10-C-i

APPENDIX 10-C. NATIONAL NET PRESENT VALUE OF CONSUMER BENEFITS USING 

ALTERNATIVE PRODUCT PRICE FORECASTS

TABLE OF CONTENTS

10-C.1 INTRODUCTION .........................................................................................................1

10-C.2 EXPERIENCE RATE ESTIMATION ..........................................................................1

10-C.3 PRODUCT PRICE TRENDS FORECASTS ................................................................4

10-C.4 RESIDENTIAL CLOTHES WASHER NPV RESULTS USING 

ALTERNATIVE LEARNING RATES.........................................................................6

LIST OF TABLES

Table 10-C.4.1 Residential Clothes Washers: Net Present Value of Consumer Impacts 

Under Alternative Product Price Forecasts (3 Percent Discount Rate) .............6

Table 10-C.4.2 Residential Clothes Washers: Net Present Value of Consumer Impacts 

Under Alternative Product Price Forecasts (7 Percent Discount Rate) .............7
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APPENDIX 10-C. NATIONAL NET PRESENT VALUE OF CONSUMER BENEFITS USING 

ALTERNATIVE PRODUCT PRICE FORECASTS

10-C.1 INTRODUCTION

The NPV results presented in chapter 10 reflect a price trend based on historical PPI data 

(1991-2010) for household laundry equipment. DOE also investigated the impact of different 

product price forecasts on the consumer net present value (NPV) for the considered TSLs for 

residential clothes washers. DOE considered three product price forecast sensitivity cases: (1) a 

trend based on the experience curve approach; (2) a trend based on the “chained price index--

other consumer durable goods except ophthalmic” that was forecasted for AEO2010; (3) constant 

prices at 2010 levels. 

10-C.2 EXPERIENCE RATE ESTIMATION

For one sensitivity case, DOE using the experience curve method to forecast future prices 

of clothes washers.aIn the experience curve method, the real product price (or proxy thereof) is 

related to the cumulative production or “experience” with a product. A common functional 

relationship used to model the evolution of production costs is:

Y = aX-b

Where:

a = an initial price (or cost), 

b = a positive constant known as the learning rate parameter, 

X = cumulative production, and 

Y = the price as a function of cumulative production.

Thus, as experience (production) accumulates, the cost of producing the next unit 

decreases. The percentage reduction in cost that occurs with each doubling of cumulative 

production is known as the learning or experience rate (ER), and is given by:

ER = 1 – 2

-b

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

two historical data series: price (or cost) and cumulative production, which is a function of 

shipments during a long time span.

 

a A draft paper, “Using the Experience Curve Approach for Appliance Price Forecasting,” posted on the DOE web 

site at http://www.eere.energy.gov/buildings/appliance_standards, summarizes the data and literature currently 

available to DOE that is relevant to price forecasts for selected appliances and equipment.
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To derive an experience rate parameter for residential clothes washers, DOE obtained 

historical Producer Price Index (PPI) data for household laundry equipment spanning the time 

period 1980-2010 from the Bureau of Labor Statistics’ (BLS). DOE used PPI data for household 

laundry equipment as representative of residential clothes washers because PPI data specific to 

residential clothes washers are not available. An inflation-adjusted price index for household 

laundry equipment was calculated by dividing the PPI series by the Consumer Price Index (CPI)

“all items” index for the same years. This inflation-adjusted price index (shown in Figure 10-

D.2.1) was used in subsequent analysis steps.

Figure 10-C.2.1 Historical Real Price Index for Household Laundry 

Equipment

DOE assembled a time-series of annual shipments for 1972-2008 for clothes washers and 

for 1946-2008 for clothes dryers. Decadal shipments for the 1940s, 1950s, 1960s and 1970s for 

clothes washers were obtained from the 2005 AHAM Fact Book. The annual and decadal 

shipments data were used to estimate cumulative shipments (production). Projected shipments 

after 2008 were obtained from the base case projections made for the NIA (see chapter 9 of this 

TSD). Figure 10-D.2.2 shows the shipments time series used in the analysis.
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Figure 10-C.2.2 Historical Total Shipments of Household Laundry 

Equipment

To estimate an experience rate parameter, a least-squares power-law fit was performed on 

the unified price index versus cumulative shipments. See Figure 10-D.2.3. The form of the fitting 

equation is:

P(X) = PoX

-b

,

where the two parameters, b (the learning rate parameter) and Po (the price or cost of the first 

unit of production), are obtained by fitting the model to the data. DOE notes that the cumulative 

shipments on the right hand side of the equation can have a dependence on price, so there is an 

issue with simultaneity where the independent variable is not truly independent. DOE’s use of a 

simple least squares fit is equivalent to an assumption of no significant first price elasticity 

effects in the cumulative shipments variable.

