APPENDIX 10B. NATIONAL NET PRESENT VALUE OF CONSUMER BENEFITS

USING ALTERNATIVE PRODUCT PRICE FORECASTS

TABLE OF CONTENTS

10B.1 INTRODUCTION .................................................................................................10B-1

10B.2 ALTERNATIVE MISCELLANEOUS REFRIGERATION PRODUCT 

PRICE TREND SCENARIOS...............................................................................10B-1

10B.2.1 Low Price Decline Scenario...................................................................................10B-1

10B.2.2 High Price Decline Scenario..................................................................................10B-3

10B.2.3 Summary................................................................................................................10B-4

10B.3 NET PRESENT VALUE RESULTS USING ALTERNATIVE PRODUCT 

PRICE TRENDS....................................................................................................10B-5

LIST OF TABLES

Table 10B.2.1 Price Trend Sensitivities............................................................................10B-4

Table 10B.3.1 NPV Using Alternative Product Price Trend (Low Price Decline), 

Discounted at 3 Percent, for Cooled Cabinets (billion 2013$)..................10B-5

Table 10B.3.2 NPV Using Alternative Product Price Trend (Low Price Decline), 

Discounted at 7 Percent, for Cooled Cabinets (billion 2013$)..................10B-6

Table 10B.3.3 NPV Using Alternative Product Price Trend (Low Price Decline), 

Discounted at 3 Percent, for Non-Compressor Thermoelectric 

Refrigerators (billion 2013$) .....................................................................10B-6

Table 10B.3.4 NPV Using Alternative Product Price Trend (Low Price Decline), 

Discounted at 7 Percent, for Non-Compressor Thermoelectric 

Refrigerators (billion 2013$) .....................................................................10B-7

Table 10B.3.5 NPV Using Alternative Product Price Trend (Low Price Decline), 

Discounted at 3 Percent, for Ice Makers (billion 2013$)...........................10B-7

Table 10B.3.6 NPV Using Alternative Product Price Trend (Low Price Decline), 

Discounted at 7 Percent, for Ice Makers (billion 2013$)...........................10B-8

Table 10B.3.7 NPV Using Alternative Product Price Trend (High Price Decline), 

Discounted at 3 Percent, for Cooled Cabinets (billion 2013$)..................10B-8

Table 10B.3.8 NPV Using Alternative Product Price Trend (High Price Decline), 

Discounted at 7 Percent, for Cooled Cabinets (billion 2013$)..................10B-9

Table 10B.3.9 NPV Using Alternative Product Price Trend (High Price Decline), 

Discounted at 3 Percent, for Non-Compressor Thermoelectric 

Refrigerators (billion 2013$) .....................................................................10B-9

Table 10B.3.10 NPV Using Alternative Product Price Trend (High Price Decline), 

Discounted at 7 Percent, for Non-Compressor Thermoelectric 

Refrigerators (billion 2013$) ...................................................................10B-10

Table 10B.3.11 NPV Using Alternative Product Price Trend (High Price Decline), 

Discounted at 3 Percent, for Ice Makers (billion 2013$).........................10B-10

10B-i
Table 10B.3.12 NPV Using Alternative Product Price Trend (High Price Decline), 

Discounted at 7 Percent, for Ice Makers (billion 2013$).........................10B-11

Table 10B.3.13 Comparison of Total NPV of Cooled Cabinets for Alternative Product 

Price Forecast...........................................................................................10B-11

Table 10B.3.14 Comparison of Total NPV of Non-Compressor Refrigerators for 

Alternative Product Price Forecast ..........................................................10B-12

Table 10B.3.15 Comparison of Total NPV of Portable Ice Makers for Alternative 

Product Price Forecast .............................................................................10B-12

Table 10B.3.16 Comparison of Total NPV of Non-Portable Ice Maker, Cooled Storage 

for Alternative Product Price Forecast.....................................................10B-12

Table 10B.3.17 Comparison of Total NPV of Non-Portable Ice Maker, Uncooled 

Storage for Alternative Product Price Forecast .......................................10B-13

LIST OF FIGURES

Figure 10B.2.1 Deflated Household Refrigerator and Home Freezer Manufacturing 

PPI versus Year, with Exponential Fit from 1976 to 1990........................10B-2

Figure 10B.2.2 Deflated Household Refrigerator and Home Freezer Manufacturing 

PPI versus Year, with Exponential Fit from 1991 to 2013........................10B-3

Figure 10B.2.3 Miscellaneous Refrigeration Product Price Forecast Indexes ...................10B-4

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

USING ALTERNATIVE PRODUCT PRICE FORECASTS

10B.1 INTRODUCTION

DOE applied constant price assumption as the default product price trend to project the 

prices of miscellaneous refrigeration products sold in each year in the forecast period (2021-

2050), and the NIA analysis described in chapter 10 used this default price trend to estimate the 

net present value (NPV) results. In order to investigate the impact of different product price 

forecasts on the consumer NPV for the considered ELs for miscellaneous refrigeration products, 

DOE also considered two alternative price trends for the sensitivity analysis: (1) low price 

decline scenario, and (2) high price decline scenario. The following sections describe the 

methodology used to derive these two alternative price trends and compares NPV results for all 

two scenarios with the default price trend. 

