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 CURVE ESTIMATION – LOW PRICE DECLINE 

SCENARIO FOR PORTABLE DEHUMIDIFIERS.....................................................1

10-C.3 EXPOTENTIAL FIT APPROACH – LOW PRICE DECLINE SCENARIO 

FOR WHOLE-HOME DEHUMIDIFIERS ...................................................................4

10-C.4 ANNUAL ENERGY OUTLOOK 2013 PRICE FORECAST – HIGH PRICE 

DECLINE SCENARIO FOR PORTABLE AND WHOLE-HOME 

DEHUMIDIFIERS ........................................................................................................6

10-C.5 SUMMARY...................................................................................................................6

10-C.6 RESIDENTIAL DEHUMIDIFIERS NPV RESULTS USING 

ALTERNATIVE LEARNING RATES.........................................................................8

LIST OF TABLES

Table 10-C.5-1 Price Trend Scenarios........................................................................................6

Table 10-C.6-1 Residential Dehumidifiers: Net Present Value of Consumer Impacts 

Under Alternative Product Price Forecasts (3 Percent Discount Rate) .............8

Table 10-C.6-2 Residential Dehumidifiers: Net Present Value of Consumer Impacts ...............9

LIST OF FIGURES

Figure 10-C.2-1 Historical Real Price Index for Small Electric Household Appliacnes .............2

Figure 10-C.2-2 Historical and Projected Shipments of Portable Dehumidifiers......................3

Figure 10-C.2-3 Relative Price versus Cumulative Shipments of Portable 

Dehumidifiers, with Power Law Fit...................................................................4

Figure 10-C.3-1 Relative Price of Air-Conditioning, Refrigeration, and Forced Air 

Heating Equipment versus Year, with Exponential Fit .....................................5

Figure 10-C.5-1 Portable Dehumidifier Price Factor Indexes for the Default Case and 

Sensitivity Cases................................................................................................7

Figure 10-C.5-2 Whole-Home Dehumidifier Price Factor Indexes for the Default Case 

and Sensitivity Cases.........................................................................................7

10--C-i
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 are based on future price projection derived

from historical PPI data from the Bureau of Labor Statistics (BLS). DOE collected PPI data of 

“small electric household appliances, except fans” from 1983 to 2012 to project future price for 

portable dehumidifiers and PPI data of “room AC and dehumidifiers” to project future price for 

whole-home dehumidifiers. DOE also investigated the impact of different product price forecasts 

on the consumer net present value (NPV) for the considered TSLs of both types of 

dehumidifiers. For portable dehumidifiers, DOE considered two price sensitivity scenarios: (1) a 

trend based on the experience curve approach, and (2) a trend based on the “furniture and 

appliances” that was forecasted in AEO2013. Similarly, DOE also considered two price 

sensitivity scenarios for whole-home dehumidifiers: (1) a trend based on “air-conditioning, 

refrigeration, and forced air heating equipment” PPI, and (2) a trend based on the “furniture and 

appliances” that was forecasted in AEO2013.

10-C.2 EXPERIENCE CURVE ESTIMATION – LOW PRICE DECLINE 

SCENARIO FOR PORTABLE DEHUMIDIFIERS

For this sensitivity case, DOE is using the experience curve approach to forecast future 

prices of portable dehumidifiers. In the experience curve method, the real cost of production is 

related to the cumulative production, or experience, with a manufactured product. That 

experience usually is measured in terms of cumulative production. 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 rate. DOE was not 

able to apply the same shipment-based learning curve approach to whole-home dehumidifiers 

because the historical shipment data are insufficient. 

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

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.

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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 portable dehumidifiers, DOE 

obtained historical Producer Price Index (PPI) data for small electric household appliances 

spanning the time period 1983-2012 from the Bureau of Labor Statistics’ (BLS). a DOE used PPI 

data for this industry as representative of residential portable dehumidifiers because PPI data 

specific to residential portable dehumidifiers are not available. An inflation-adjusted price index

for small electric household appliances 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-C.2-1) was used in subsequent analysis steps.

Figure 10-C.2-1 Historical Real Price Index for Small Electric 

Household Appliacnes

a

 Series ID PCU33521033521014; http://www.bls.gov/ppi/

10-C-2

 
DOE assembled a time-series of annual shipments from 1972-2010 for portable 

dehumidifiers, which were obtained from the AHAM Fact Book. This annual historical 

shipments data were used to estimate cumulative shipments (production) for portable 

dehumidifiers. Projected shipments after 2010 were obtained from the base case projections 

made for the NIA. Figure 10-C.2-2 shows the shipments time series used in the analysis.

