10B

- i APPENDIX 10B. NATIONAL NET PRESENT VALUE OF CONSUMER BENEFITS

USING ALTERNATIVE PRODUCT PRICE FORECASTS

TABLE OF CO NTENTS

10B.1 INTRODUCTION

................................ ................................ ................................ . 10B

- 1

10B.2 PRODUCT PRICE TRENDS FORECASTS

................................ ........................ 10B

- 1

10B.2.1 Exponential Fit Using PPI from 1991 to 2010 (High Price Decline Scenario)

..... 10B

- 1

10B.2.2 E xperience Curve Using PPI from 1991 to 2000 (Low Price Decline Scenario)

.. 10B

- 2

10B.2.3 Summary of Forecasts

................................ ................................ ............................ 10B

- 5

10B.3 RESIDENTIAL DISHWASH ER NPV RESULTS USING ALTERNATIVE

PRODUCT PRICE FORECA STS

................................ ................................ ......... 10B

- 7

LIST OF TABLES

Table 10B.2.1 Price Trend Sensitivities for Residential Dishwashers

............................. 10B

- 6

Table 10B.3.1 Residential Dishwashers: Present Value of Consumer Impacts Under Alternative Product Price Forecasts (3 Percent Discount Rate)

................ 10B

- 7

Table 10B.3.2 Residential Dishwashers: Present Value of Consumer Impacts Under Alternative Product Price Forecasts (7 Percent Discount Rate)

................ 10B

- 7

LIST OF FIGURES

Figure 10B.2.1 High Price Decline Scenario (1991

- 2010): Relative Price of Miscellaneous Household Appliances versus Year, with Exponential

Fit

................................ ................................ ................................ ............... 10B

- 2 Figure 10B.2.2 Historical Real Price Index for Miscellaneous Household Appliances

..... 10B

- 3 Figure 10B.2.3 Historical Total Shipments of Dishwashers

................................ ............... 10B

- 4 Figure 10B.2.4 Low Price Decline Scenario (1991

- 2000): Relative Price of Miscellaneous Household Appliances versus Cumulative Shipments of Dishwashers, with Power Law Fit

................................ ............................. 10B

- 5 Figure 10B.2.5 Miscellaneous Household Appliances Price Factor Indexes for the Default Case and Sensitivity Cases

................................ ............................ 10B

- 610B

- 1 APPENDIX 10B. NATIONAL NET PRESENT VALUE OF CONSUMER BENEFITS

USING ALTERNATIVE PRODUCT PRICE FORECA STS

10B.1 INTRODUCTION

The NPV results presented in chapter 10 reflect a price trend based on an experience rate

estimated for miscellaneous household appliances for 1988

- 2010

. DOE used PPI data for

miscellaneous household appli ances a s representative of residential dishwashers b ecause PPI data specific to residential dishwashers are not available. DOE also investigated the impact of

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

TSLs for residential dish washers

. DOE considered two alternative price trends for a sensitivity analysis. This appendix describes the alternative price trends and compares NPV results for these

scenarios with the default forecast.

10B.2 PRO DUCT PRICE TRENDS FORECAS T S

DOE considered two alternative price trends for a sensitivity analysis. Based on different analytical approaches with different periods of data for miscellaneous household appliances

, DOE developed one forecast in which prices decline faster than the default case after 201 0 (high price decline scenario), and the one in which prices decline slower than the default case after 2010 (low price decline scenario)

. The high price decline scenario us es the exponential fit approach with the deflated PPI for miscellaneous household appliances from 1991 to 2010. The low price decline scenario us es the experience curve approach with the deflated PPI for miscellaneous household appliances from 1991 to 2000.