0

1

2

3

4

5

6

7

8

9

10

1940 1950 1960 1970 1980 1990 2000 2010 2020

Annual Total Shipments (millions)

Year

Clothes Dryers (Historical) Clothes Washers (Historical)
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Figure 10-C.2.3 Relative Price versus Cumulative Shipments of 

Household Laundry Equipment, with Power Law 

Fit

The parameter values obtained are:

Po = 

 

(95% confidence) for household laundry equipment, and 

b = 0.775±0.034 (95% confidence) for household laundry equipment.

The estimated experience rate (defined as the fractional reduction in price expected from 

each doubling of cumulative production) is 

 % (95% confidence). 

10-C.3 PRODUCT PRICE TRENDS FORECASTS

DOE derived a price factor index, with 2010 equal to 1, to forecast prices in each future 

year in the analysis period. DOE applied the same value to forecast prices for each residential 

clothes washer product class at each considered efficiency level.

For the experience rate sensitivity case, the index value in a given year is a function of 

the experience rate and the cumulative production forecast through that year, which is based on 

the shipments forecast described in chapter 9.

In addition to using the above case, DOE examined a constant real price sensitivity case. 

DOE also used a forecast based on the “chained price index--other consumer durable goods 

except ophthalmic” that was forecasted for AEO2010. This index is the most disaggregated 
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category that includes appliances. To develop an inflation-adjusted index, DOE normalized the 

above index with the chained price index--gross domestic product forecasted for AEO2010.b

Figure 10-D.3.1 shows the default price factor index and the indexes corresponding to 

each of the sensitivities. All indexes are adjusted for inflation. 

Figure 10-C.3.1 Household Laundry Equipment Price Factor 

Indexes for the Default Case and Sensitivity Cases

 

b To extend the adjusted index past 2035, DOE used the average annual growth rate in 2026-2035.

0.000

0.200

0.400

0.600

0.800

1.000

1.200

201020122014201620182020202220242026202820302032203420362038204020422044

Price Factor Index (2010=1)

Year

Price Factor Indexes

Experience Rate

Constant Price Index

PPI Exponential Fit

(Default)

AEO Price Index
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10-C.4 RESIDENTIAL CLOTHES WASHER NPV RESULTS USING 

ALTERNATIVE LEARNING RATES

Table 10-C.4.1 Residential Clothes Washers: Net Present Value of Consumer Impacts

Under Alternative Product Price Forecasts (3 Percent Discount Rate) 

Product Price Trend Case

Trial 

Standard 

Level

Default

Experience 

Rate

Experience 

rate

AEO Price 

Index

Constant 

real prices

Billion 2010$

1

Incr. Installed 

Cost 1.179 1.273 1.290 1.809

Operating 

Cost Savings 21.361 21.361 21.361 21.360

Net Present 

Value 20.182 20.088 20.071 19.552

2

Incr. Installed 

Cost 2.214 2.392 2.422 3.401

Operating 

Cost Savings 20.686 20.686 20.686 20.685

Net Present 

Value 18.472 18.294 18.263 17.284

3

Incr. Installed 

Cost 4.153 4.524 4.561 6.598

Operating 

Cost Savings 35.444 35.443 35.443 35.442

Net Present 

Value 31.291 30.920 30.883 28.843

4

Incr. Installed 

Cost 12.959 14.003 14.181 19.930

Operating 

Cost Savings 54.561 54.559 54.559 54.554

Net Present 

Value 41.602 40.556 40.378 34.624

5

Incr. Installed 

Cost 15.963 17.249 17.468 24.545

Operating 

Cost Savings 66.438 66.436 66.435 66.428

Net Present 

Value 50.475 49.187 48.968 41.883

Parentheses indicate negative (-) values.
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Table 10-C.4.2 Residential Clothes Washers: Net Present Value of Consumer Impacts

Under Alternative Product Price Forecasts (7 Percent Discount Rate) 

Product Price Trend Case

Trial 

Standard 

Level

Default

Experience 

Rate

Experience 

rate

AEO Price 

Index

Constant 

real prices

Billion 2010$

1

Incr. Installed 

Cost 0.695 0.738 0.757 1.000

Operating 

Cost Savings 9.424 9.424 9.424 9.424

Net Present 

Value 8.729 8.686 8.667 8.423

2

Incr. Installed 

Cost 1.301 1.383 1.419 1.877

Operating 

Cost Savings 9.072 9.072 9.072 9.072

Net Present 

Value 7.771 7.689 7.653 7.194

3

Incr. Installed 

Cost 2.302 2.469 2.521 3.455

Operating

Cost Savings 15.313 15.313 15.313 15.312

Net Present 

Value 13.012 12.844 12.792 11.858

4

Incr. Installed 

Cost 7.605 8.085 8.291 10.981

Operating 

Cost Savings 24.024 24.024 24.024 24.022

Net Present 

Value 16.420 15.939 15.733 13.041

5

Incr. Installed 

Cost 9.370 9.961 10.215 13.528

Operating 

Cost Savings 29.288 29.288 29.287 29.285

Net Present 

Value 19.918 19.326 19.072 15.757

Parentheses indicate negative (-) values.