10C-i

APPENDIX 10C. NATIONAL NET PRESENT VALUE OF CONSUMER BENEFITS

USING ALTERNATIVE PRODUCT PRICE FORECASTS

TABLE OF CONTENTS

10C-1 INTRODUCTION .................................................................................................10C-1

10C-2 ALTERNATIVE PRICE TREND SCNEARIOS..................................................10C-1

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

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

10C-3 SUMMARY...........................................................................................................10C-3

10C-4 NET PRESENT VALUE USING ALTERNATIVE PRICE TRENDS................10C-4

LIST OF TABLES

Table 10C-3-1 Price Trend Scenarios................................................................................10C-4

Table 10C-4-1 NPV of Impacts for Residential and Commercial Purchases Under 

Alternative Product Price Forecasts (3-Percent Discount Rate)................10C-5

Table 10C-4-2 NPV of Impacts for Residential and Commercial Purchases Under 

Alternative Product Price Forecasts (7-Percent Discount Rate)................10C-5

LIST OF FIGURES

Figure 10C-2.1 Nominal and Deflated PPI Series for Small Electric Household 

Appliances, 1998–2013..............................................................................10C-2

Figure 10C-2.2 Deflated PPI with Exponential Fit for Small Electric Household 

Appliances, 1998–2013..............................................................................10C-3

Figure 10C-3.1 Price Factor Indexes for the Default and Sensitivity Cases for Portable 

ACs ............................................................................................................10C-4
10C-1

APPENDIX 10C. NATIONAL NET PRESENT VALUE OF CONSUMER BENEFITS

USING ALTERNATIVE PRODUCT PRICE FORECASTS

10C-1 INTRODUCTION

The net present value (NPV) results presented in chapter 10 are based on projections of 

future prices derived from historical Producer Price Index (PPI) data obtained from the Bureau of 

Labor Statistics (BLS). DOE collected PPI data on “small electric household appliances, except 

fans” for 1983–2013 to project future prices of portable air conditioners (ACs). To investigate 

the effect of different product price trends on the consumer NPV for the energy efficiency 

standards considered for portable ACs, DOE evaluated two alternatives, a low and a high price 

decline scenario. The following sections describe the methods DOE used to derive the two 

alternative price trends and the NPV results for all three scenarios. 

10C-2 ALTERNATIVE PRICE TREND SCNEARIOS

DOE obtained historical PPI data for “small electric household appliances, except fans” 

as a proxy for portable ACs. DOE understands that the PPI series encompasses a range of 

products unconnected to portable ACs, but it is the most disaggregated price series that includes

portable ACs. DOE obtained the PPI data for 1983–2013 from the BLS.a DOE assumed that 

prices of all portable AC product classes will continue to show the same trend as for 1983–2013.

DOE developed the low price decline scenario based on an exponential fit to the PPI data from 

the more limited period of 1998–2013. The high price decline scenario is based on the projection

for the “furniture and appliances” industry series in the Energy Information Administration's 

Annual Energy Outlook 2014 (AEO 2014).

10C-2.1 Low Price Decline Scenario 

For the low price decline scenario, DOE used the BLS' inflation-adjusted PPI for small 

electric household appliances spanning 1998–2013 to fit an exponential model having year as the 

explanatory variable. The PPI during that period shows a shallower downward trend than does

the longer PPI series starting in 1983 and ending in 2013. The exponential fit based on the 

shorter period of historical PPI represents the low price decline scenario for projecting future 

prices. In this case, the exponential function takes the form of:

Y = a ∙ e

bX

where Y is the PPI for small electric household appliances, X is the time variable, a is the 

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

The PPI data reflect nominal prices, adjusted for changes in product quality. DOE 

developed an inflation-adjusted (deflated) price index for small electric household appliances by 

 

a PPI series ID: PCU33521033521014 http://www.bls.gov/ppi/
10C-2

dividing the PPI series by the chained price index for the gross domestic product. Figure 10C-2.1

presents the nominal and inflation-adjusted PPI trends for small electric household appliances

from 1998—2013. The deflated price index is presented in 2013$. 