10B.2 ALTERNATIVE MISCELLANEOUS REFRIGERATION 

PRODUCT PRICE TREND SCENARIOS

DOE obtained historical PPI data for “household refrigerator and home freezer 

manufacturing” during the time period of 1976 to 2013 from the Bureau of Labor Statistics as a 

proxy to miscellaneous refrigeration products.a DOE understands that this PPI series 

encompasses products not specific to these miscellaneous refrigeration products, but given the 

similar functionality of these products, DOE assumed the price trend observed in PPI data for 

“household refrigerator and home freezer manufacturing” to be the most representative of 

miscellaneous refrigeration products among all price indexes. In addition, DOE assumed that 

each product class is experiencing a similar price trend and will continue with the same trend in 

the future. DOE developed the low and high price decline scenario for the sensitivity analysis by 

dividing the household refrigerator and home freezer manufacturing PPI series into two time 

segments where one has shallower price decline and the other has steeper price decline. The low

price decline scenario is based on an exponential fit to the PPI data for household refrigerator 

and home freezer manufacturing from 1976 to 1990. The high price decline scenario is based on 

an exponential fit to the same PPI data from 1991 to 2013. 

10B.2.1 Low Price Decline Scenario 

For the low price decline scenario, DOE used an inflation-adjusted household refrigerator 

and home freezer manufacturing Producer Price Index (PPI) spanning the time period of 1976-

1990 from the Bureau of Labor Statistics’ (BLS) to fit an exponential model with year as the 

explanatory variable.b The PPI during this period of time showed a shallower downward trend, 

b Series ID PCU 335222335222; http://www.bls.gov/ppi/

10B-1

 
so the exponential fit based on this part of the historical PPI represents the low price decline

scenario of future price projection. 

The PPI data reflect nominal prices, adjusted for product quality changes. An inflationadjusted (deflated) price index for household refrigerator and home freezer manufacturing was 

calculated by dividing the PPI series by the Gross Domestic Product Chained Price Index. The 

deflated price index is presented in 2013 dollar values. In this case, the exponential function 

takes the form of:

Y = a ∙ ebX

where Y is the “household refrigerator and home freezer” PPI, 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 price index versus year from 1976 to 1990. See Figure 10-B.2.1.

Figure 10B.2.1 Deflated Household Refrigerator and Home Freezer 

Manufacturing PPI versus Year, with Exponential 

Fit from 1976 to 1990

The regression performed as an exponential trend line fit results in an R-square of 0.94, 

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

Y = 5.978 × 1016 ∙ e(−0.0192)X

10B-2
DOE then derived a price factor index for this scenario, renormalized with 2013 equal to 

1, to project product 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 High Price Decline Scenario

A similar approach was applied for the high price decline scenario. DOE used an 

inflation-adjusted household refrigerator and home freezer manufacturing Producer Price Index 

(PPI) spanning the time period of 1991-2013 from the Bureau of Labor Statistics’ (BLS) to fit an 

exponential model with year as the explanatory variable. The PPI during this period of time 

shows a steeper downward trend, so the exponential fit based on this part of the historical PPI 

represents the high price decline scenario of future price projection. The PPI data reflect nominal 

prices, adjusted for product quality changes. An inflation-adjusted (deflated) price index for 

household refrigerator and home freezer manufacturing was calculated by dividing the PPI series 

by the Gross Domestic Product Chained Price Index. The deflated price index is presented in 

2013 dollar values. In this case, the exponential function takes the form of:

Y = a ∙ ebX

where Y is the household refrigerator and home freezer PPI, 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 price index versus year from 1991 to 2013. See Figure 10-B.2.2.

Figure 10B.2.2 Deflated Household Refrigerator and Home Freezer 

Manufacturing PPI versus Year, with Exponential 

Fit from 1991 to 2013

10B-3
The regression performed as an exponential trend line fit results in an R-square of 0.92,

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

Y = 5.839 × 10(21) ∙ e(−0.0249)X

DOE then derived a price factor index for this scenario, renormalized with 2013 equal to 

1, to project product 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.2.3 Summary

Table 10-B.2.1 shows the summary of the average annual rates of change for the product 

price index in each scenario. Figure 10-B.2.3 shows the resulting price trends projected from 

2021 to 2050.

