case 4) Energy Information Administration Annual Energy Outlook 1998, LowEconomic Growth · 5) Gas Rese!lrch Institute 1998 Baseline Projection · Figure 6 shows the projections. 

### CurrentAssumption: Time trend fromAEO 1998Reference.Case.



# 6.51 6.0 

## .a 

# 5.5**·'~··** 

# .... ·--- 

# I so 

### Gas Price H"gh G · h
· · - 1 rowt 

### w/o fixed cost**-·~AEO** 1998 -GRI 1998 -Low Growth

4.5 4.0**-1---~------~------** 1995 2000 2005 2010 2015 2020 2025 2030



### · Location: Figure 6 Residential Gas Price Trends

File: ·LCC W ASHER.XLS Sheet: LCC .Button: List Inputs Clink on: Energy Price Projection

11

### OIL PRICES Definition: 

### Residential price

# ofdistillate Approach: 

### Similar to approach for electric and gas prices.
. Variability in prices from RECS sample. No attempt to define a consumer**margin~** 

### energy rate. Figure 7 shows the time trend. · CurrentAssumptions:
. Variability inprice from 1993RECSsample of households owningwashers anddryers. Time trend fromAEO 1998Reference Case.

9.0 8.5 

### Oil Price



# ------------·- 8.0 

## .a 7.5**-·~**

# ..

# ,.,.······•····-- .

# --.

# -**.~.,.....** 

# .

. 

### ..

# ...•.

____ 

# e**~** 7.0

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# ··.--,··· \

.



### • - -- i$LW.
.................... ...

# ::~ 1·· . ' 5.5

- 5.0 

### +----------------- -High.Growth -•-AEO 1998 -Low Growth ___,;,...GR! 1998 1995 2000 2005 2010 2015 2020 2025 2030 Figure 

### 7 Residential Oil Price Trends

12WATER PER CYCLE Definition: 

### Water consumed by clothes washer in**on~** 

### cycle Approach: 

### Data as submitted by AHAM. · Location:. 

### File: LCC WASHER.XLS



### - Sheet: Engineering 

### CurrentAssumption:
. Use numericalvalues for baseline and

### each efficiency level, asprovided_byAHAM. Figure 8 shows the water useper cycle vs. MEF. ·

40

- 35, c.l 

# to 30 :::::i
. 

## :ii 25 

# -**~** 

### 20

### ~ 

## t 15



### .....**~** 

### 10

### ~ 5 ·O 0.82 0.86 0.91 0.96 1.02 1.09 1.26 1.36 1.49 1.63
. MEF Figure 8 

### Water Use per cycle vs. MEF

. 13WATER RATE· Definition: Residential customer rate for water and waste water (sewage)($/thousand gallons), ·excluding fixed charges Approach:
. An existing survey ofwater and sewage rates represents the population-weighted distribution ofU.S. water rates in 1994. (Al Dieteman, personal communication, 1995) Research continues to: 1) update that estimate; 2)-estimate historical change in those rates; and 3) obtain projections offuture change in those rates. Figure 9 shows the distribution ofthe sum ofwater and sewage rates. 

### CurrentAssumption: 1994diStribution ofU.S. values for waterandsewage rates. Future annualpercent change in rea{ rates is assumedto be zero, pending further research.

,.........



# . 

# - 9

### ~8 7 

# c. 

# £ 6 

## =**~** 5 

## < 4**~**

·- 3 

### i: 

## J5 2 

### Net Water+ Sewer Charges

g**~ ~**  :!:**~ ~** **~** 0- 0 0 -· - - -**~ ~** **~ ~** **~ ~-~**  

### N**~ ~** **~**

- - - - - - N N N**~** N NetWater& SewerperCCF Figure 9 Distribution ofNet Water and Sewer Charges

14-i 

### ·- "
DISCOUNT RATE Definition: The rate at which future expenditures are discounted to-establish their present value Approach: A distribution of discount rates was derived to represent the variability in financing methods consumers use in purchasing appliances. The resulting distribution ofdiscount rates 

### will be used to calculate a distribution oflife cycle costs for clothes washers. FINANCINGMETHODS Consumers purchase appliances in new homes, and as retail purchases. The retail purchases are paid by cash, credit cards, or retailer loans. 

### A comment (Whirlpool, 1990) indicated that for white goods about 40% ofretail purchases are paid in cash, 35% use credit cards, and 25% use retailer loans. The same coinment indicates25% ofappliance purchases are for new homes. (For clothes washers, LBNL estimates that purchases for new homes are now about 20%.) ' INTEREST RATES We estimated a range ofinterest rates that may reasonably be expected to apply in the future"_These are estimates, based upon historical data andjudgment about how the future inay differ from· the historical period: Fornew housing, we estimate nominal mortgage rates (5-8%), derive the a'fter-tax rate assuming a tax of28%, then

### su~tract the inflation rate (assume 2%). The result is a range ofreal mortgage rates of 1.60-3.76%. 

### (EXAMPLE: 5% 

## * (100%-28%)

- 2% = 1.6%) Forcash, the minimum is 0%. This applies to purchasers who have no savings, and are making cash purchases. Forthe maximum, we take the opportunity cost represented by the interest that could have been earned in a savings account. The historical nominal maximum savings rate ranged from 4.5-5.5% from 1970 to 1986 (real rates of-8.27 to +3.58%). We selected a real rate of3% as indicative ofthe maximum.- The interest rates for retailer loans and credit cards are assumed to have the same range. The minimum credit card rate is taken as 6% real. Introductory rates on some credit cards today are 5.9% nominal, but after the introductory period (often 6 months), the rate becomes much higher. Maximum rates are over 20% nominal. On the other hand, we do not believe that most retail purchasers

### 'will
. make payments for a clothes washer over the entire lifetime (12-17 years) ofthe appliance. 

### Ifthe purchase is paid for initially by a credit card, but the consumer pays offthe balance in less than the life ofthe washer, then the effective interest rate is lower than the nominal credit card rate. The current

.assumption is a range of6-15% real.

15

### Location: 

### File: LCC WASHER.XLS Sheet: LCC Cell: I 36 

### CurrentAssumption: Figure 10shows the distribution of realdiscount rates, ranging from 0 to 15%; with a mean of 6%.
I 

### ConsumerReal Discount Rate
·2001o 16%

rll 12% 

# - .c Oil 

# ·-**~** 8%**~** 4% 00/o00/o 2% 4% 6% 8% 10% 12% 14% 16% 

### Discount Rate Figure 10 

### Distribution ofConsumer Discount Rates

16