10

- C

- i APPENDIX 10

- C. NATIONAL NET PRESENT VALUE OF CONSUMER BENEFITS USING

ALTERNATIVE PRODUCT PRICE FORECASTS

TABLE OF CO NTENTS

10

- C.1 INTRODUCTION

................................ ................................ ................................ ......... 1
10

- C.2 EXPERIENCE RATE ESTI MATION

................................ ................................ .......... 1
10

- C.3 PRODUCT PRICE TRENDS FORECASTS

................................ ................................ 4
10

- C.4 RESIDENTIAL CLOTHES WASHER NPV RESULTS U SING

ALTER NATIVE LEARNING RATE S

................................ ................................ ......... 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)

............. 710

- C

- 1 APPENDIX 10

- C. NATIONAL NET PRESENT VALUE OF CONSUMER BENEFITS USING

ALTERNATIVE PRODUCT PRICE FORECA STS

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 “c hained price index

-- other consumer durable goods except ophthalmic ” that was forecasted for AEO2010 ; (3) constant prices at 2010 levels

.

10

- C.2 EXPERIENCE RATE ESTI MATION

For one sensitivity case, DOE using the experience curve method to forecast future prices
of clothes washers. a In 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

W here :

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 ( E R ), and is given by:

E R = 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.10

- C

- 2

To derive an experience r ate parameter for residential clothes washers, DOE obtained
historical Producer Price Index (PPI) data for household laundry equipment spanning the time period 19 80

- 2010 from the Bureau of Labor Statistics’ (BLS). DOE used PPI data for household laundry eq uipment a s representative of residential clothes washers b ecause 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) w as used in subsequent analysis steps.

Figure 10

- C.2.1 H istorical 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 d ecadal shipments data were used to estimate cumulative shipments (production). Projected shipments
after 2008 w ere obtained from the base case projections made for the NIA (see chapter 9 of this TSD)

. Figure 10

- D .2.2 show s the shipments time series used in the analysis.10

- C

- 3 Figure 10

- C.2.2 H istorical Total Shipments of Household Laundry

Equipment

To estimate a n 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) = P
o X - b

,

where the two parameters, b (the learning rate parameter) and P
o (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 ass umption 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)10

- C

- 4 Figure 10

- C.2.3 R elative Price versus Cumulative Shipments of

Household Laundry Equipment , with Power Law
Fit

The parameter values obtained are:

P
o = (95% confidence) for household laundry equipment , and
b = 0.775±0.034 (95% confidence) for household laundry equipment

.

T he 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 FORECAS T S

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
cloth es 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 sh ipments 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 “c hained price index

-- other consumer durable goods except ophthalmic ” that was foreca sted for AEO2010. This index is the most disaggregated10

- C

- 5

category that includes appliances. To develop an inflation

- adjusted index, DOE normalized the
above index with the c hained 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

2010 2012 2014 2016 2018 2020 2022 2024 2026 2028 2030 2032 2034 2036 2038 2040 2042 2044 Price Factor Index (2010=1)

Year 

## Price Factor Indexes

Experience Rate

Constant Price Index

PPI Exponential Fit (Default)
AEO Price Index10

- C

- 6

10

- C.4 R ESIDENTIAL CLOTHE S WASHER NPV RESULTS USING

ALTERNATIVE LEARNI N G 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.10

- C

- 7

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.