10B.2.1 Exponential Fit Using PPI from 199 1 to 2010 (High Price Decline Scenario)

To forecast the price trend in the high price decline scenario, DOE used an inflation

adjusted miscellaneous household appliances PPI from 19 91

- 2010 to fit an exponential model

with year as the explanatory variable. DOE obtained historical PPI data for miscellaneous household appliances spanning the time period 19 91

- 2010 from the Bureau of Labor Statistics (BLS). a

Y = a × e bX The PPI data reflect nominal prices, adjusted for product quality changes. An inflation

adjusted (deflat ed) price index for miscellaneous household appliances was calculated by dividing the PPI series by the Gross Domestic Product Chained Price Index. In this case, the exponential function takes the form of:

where Y is the price index for misc ellaneous houshold appliances

, X is the time variable, a is the

constant and b is the slope parameter of the time variable.

a Series ID PCU3352283352285 ; http://www.bls.gov/ppi/10B

- 2 To estimate these exponential parameters, a least

- square fit was performed on the

inflation

- adjusted price index for miscelleneou s houshold appliances versus year from 19 91 to

2010. See Figure 10

- B.2

. 1

.

Figure 10B.2

. 1 High Price Decline Scenario (19 91

- 2010): Relative Price of Miscellaneous Household Appliances versus Year, with Exponenti al

Fit

The final estimated exponential function for the low price scenario is:

Y = 2

. 864 × 10 22

∙ e (

− 0

. 026 ) X

The regression performed as an exponential fit results in an R

- square of 0.98, which indicates a good fit to the data. DOE then derived a price factor index for this high price decline scenario, with 2010 equal to 1, to forecast prices in each future year in the analysis period

considered in the NIA. The index value in a given year is a function of the exponential paramete r and year

.

10B.2.2 Experience Curve Using PPI from 1991 to 2000 (Low Price Decline

Scenario)

In the low price decline scenario, DOE using the experience curve method to forecast future prices of residential dishwashers . In the experience curve method, the real pr oduct 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 = 3E+22e

- 0.026x

R2 = 0.9809

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

1990 1995 2000 2005 2010Deflated Misc. Household Appliaces PPI (2010=1)

Year

Exponential Fit on Deflated PPI from 1991 to 2010

Expon. (Exponential Fit on Deflated PPI from 1991 to 2010)10B

- 3 Y = aX - b

W here :

a = an initial price (or cost),

b = a posit ive 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 reduct ion 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.

To derive an experience rate parameter for residential dishwashers , DOE obtained

historical Producer Price Index (PPI) data for miscellaneous household appliances equipment spanning the time period 19 91

- 20 00 from the Bureau of Labor Statistics’ (BLS). An inflation

adjusted price index for household laundry equipment was calculated by dividing the PPI series by the Gross Domestic Product Chained Price Index for the same years . This inflation

- adjusted price index (shown in Figure 10

- B.2

. 2 ) w as used in subsequent analysis steps.

Figure 10B.2

. 2 Historical Real Price Index for Miscellaneous Household Appliances 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.619911992199319941995199619971998199920002001200220032004200520062007200820092010Defalted Misc. Household Appliances PPI(2010=1)

Year Defalted Other Misc. Household Appliance PPI (2010

-

...10B

- 4 DOE assembled a time

- series of historical annual shipments for 1972

- 2010 for

dishwashers from the 2005 AHAM Fact Book. The historical annual shipments data were used to estimate cumulative shipments (production). Figure 10

- B.2

. 3 show s the shipments time series used in the analysis.

Figure 10B.2

. 3 Historical Total Shipments of Dishwashers

To estimate an experience rate parameter, a least

- squares power

- law fit was performed on

the unified price index for 1991

- 2000 versus cumulative shipments 1991

- 2000

. See Figure 10

- B.2

. 4

. 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 assumption of no significant f irst price elasticity effects in the cumulative shipments variable. 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00

1970 1980 1990 2000 2010 2020Shipments (millions)

Year

Historical Dishwashers Shipment10B

- 5 Figure 10B.2

. 4 Low Price Decline Scenario (19 91

- 2000): Relative Price of Miscellaneous Household Appliances versus Cumulative Shipments of

Dishwashers , with Power Law Fit

The final power law function looks like :

Y = 8

. 2356

∙ X − 0

. 403

The r egression performed as an power law fit results in an R

- square of 0.985, which indicates a good fit to the data. T he est imated experience rate (defined as the fractional reduction in price expected from each doubling of cumulative production) is 24.4%

. DOE then derived a price factor index for this low price decline scenario, with 2010 equal to 1, to forecast prices in each future year in the analysis period considered in the NIA.

