•7--· ·-~· 

• 

. QUANTITIES AND CURRENT ASSUMPTIONS 

FOR CALCULATING LlFE CYCLE COSTS OF 

CLOTHES WASHERS 

James E. McMahon, Ph.D. 

Ernest Orlando Lawrence Berkeley Natio.nal Laboratory. 

March 11, 1998 

I 
PURCHASE EXPENSE 

Definition: ConsuJner expense for purchasing ~ appliance 

Approach: 

Consumer. purchase expense includes the retail price of the 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 of baseline purchase expense plus the incremental purchase expense for the . 

· efficiency level. The incremental purchase expense is the product of incremental 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 of LO to 1.35, triangular distribution), retail markup is 1.40, and sales 

tax adds 5.2% of the 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. 

Current Assumptions: 

AHAM data for manufacturing costs. ADL report for markups and sales tax. 

2 
LIFETIME 

Definition: The period oftime the clothes washer will provide service. 

Approach: 

The lifetime is estimated by comparing historical shipments to percent of households currently owning· 

the appliance (MTSC, 1980). 

Location: 

File: LCC WASHER.XLS - Sheet: "Lifetime" 

Current Assumption: 

For clothes washers, lifetimes range from 12 to 17 years, with an average of 14 years. 

3 
CYCLES PER YEAR 

Definition: loads oflaundry washed per household per year 

Approach: 

The DOE test procedure assumes 392 cycles per year. In actuality, the number ofloads oflaundry 

washed per household per year depends upon the number of persons in the household; and probably 

on other factors. A survey of U.S. households indicates a relationship between family size and cycles 

per year. (John T. Erikson, personal communication, 1995) · 

Using the sample of households having both a clothes washer and a.clothes dryer from the Energy 

Information Administration,1993 Residential Energy Consumption Survey, we assigned these cycles 

per year to each household according to the persons per household. The weighted average result is 

379 cycles per year for the U.S. mix of households. This is in good agreement (within 4%) with the 

DOE test procedure: To the extent that the groups of households using different fuels for water 

heater and clothes dryers differ, the cycles per year also differ among those groups. 

Current Assumption: _ 

For simulating a sample of househ.olds, each household is assigned cycles per year based upon the 

following table (scaled so the average agrees with th(! test procedure assumption). Figure 1 shows 

the weighting for the number of washer cycles per year. 

Per$ons per household 

1 

2 

3-4 

5+ 

Cycles per year (RECS) 

200 

310 

454 

624 

Cycles per year (scaled) 

210 

321 

469 

645 

Number of Washer Cycles per Year 

40% 35.1% 36.5% 

30% ~ 

..... 

.c 

Oil 20% ·as 

~ 10% 

0% 

207 321 469 645 

Washer Cycles 

Figure 1 Weighting of the number of washer cycles per year 

4 
ENERGY 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" 

Current Assumptions: 

Each of these components of energy consumed per cycle. is obtained from the data submitted by 

AHAM, for baseline and for each of the efficiency levels. Figure 2 shows the energy use per cycle 

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· of savings; 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 of using 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 of the water heater 

and clothes dryer, persons per household) that affect energy consumption. · 

Current Assumption: All those households from the Energy Information Administration's 1993 

Residential Energy Consumption Survey (RECS) survey which .have both a clothes washer and a 

clothes dryer are being used Energy prices are reported in the survey results for each household 

These households are assigned weights to represent the U.S. Figure 3 shows residential electricity 

prices ranging from 2to17 cents/kWh. 

b) Value of savings 

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 per kilowatt-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 of the quantity of kilowatt-hours used, including seasonal and/or time of day pricing). In 

general, such detailed information is not known. 

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

for electricity (including fixed charges) to kWh consumed; 2) partial adjustment of known . 

6 
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. 

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. 

ADV ANT AGE: Approximately accounts for fixed charges. Edison Electric Institute has 

assembled information on fixed charges for average general service residential rates for a large 

number of utilities that show fixed charges on average represent about 7. 5% of average. rates. 

DISADVANTAGE: By reducing the value of energy 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 of consumer 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. -

Current Assumption (Approach # 2): Subtract a fixed percentage (7. 5% from each household's 

e/ectriciry price) representing the average fixed charge. 

4.0% 

:;- 3.5% 

.~ 3.0% 

-ca 2.5% E 

= 2.0% 

= 

- 1.5% 

-

"' .c 

1:11) 1.0% •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 , 

7 
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 rat~s offered by that utility obtained from surveys, restructuring 

means that households will be able to purchase electricity from a larger set of suppliers. 

A projected trend in national average prices is applied to each household's energy prices, after 

accounting for "value of savings" (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 of those projections. 

Current Assumption: Time trend from AE098 Reference 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 of saving 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 of savings; 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 of using 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 of the water heater and 

clothes dryer, persons per household) that affect ·energy consumption. 