 Figure 10-C.2-2 Historical and Projected Shipments of 

Portable Dehumidifiers

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-C.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.

10-C-3
Figure 10-C.2-3 Relative Price versus Cumulative Shipments of 

Portable Dehumidifiers, with Power Law Fit

The regression performed as power-law fit results in an R-square of 0.986, which 

indicates a great fit to the data. The parameter values obtained are:

Po = 3.301−1.462

+1.613 (95% confidence) for household laundry equipment, and 

b = 0.328±0.015 (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 20.3−0.8

+0.8% (95% confidence). DOE then derived a 

price factor index for this scenario, and 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.

10-C.3 EXPOTENTIAL FIT APPROACH – LOW PRICE DECLINE SCENARIO 

FOR WHOLE-HOME DEHUMIDIFIERS

As mentioned above, the historical shipments for whome-home dehumidifiers are not 

sufficient enough to perform an experence curve estimation. Therefore, for this scenario, DOE 

used an inflation-adjusted air-conditioning, refrigerationm and forced air heating equipment 

Producer Price Index (PPI) from 1978-2012 to fit an exponential model with year as the 

10-C-4
explanatory variable.b DOE chose this PPI series because this is the more aggregated industry 

including whole-home dehumidifiers than the room AC and dehumidifiers industry used in the 

default price scenario. The PPI data reflect nominal prices, adjusted for product quality changes. 

An inflation-adjusted (deflated) price index for air-conditioning, refrigeration and forced air 

heating equipment was calculated by dividing the PPI series by the Gross Domestic Product 

Chained Price Index. The deflated price index is now presented in 2012 dollar values. In this 

case, the exponential function takes the form of:

Y = a ∙ ebX

where Y is the motor price index, X is the time variable, a is the constant and b is the slope 

parameter of the time variable. 

To estimate these exponential parameters, a least-square fit was performed on the 

inflation-adjusted air-conditioning, refrigerationm and forced air heating equipment PPI versus 

year from 1978 to 2012. See Figure 10-C.3-1.

Figure 10-C.3-1 Relative Price of Air-Conditioning, Refrigeration, 

and Forced Air Heating Equipment versus Year, 

with Exponential Fit

The regression performed as an exponential trend line fit results in an R-square of 0.85, 

which indicates a good fit to the data. The final estimated exponential function is:

b

 Series ID PCU333415333415; http://www.bls.gov/ppi/

10-C-5

 
Y = 7.393 × 106 ∙ e(−0.0079)X 

DOE then derived a price factor index for this scenario, with 2012 equal to 1, to project

prices in each future year in the analysis period considered in the NIA since 2012. The index 

value in a given year is a function of the exponential parameter and year.

10-C.4 ANNUAL ENERGY OUTLOOK 2013 PRICE FORECAST – HIGH PRICE 

DECLINE SCENARIO FOR PORTABLE AND WHOLE-HOME 

DEHUMIDIFIERS

DOE also examined a forecast based on the “chained price index—furniture and 

appliances” that was forecasted for AEO2013 out to 2040. This index is the most disaggregated 

category that includes both types of dehumidifiers. To develop an inflation-adjusted index, DOE 

normalized the above index with the “chained price index—gross domestic product” forecasted 

for AEO2013. To extend the price index beyond 2040, DOE used the average annual price 

growth rate in 2031 to 2040. 

10-C.5 SUMMARY

Table 10-C.5-1shows the summary of the average annual rates of changes for the product 

price index in each scenario. Figure 10-C.5-1 and Figure 10-C.5-2shows the resulting price 

trends for portable and whole-home dehumidifiers respectively.