Table 10B.2.1 Price Trend Sensitivities

Sensitivity Price Trend Average Annual Rate 

of Change %

Constant Price 

Scenario (Default)

No price learning 0.00

Low Price Decline 

Scenario

Exponential Fit using PPI data from 1976 to 

1990 -1.90

High Price Decline 

Scenario

Exponential Fit using PPI data from 1991 to 

2013 -2.46

Figure 10B.2.3 Miscellaneous Refrigeration Product Price Forecast Indexes

10B-4
10B.3 NET PRESENT VALUE RESULTS USING ALTERNATIVE 

PRODUCT PRICE TRENDS

This section presents the NPV results using the alternative product price trend for each 

product class considered for miscellaneous refrigeration products. The results are more sensitive 

to the high and low price decline scenario for cooled cabinets and non-compressor refrigerators, 

but less sensitive for ice makers, as compared to the default price scenario.

Table 10B.3.1 NPV Using Alternative Product Price Trend (Low Price Decline), 

Discounted at 3 Percent, for Cooled Cabinets (billion 2013$)

Efficiency Level Cooled Cabinet

Vapor 

Compression 

Cooled Cabinet

Thermoelectric 

Cooled Cabinet

CC CC-1 CC-2

Billion 2013 dollars

1 0.316 0.000 0.316

2 0.845 0.000 0.845

3 1.771 0.000 1.771

4 3.138 0.000 3.138

5 3.732 0.009 3.724

6 3.840 0.048 3.792

7 3.887 0.087 3.800

8 4.104 0.106 3.998

9 4.323 0.128 4.195

10 1.661 -0.382 2.043

11 -0.918 -0.872 -0.045

10B-5
Table 10B.3.2 NPV Using Alternative Product Price Trend (Low Price Decline), 

Discounted at 7 Percent, for Cooled Cabinets (billion 2013$)

Efficiency Level Cooled Cabinet

Vapor 

Compression 

Cooled Cabinet

Thermoelectric 

Cooled Cabinet

CC CC-1 CC-2

Billion 2013 dollars

1 0.134 0.000 0.134

2 0.359 0.000 0.359

3 0.754 0.000 0.754

4 1.336 0.000 1.336

5 1.588 0.003 1.585

6 1.583 0.017 1.566

7 1.539 0.028 1.511

8 1.582 0.028 1.554

9 1.624 0.028 1.596

10 0.203 -0.243 0.446

11 -1.150 -0.501 -0.649

Table 10B.3.3 NPV Using Alternative Product Price Trend (Low Price Decline), 

Discounted at 3 Percent, for Non-Compressor Thermoelectric 

Refrigerators (billion 2013$)

Efficiency Level

Non-Compressor 

Refrigerator

Thermoelectric 

Refrigerator

Absorption 

Refrigerator

NCR NCR-1 NCR-2

Billion 2013 dollars

1 0.472 0.472 0.000

2 1.002 0.944 0.058

3 1.532 1.415 0.117

4 1.877 1.722 0.155

5 2.285 2.085 0.199

6 2.812 2.555 0.257

7 3.149 2.855 0.295

8 3.094 2.806 0.288

10B-6
Table 10B.3.4 NPV Using Alternative Product Price Trend (Low Price Decline),

Discounted at 7 Percent, for Non-Compressor Thermoelectric 

Refrigerators (billion 2013$)

Efficiency Level

Non-Compressor 

Refrigerator

Thermoelectric 

Refrigerator

Absorption 

Refrigerator

NCR NCR-1 NCR-2

Billion 2013 dollars

1 0.209 0.209 0.000

2 0.444 0.418 0.026

3 0.678 0.627 0.052

4 0.818 0.751 0.067

5 0.989 0.904 0.086

6 1.223 1.111 0.112

7 1.358 1.232 0.126

8 1.322 1.200 0.122

Table 10B.3.5 NPV Using Alternative Product Price Trend (Low Price Decline), 

Discounted at 3 Percent, for Ice Makers (billion 2013$)

Efficiency Level

Portable Ice Maker Non-Portable Ice 

Maker, cooled storage

Non-Portable Ice 

Maker, uncooled 

storage

IM-P IM-C IM-U

billion 2013 dollars

1 0.084 0.010 0.058

2 0.169 0.019 0.116

3 0.253 0.029 0.174

4 0.337 0.039 0.232

5 0.422 0.048 0.290

6 0.506 0.049 0.348

7 0.550 0.406

8 0.435

10B-7
Table 10B.3.6 NPV Using Alternative Product Price Trend (Low Price Decline), 