Figure 10C-2.1 Nominal and Deflated PPI Series for Small Electric 

Household Appliances, 1998–2013

To estimate the exponential parameters, a least-square fit was performed on the inflationadjusted (deflated) price index versus year from 1998 to 2013. Figure 10C-2.2 shows the results.
10C-3

Figure 10C-2.2 Deflated PPI with Exponential Fit for Small Electric 

Household Appliances, 1998–2013

The regression performed as an exponential trend line fit results in an R-square of 0.97, 

which indicates an excellent fit to the data. The final estimated exponential function is:

Y = 2.384 × 1013 ∙ e

(−0.0153)X

DOE then derived a price factor index for the low price decline scenario, renormalized 

with 2013 equal to 1, to project product prices in each future year in the analysis period. The 

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

10C-2.2 High Price Decline Scenario

 DOE also examined a forecast based on the "deflator—furniture and appliances” that the 

AEO 2014 included out to 2040. AEO 2014 offers the most current price trend projections DOE 

could acquire. The index also represents the most disaggregated category that includes portable 

ACs. To develop an inflation-adjusted index, DOE normalized the index using the AEO 2014

"chained price index—gross domestic product,” with 2013 equal to 1. To extend the price index 

beyond 2040, DOE used the average annual price growth rate for 2031–2040. 

10C-3 SUMMARY

Table 10C-3-1 presents the average annual rates of change for the product price index 

under the default, high, and low price scenarios. Figure 10C-3.1 shows the resulting price factor 

indexes (price trends) for portable ACs.
10C-4

Table 10C-3-1 Price Trend Scenarios

Scenario Price Trend

Average Annual 

Rate of Change 

%

Default Exponential fit using PPI for small electric 

household appliances (1983–2013)

-1.99

High price 

decline

AEO 2014 “chained price index—furniture 

and appliances” -2.59

Low price 

decline

Exponential fit using PPI for small electric 

household appliances (1998–2013)

-1.52

Figure 10C-3.1 Price Factor Indexes for the Default and Sensitivity 

Cases for Portable ACs

10C-4 NET PRESENT VALUE USING ALTERNATIVE PRICE TRENDS

Table 10C-4-1 presents the NPV of financial impacts under the three alternative product 

price trends for all four CSLs for purchases in both the residential and commercial sectors at a 3-

percent discount rate. Table 10C-4- presents similar results for a 7-percent discount rate.
10C-5

Table 10C-4-1 NPV of Impacts for Residential and Commercial Purchases Under 

Alternative Product Price Forecasts (3-Percent Discount Rate) 

Price Trend CSL Residential

Billion 2013$

Commercial

Billion 2013$

Total

Billion 2013$

Default

1 3.972 0.060 4.031

2 5.099 0.079 5.178

3 6.022 0.092 6.114

4 6.023 0.113 6.137

Decreasing 

1 3.972 0.060 4.031

2 5.100 0.078 5.178

3 6.024 0.092 6.116

4 6.088 0.114 6.202

Increasing

1 3.971 0.060 4.031

2 5.098 0.079 5.176

3 6.018 0.093 6.111

4 5.942 0.113 6.054

Table 10C-4-2 NPV of Impacts for Residential and Commercial Purchases Under 

Alternative Product Price Forecasts (7-Percent Discount Rate) 

Price Trend CSL Residential

Billion 2013$

Commercial

Billion 2013$

Total

Billion 2013$

Default

1 1.703 0.026 1.728

2 2.187 0.034 2.221

3 2.581 0.040 2.621

4 2.482 0.048 2.529

Decreasing

1 1.704 0.025 1.729

2 2.188 0.034 2.221

3 2.583 0.039 2.623

4 2.510 0.048 2.558

Increasing

1 1.702 0.026 1.727

2 2.185 0.034 2.219

3 2.579 0.040 2.618

4 2.443 0.047 2.490