10B-i

APPENDIX 10B. NATIONAL NET PRESENT VALUE OF CONSUMER BENEFITS

USING ALTERNATIVE PRODUCT PRICE FORECASTS

TABLE OF CONTENTS

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 Experience Curve Using PPI from 1991 to 2000 (Low Price Decline Scenario)..10B-2

10B.2.3 Summary of Forecasts............................................................................................10B-5

10B.3 RESIDENTIAL DISHWASHER NPV RESULTS USING ALTERNATIVE 

PRODUCT PRICE FORECASTS.........................................................................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-6
10B-1

APPENDIX 10B. NATIONAL NET PRESENT VALUE OF CONSUMER BENEFITS

USING ALTERNATIVE PRODUCT PRICE FORECASTS

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 appliances as representative of residential dishwashers because 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 dishwashers. 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 PRODUCT PRICE TRENDS FORECASTS

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 2010 (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 uses the exponential fit 

approach with the deflated PPI for miscellaneous household appliances from 1991 to 2010. The 

low price decline scenario uses the experience curve approach with the deflated PPI for 

miscellaneous household appliances from 1991 to 2000. 

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

To forecast the price trend in the high price decline scenario, DOE used an inflationadjusted miscellaneous household appliances PPI from 1991-2010 to fit an exponential model 

with year as the explanatory variable. DOE obtained historical PPI data for miscellaneous 

household appliances spanning the time period 1991-2010 from the Bureau of Labor Statistics

(BLS).a

Y = a × ebX

The PPI data reflect nominal prices, adjusted for product quality changes. An inflationadjusted (deflated) 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 miscellaneous 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 miscelleneous houshold appliances versus year from 1991 to 

2010. See Figure 10-B.2.1.

Figure 10B.2.1 High Price Decline Scenario (1991-2010): Relative Price of 

Miscellaneous Household Appliances versus Year, with Exponential 

Fit

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

Y = 2.864 × 1022 ∙ 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 parameter 

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 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 = 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 2010

Deflated 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

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.

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 1991-2000 from the Bureau of Labor Statistics’ (BLS). An inflationadjusted 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) was 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

1.6

19911992199319941995199619971998199920002001200220032004200520062007200820092010

Defalted 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 shows 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) = 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.

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

1970 1980 1990 2000 2010 2020

Shipments (millions)

Year

Historical Dishwashers Shipment
10B-5

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

The final power law function looks like:

Y = 8.2356 ∙ X−0.403

The regression performed as an power law fit results in an R-square of 0.985, which 

indicates a good fit to the data. The estimated 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 Summary of Forecasts

Table 10-B.3.1 shows the summary 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 the sensitivities.

y = 8.2356x-0.403

R2 = 0.9853

0.500

0.700

0.900

1.100

1.300

1.500

1.700

- 50.000 100.000 150.000 

Price Index (2010=1)

Cumulative Shipments (millions)

Dishwashers Experience 

Curve_1991-2000

Power (Dishwashers 

Experience Curve_1991-

2000)
10B-6

Table 10B.2.1 Price Trend Sensitivities for Residential Dishwashers

Sensitivity Price Trend Average Annual 

Rate of Change %

Medium (Default) Experience curve using data from 1988 to 2010 -1.27

High Price Decline 

Scenario

Exponential fit using data from 1991 to 2010 -2.54

Low Price Decline 

Scenario

Experience curve using data from 1991 to 2000 -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

1.200

2010201320162019202220252028203120342037204020432046

Price Factor Index (2010=1)

Year

Exponential Fit (1991-

2010)_high price 

decline

Experience Curve 

(1988-201)_default

Experience Curve 

(1991-2000)_low price 

decline
10B-7

10B.3 RESIDENTIAL DISHWASHER NPV RESULTS USING ALTERNATIVE 

PRODUCT PRICE FORECASTS

Table 10B.3.1 Residential Dishwashers: 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 Dishwashers: 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.