Discounted at 7 Percent, for Ice Makers (billion 2013$)

Efficiency Level

Portable Ice Maker Non-Portable Ice 

Maker, cooled storage

Non-Portable Ice 

Maker, uncooled 

storage

IM-P IM-C IM-U

billion 2013 dollars

1 0.037 0.004 0.025

2 0.074 0.008 0.051

3 0.111 0.013 0.076

4 0.148 0.017 0.101

5 0.185 0.021 0.127

6 0.222 0.021 0.152

7 0.241 0.178

8 0.190

Table 10B.3.7 NPV Using Alternative Product Price Trend (High Price Decline), 

Discounted at 3 Percent, for Cooled Cabinets (billion 2013$)

Efficiency Level Cooled Cabinet

Vapor 

Compression 

Cooled Cabinet

Thermoelectric 

Cooled Cabinet

CC CC-1 CC-2

Billion 2013 dollars

1 0.324 0.000 0.324

2 0.867 0.000 0.867

3 1.818 0.000 1.818

4 3.222 0.000 3.222

5 3.834 0.011 3.823

6 4.022 0.055 3.967

7 4.167 0.103 4.064

8 4.466 0.136 4.330

9 4.767 0.172 4.595

10 2.487 -0.268 2.755

11 0.241 -0.695 0.935

10B-8
Table 10B.3.8 NPV Using Alternative Product Price Trend (High Price Decline), 

Discounted at 7 Percent, for Cooled Cabinets (billion 2013$)

Efficiency Level Cooled Cabinet

Vapor 

Compression 

Cooled Cabinet

Thermoelectric 

Cooled Cabinet

CC CC-1 CC-2

Billion 2013 dollars

1 0.138 0.000 0.138

2 0.370 0.000 0.370

3 0.775 0.000 0.775

4 1.374 0.000 1.374

5 1.634 0.003 1.630

6 1.665 0.020 1.645

7 1.666 0.035 1.630

8 1.745 0.041 1.704

9 1.825 0.048 1.778

10 0.572 -0.192 0.764

11 -0.633 -0.421 -0.212

Table 10B.3.9 NPV Using Alternative Product Price Trend (High Price Decline), 

Discounted at 3 Percent, for Non-Compressor Thermoelectric 

Refrigerators (billion 2013$)

Efficiency Level

Non-Compressor 

Refrigerator

Thermoelectric 

Refrigerator

Absorption 

Refrigerator

NCR NCR-1 NCR-2

Billion 2013 dollars

1 0.472 0.472 0.000

2 1.003 0.945 0.058

3 1.534 1.417 0.117

4 1.899 1.742 0.157

5 2.320 2.117 0.203

6 2.849 2.587 0.261

7 3.207 2.906 0.301

8 3.169 2.873 0.297

10B-9
Table 10B.3.10 NPV Using Alternative Product Price Trend (High Price Decline), 

Discounted at 7 Percent, for Non-Compressor Thermoelectric 

Refrigerators (billion 2013$)

Efficiency Level

Non-Compressor 

Refrigerator

Thermoelectric 

Refrigerator

Absorption 

Refrigerator

NCR NCR-1 NCR-2

Billion 2013 dollars

1 0.209 0.209 0.000

2 0.444 0.418 0.026

3 0.679 0.627 0.052

4 0.828 0.760 0.068

5 1.006 0.918 0.088

6 1.239 1.126 0.113

7 1.384 1.255 0.129

8 1.356 1.230 0.126

Table 10B.3.11 NPV Using Alternative Product Price Trend (High Price Decline), 

Discounted at 3 Percent, for Ice Makers (billion 2013$)

Efficiency Level

Portable Ice Maker Non-Portable Ice 

Maker, cooled storage

Non-Portable Ice 

Maker, uncooled 

storage

IM-P IM-C IM-U

billion 2013 dollars

1 0.085 0.010 0.059

2 0.170 0.020 0.117

3 0.255 0.029 0.176

4 0.340 0.039 0.234

5 0.425 0.049 0.293

6 0.510 0.050 0.351

7 0.554 0.410

8 0.439

10B-10
Table 10B.3.12 NPV Using Alternative Product Price Trend (High Price Decline), 

Discounted at 7 Percent, for Ice Makers (billion 2013$)