Current Assumption: All those households from the Energy Informdtion Administration's 1993 

Residential Energy Consumption Survey (RECS) survey which have both a clothes washer and a 

clothes dryer are being used. For each household, relevant energy prices are reported. These 

households are assigned weights to represent the U.S. Figure 5 shows residential gas prices ranging 

from 3.8to10.9 $/MMBtu. · 

b) Value of savings 

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 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 as a function of the quantity of energy used, including 

seasonal pricing). In general, such detailed information is not known. 

Three approaches are considered: 1) average rates, calculated as the ratio of household expenditures 

for gas (including fixed charges) to gas consumed; 2) partial adjustment of known inaccuracies by 

subtracting the average fraction corresponding to fixed. charges from average rates; and 3) estimating 

the actual consumer marginal energy rate. 

1) Average rates. 

ADV ANT AGE: Simple. Available in published historical data and in forecasts. 

9 
DISADVANTAGE: May over- or.under-estimate the actual consumer marginal energy rate. 

2) Subtract average fixed charge everywhere. 

ADV ANT AGE: 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% of average rates .. 

DISADVANTAGE: By reducing the value of e!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 of consumer marginal energy rates. 

ADV ANT AGE: 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. ; 

Month by 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. 

Current Assumption (Approach # 2): Subtract a fixed percentage ( 12% from each household's gas 

price) representing the average.fixed charge. 

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/MM Btu 

--with Fbed 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 

13 
I 

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 of suppliers. . 

A projected trend in national average prices is applied to each household's energy prices, after 

accounting.for "value of savings" (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, Low Economic Growth · 

5) Gas Rese!lrch Institute 1998 Baseline Projection · 

Figure 6 shows the projections. 

Current Assumption: Time trend from AEO 1998 Reference.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 of distillate 

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. · 

Current Assumptions: . 

Variability in price from 1993 RECS sample of households owning washers and dryers. 

Time trend from AEO 1998 Reference Case. 

9.0 

8.5 

Oil Price 

8.0 ------------·-

.a 7.5 .~.,..... -·~ .. . ,.,. ······•···· --. --. - . .. ...•. ____ e 

~ 7.0 

~ 

··.--,··· \ . 

• 

- -- 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 

12 
WATER PER CYCLE 

Definition: Water consumed by clothes washer in on~ cycle 

Approach: Data as submitted by AHAM. · 

Location:. 

File: LCC WASHER.XLS - Sheet: Engineering 

Current Assumption: . 

Use numerical values for baseline and each efficiency level, as provided _by AHAM. Figure 8 shows 

the water use per 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 

. 13 
WATER RATE· 

Definition: Residential customer rate for water and waste water (sewage)($/ thousand gallons), 

·excluding fixed charges 

Approach: . 

An existing survey of water and sewage rates represents the population-weighted distribution of U.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 of future change 

in those rates. 

Figure 9 shows the distribution of the sum of water and sewage rates. 

Current Assumption: 

1994 diStribution of U.S. values for water and sewage rates. Future annual percent change in rea{ 

rates is assumed to 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 

Net Water& SewerperCCF 

Figure 9 Distribution of Net Water and Sewer Charges 

14 
-i 

·-

" 

DISCOUNT RA TE 

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 of discount rates will be used to 

calculate a distribution of life cycle costs for clothes washers. 

FINANCING METHODS 

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% of retail purchases are paid in cash, 35% use credit cards, and 25% use retailer loans. The 

same coinment indicates 25% of appliance 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 of interest rates that may reasonably be expected to apply in the future"_ These 

are estimates, based upon historical data and judgment about how the future inay differ from· the 

historical period: 

For new 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 of real mortgage rates of 

1.60-3.76%. (EXAMPLE: 5% * (100%-28%) - 2% = 1.6%) 

For cash, the minimum is 0%. This applies to purchasers who have no savings, and are making cash 

purchases. For the 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 of 3% as indicative of the 

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) of the appliance. If the 

purchase is paid for initially by a credit card, but the consumer pays off the balance in less than the life 

of the washer, then the effective interest rate is lower than the nominal credit card rate. The current 

. assumption is a range of 6-15% real. 

15 
Location: 

File: LCC WASHER.XLS 

Sheet: LCC 

Cell: I 36 

Current Assumption: Figure 10 shows the distribution of real discount rates, ranging from 0 to 15%; 

with a mean of 6%. 

I 

Consumer Real Discount Rate 

·2001o 

16% 

rll 

- 12% .c 

Oil 

·-~ 

~ 8% 

4% 

00/o 

00/o 2% 4% 6% 8% 10% 12% 14% 16% 

Discount Rate 

Figure 10 Distribution of Consumer Discount Rates 

16