10B.2.3 S ummary of Forecasts

Table 10

- B.3

. 1 shows the s ummary of the average annual rates of changes for the product price index in each scenario. Figure 10

- B.3

. 1 shows the resulting price trends corresponding to

each of t he sensitivities

. y = 8.2356x

- 0.403

R2 = 0.9853

0.500 0.700 0.900 1.100 1.300 1.500 1.700

- 50.000 100.000 150.000Price Index (2010=1)

Cumulative Shipments (millions) Dishwashers Experience

Curve_1991

- 2000

Power (Dishwashers

Experience Curve_1991

- 2000)1 0B

- 6 Table 10B.2

. 1 Price Trend Sensitivities for Residential Dishwashers

Sensitivity Price Trend Average Annual Rate of Change % Medium (Default) Experience c urve using data from 1988 to 2010

- 1.27 High Price Decline

Scenario Exponential f it using data from 19 91 to 2010

- 2.54

Low Price Decline

Scenario Experience c urve using data from 1991 to 200 0

- 1.18

Figure 10B.2

. 5 Miscellaneous Household Appliances Price Factor Indexes for the Default Case and Sensitivity Cases 0.000 0.200 0.400 0.600 0.800 1.000 1.2002010201320162019202220252028203120342037204020432046Price Factor Index (2010=1)

Year Exponential Fit (1991

- 2010)_high price

decline

Experience Curve
(1988

- 201)_default

Experience Curve
(1991

- 2000)_low price

decline10B

- 7 10B.3 R ESIDENTIAL DISH WASHER NPV RESULTS USING ALTERNATIVE

PRODUCT PRICE FORECA STS

Table 10B.3

. 1 Residential Dishw ashers : Present Value of Consumer Impacts Under

Alternative Product Price Forecasts (3 Percent Discount Rate)

Trial

Standard

Level Medium (Default) Low

Price Decline High Price

Decline

Billion 2010$

1 Incr. Installed Cost 0.11 0.12 0.09 Operating Cost Savings 0.23 0.23 0.24

Net Present Value 0.12 0.12 0.15

2 Incr. Installed Cost 0.88 0.90 0.75 Operating Cost Savings 1.34 1.34 1.37

Net Present Value 0.46 0.44 0.62

3 Incr. Installed Cost 5.37 5.49 4.36 Operating Cost Savings 11.88 11.86 12.13

Net Present Value 6.51 6.37 7.77

4 Incr. Installed Cost 6.82 6.96 5.58 Operating Cost Savings 24.28 24.24 24.67

Net Present Value 17.45 17.28 19.09
Parentheses indicate negative (

- ) values.

Table 10B.3

. 2 Residential Dishw ashers : Present Value of Consumer Impacts Under

Alternative Product Price Forecasts (7 Percent Discount Rate)

Trial

Standard

Level Medium (Default) Low

Price Decline High Price

Decline

Billion 2010$

1 Incr. Installed Cost 0.06 0.06 0.05 Operating Cost Savings 0.09 0.09 0.09

Net Present Value 0.03 0.03 0.04

2 Incr. Installed Cost 0.52 0.53 0.46 Operating Cost Savings 0.60 0.60 0.61

Net Present Value 0.08 0.07 0.15

3 Incr. Installed Cost 2.69 2.74 2.25 Operating Cost Savings 4.65 4.64 4.71

Net Present Value 1.96 1.90 2.45

4 Incr. Installed Cost 3.42 3.48 2.88 Operating Cost Savings 9.29 9.29 9.39

Net Present Value 5.88 5.81 6.51
Parentheses indicate negative (

- ) values.