Efficiency Level

Portable Ice Maker Non-Portable Ice 

Maker, cooled storage

Non-Portable Ice 

Maker, uncooled 

storage

IM-P IM-C IM-U

billion 2013 dollars

1 0.037 0.004 0.026

2 0.075 0.008 0.051

3 0.112 0.013 0.077

4 0.149 0.017 0.102

5 0.186 0.021 0.128

6 0.224 0.022 0.154

7 0.243 0.179

8 0.192

Table 10B.3.13 Comparison of Total NPV of Cooled Cabinets for Alternative Product 

Price Forecast

Efficiency 

Level

Default Case Low Price Decline High Price Decline

NPV 3% NPV 7% NPV 3% NPV 7% NPV 3% NPV 7%

billion 2013 dollars

1 0.278 0.118 0.316 0.134 0.324 0.138

2 0.743 0.315 0.845 0.359 0.867 0.370

3 1.559 0.661 1.771 0.754 1.818 0.775

4 2.762 1.171 3.138 1.336 3.222 1.374

5 3.278 1.388 3.732 1.588 3.834 1.634

6 3.026 1.226 3.840 1.583 4.022 1.665

7 2.629 0.989 3.887 1.539 4.167 1.666

8 2.485 0.875 4.104 1.582 4.466 1.745

9 2.337 0.758 4.323 1.624 4.767 1.825

10 -1.953 -1.367 1.661 0.203 2.487 0.572

11 -5.985 -3.345 -0.918 -1.150 0.241 -0.633

10B-11
Table 10B.3.14 Comparison of Total NPV of Non-Compressor Refrigerators for 

Alternative Product Price Forecast

Efficiency 

Level

Default Case Low Price Decline High Price Decline

NPV 3% NPV 7% NPV 3% NPV 7% NPV 3% NPV 7%

billion 2013 dollars

1 0.470 0.208 0.472 0.209 0.472 0.209

2 0.997 0.441 1.002 0.444 1.003 0.396

3 1.525 0.675 1.532 0.678 1.534 0.679

4 1.779 0.775 1.877 0.818 1.899 0.828

5 2.125 0.920 2.285 0.989 2.320 1.006

6 2.649 1.151 2.812 1.223 2.849 1.239

7 2.891 1.245 3.149 1.358 3.207 1.384

8 2.759 1.175 3.094 1.322 3.169 1.356

Table 10B.3.15 Comparison of Total NPV of Portable Ice Makers for Alternative 

Product Price Forecast

Efficiency 

Level

Default Case Low Price Decline High Price Decline

NPV 3% NPV 7% NPV 3% NPV 7% NPV 3% NPV 7%

billion 2013dollars

1 0.082 0.036 0.084 0.037 0.085 0.037

2 0.163 0.072 0.169 0.074 0.170 0.075

3 0.245 0.107 0.253 0.111 0.255 0.112

4 0.327 0.143 0.337 0.148 0.340 0.149

5 0.408 0.179 0.422 0.185 0.425 0.186

6 0.490 0.215 0.506 0.222 0.510 0.224

7 0.533 0.234 0.550 0.241 0.554 0.243

Table 10B.3.16 Comparison of Total NPV of Non-Portable Ice Maker, Cooled Storage 

for Alternative Product Price Forecast

Efficiency 

Level

Default Case Low Price Decline High Price Decline

NPV 3% NPV 7% NPV 3% NPV 7% NPV 3% NPV 7%

billion 2013 dollars

1 0.009 0.004 0.010 0.004 0.010 0.004

2 0.018 0.008 0.019 0.008 0.020 0.008

3 0.027 0.012 0.029 0.013 0.029 0.013

4 0.036 0.015 0.039 0.017 0.039 0.017

5 0.044 0.019 0.048 0.021 0.049 0.021

6 0.045 0.020 0.049 0.021 0.050 0.022

10B-12
Table 10B.3.17 Comparison of Total NPV of Non-Portable Ice Maker, Uncooled Storage 

for Alternative Product Price Forecast

Efficiency 

Level

Default Case Low Price Decline High Price Decline

NPV 3% NPV 7% NPV 3% NPV 7% NPV 3% NPV 7%

billion 2013 dollars

1 0.056 0.024 0.058 0.025 0.059 0.026

2 0.111 0.049 0.116 0.051 0.117 0.051

3 0.167 0.073 0.174 0.076 0.176 0.077

4 0.222 0.097 0.232 0.101 0.234 0.102

5 0.278 0.122 0.290 0.127 0.293 0.128

6 0.334 0.146 0.348 0.152 0.351 0.154

7 0.389 0.170 0.406 0.178 0.410 0.179

8 0.417 0.182 0.435 0.190 0.439 0.192

10B-13