Table 10-C.5-1 Price Trend Scenarios

Product Scenario Price Trend Average Annual 

Rate of Change %

Portable 

Dehumidifier Default

Exponential Fit using Small 

Electric Household Appliances 

PPI (1983 to 2012)

-2.02

High Price 

Decline

AEO2013 “chained price index—

furniture and appliances” -2.41

Low Price 

Decline

Experience Curve Estimation 

using Small Electric Household 

Appliances PPI (1983 to 2012)

-1.08

Whole-Home 

Dehumidifier Default Exponential Fit using Room AC and Dehumidifiers (1990 to 2009) -2.32

High Price 

Decline

AEO2013 “chained price index—

furniture and appliances” -2.41

Low Price 

Decline

Exponential Fit using AirConditioning, Refrigeration, and 

Forced Air Heating Equipment 

PPI (1978 to 2012)

-0.79

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Figure 10-C.5-1 Portable Dehumidifier Price Factor Indexes for the 

Default Case and Sensitivity Cases

Figure 10-C.5-2 Whole-Home Dehumidifier Price Factor Indexes for 

the Default Case and Sensitivity Cases

10-C-7
10-C.6 RESIDENTIAL DEHUMIDIFIERS NPV RESULTS USING 

ALTERNATIVE LEARNING RATES

Table 10-C.6-1 Residential Dehumidifiers: Net Present Value of Consumer Impacts 

Under Alternative Product Price Forecasts (3 Percent Discount Rate) 

Price 

Trend

Product Class 

(pints/day)

Candidate Standard Levels

CSL1 CSL 2 CSL 3 CSL 4

Default

≤20.00 1.423 1.592 1.842 2.205

20.01-30.00 0.039 0.221 0.395 0.978

30.01-35.00 0.041 0.324 0.959 1.285

35.01-44.99 0.004 0.118 0.936 1.274

≥45.00 0.119 0.144 0.144 0.226

≤8ft3 Case Volume (Whole-home) 0.006 0.006 0.006 0.013

>8ft3 Case Volume (Whole-home) 0.012 0.025 0.025 0.032

Low 

Price 

Decline

≤20.00 1.418 1.584 1.828 2.181

20.01-30.00 0.038 0.219 0.390 0.959

30.01-35.00 0.040 0.321 0.943 1.261

35.01-44.99 0.004 0.116 0.922 1.255

≥45.00 0.114 0.137 0.137 1.255

≤8ft3 Case Volume (Whole-home) 0.006 0.006 0.006 0.011

>8ft3 Case Volume (Whole-home) 0.012 0.024 0.024 0.030

High 

Price 

Decline

≤20.00 1.424 1.594 1.846 2.211

20.01-30.00 0.039 0.222 0.397 0.982

30.01-35.00 0.041 0.325 0.963 1.292

35.01-44.99 0.004 0.118 0.939 1.279

≥45.00 0.120 0.146 0.146 0.230

≤8ft3 Case Volume (Whole-home) 0.006 0.006 0.006 0.013

>8ft3 Case Volume (Whole-home) 0.012 0.025 0.025 0.032

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Table 10-C.6-2 Residential Dehumidifiers: Net Present Value of Consumer Impacts

 Under Alternative Product Price Forecasts (7 Percent Discount Rate) 

Price 

Trend

Product Class 

(pints/day)

Candidate Standard Levels

CSL1 CSL 2 CSL 3 CSL 4

Default

≤20.00 0.609 0.679 0.779 0.925

20.01-30.00 0.016 0.095 0.171 0.413

30.01-35.00 0.017 0.144 0.404 0.540

35.01-44.99 0.003 0.051 0.386 0.538

≥45.00 0.046 0.057 0.057 0.0538

≤8ft3 Case Volume (Whole-home) 0.003 0.003 0.003 0.004

>8ft3 Case Volume (Whole-home) 0.004 0.009 0.009 0.010

Low 

Price 

Decline

≤20.00 0.606 0.676 0.773 0.914

20.01-30.00 0.016 0.094 0.169 0.402

30.01-35.00 0.017 0.143 0.395 0.527

35.01-44.99 0.003 0.050 0.379 0.528

≥45.00 0.044 0.053 0.053 0.078

≤8ft3 Case Volume (Whole-home) 0.003 0.003 0.003 0.004

>8ft3 Case Volume (Whole-home) 0.004 0.008 0.008 0.009

High 

Price 

Decline

≤20.00 0.609 0.680 0.781 0.927

20.01-30.00 0.016 0.095 0.171 0.413

30.01-35.00 0.017 0.144 0.404 0.540

35.01-44.99 0.003 0.051 0.386 0.538

≥45.00 0.046 0.057 0.057 0.087

≤8ft3 Case Volume (Whole-home) 0.003 0.003 0.003 0.004

>8ft3 Case Volume (Whole-home) 0.004 0.009 0.009 0.010

10-C-9