APPENDIX 10B. NIA SENSITIVITY ANALYSIS FOR ALTERNATIVE 

PRODUCT PRICE TREND SCENARIOS

TABLE OF CONTENTS 

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

10B.2 ALTERNATIVE SPVU PRICE TREND SCENARIOS ..............................................10B-1

10B.2.1 Exponential Fit Approach (High Price Scenario)...........................................10B-2

10B.2.2 Annual Energy Outlook 2013 Price Forecast (Low Price Scenario).............10B-3

10B.2.3 Summary ...........................................................................................................10B-3

10B.3 NPV RESULTS BY ALTERNATIVE PRICE TREND SCENARIO .........................10B-4

LIST OF TABLES

Table 10B.2.1 Price Trend Sensitivities......................................................................................10B-3

Table 10B.3.1. Summary of Cumulative Net Present Value for SPVUs: Low Price 

Scenario (Seven Percent Discount Rate) .....................................................10B-4

Table 10B.3.2. Summary of Cumulative Net Present Value for SPVUs: Low Price 

Scenario (Three Percent Discount Rate)......................................................10B-4

Table 10B.3.3. Summary of Cumulative Net Present Value for SPVUs: High Price 

Scenario (Seven Percent Discount Rate) .....................................................10B-5

Table 10B.3.4. Summary of Cumulative Net Present Value for SPVUs: High Price 

Scenario (Three Percent Discount Rate)......................................................10B-5

LIST OF FIGURES

Figure 10B.2.1 Relative Price of SPVUs versus Year, with Exponential Fit......................10B-2

Figure 10B.2.2 SPVU Price Forecast Indexes.......................................................................10B-4

10B-i
APPENDIX 10B. NIA SENSITIVITY ANALYSIS FOR 

ALTERNATIVE PRODUCT PRICE TREND SCENARIOS

10B.1 INTRODUCTION

DOE used a constant price assumption for the default forecast in the NIA described in 

Chapter 10. In order to investigate the impact of different product price forecasts on the 

consumer net present value (NPV) for the considered TSLs for SPVUs, DOE also 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. 

In recent rulemakings for several residential products, DOE has used the experience 

curve method to derive learning rates to forecast future prices. 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. A recent report from Lawrence Berkeley National Laboratory by Taylor and 

Fujita provides an overview of some of the major findings of the academic literature on learning 

curves, and describes the application of a component-based learning curve approach (by the 

Environmental Protection Agency and the National Highway Transportation Safety 

Administration) and a price-based learning curve approach (by DOE) in regulatory impact 

assessment.1

For some commercial and industrial products, there are insufficient data to apply a pricebased learning curve approach, particularly with respect to cumulative production. In such cases, 

DOE used a constant price assumption for the default forecast in the NIA, but made use of price 

indexes that are relevant for the product in question to derive alternative price trends for 

sensitivity analysis.a This approach was used for SPVU.

10B.2 ALTERNATIVE SPVU PRICE TREND SCENARIOS 

For SPVU, DOE considered two alternative price trends for sensitivity analysis. One of 

these used an exponential fit on the deflated Producer Price Index (PPI) for all other 

miscellaneous refrigeration and air-conditioning equipments, and the other is based on the 

“deflator— other durables excluding medical” that was forecasted for EIA’s Annual Energy 

Outlook 2013 (AEO2013). 

a

 See appendix 10C of the final rule TSD for distribution transformers. 

http://www.regulations.gov/#!documentDetail;D=EERE-2010-BT-STD-0048-0760

10B-1

 
10B.2.1 Exponential Fit Approach (High Price Scenario) 

For this scenario, DOE used an inflation-adjusted all other miscellaneous refrigeration 

and air-conditioning equipment PPI from 2001-2012 to fit an exponential model with year as the 

explanatory variable. DOE obtained historical Producer Price Index (PPI) data all other 

miscellaneous refrigeration and air-conditioning equipment spanning the time period 2001-2012 

from the Bureau of Labor Statistics’ (BLS). b The PPI data reflect nominal prices, adjusted for 

product quality changes. An inflation-adjusted (deflated) price index for all other miscellaneous 

refrigeration and air-conditioning 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:

YY = aa ∙ eebbbb 

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

parameter of the time variable.c

 

 

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

inflation-adjusted SPVU price index versus year from 2001 to 2012. See Figure 10B.2.1. 

Figure 10B.2.1 Relative Price of SPVUs versus Year, with Exponential Fit

b

 Series ID PCU3334153334159; www.bls.gov/ppi/ c

 During analysis for the Final Rule, DOE will consider alternate fits to these data.

y = 4E-14e0.0153x

R2 = 0.7479

0.820

0.840

0.860

0.880

0.900

0.920

0.940

0.960

0.980

1.000

1.020

2000 2005 2010 2015

Deflated Price Index (2012=1)

Year

Exponential Fit on

Deflated PPI from

2001 to 2012

Expon. (Exponential

Fit on Deflated PPI

from 2001 to 2012)

10B-2

 
The regression performed as an exponential trend line fit results in an R-square of 0.75, 

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

YY = 4.054 × 10(−14) ∙ ee0.0153 

DOE then derived a price factor index for this scenario, with 2013 equal to 1, to project

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 Annual Energy Outlook 2013 Price Forecast (Low Price Scenario) 

 

DOE also examined a forecast based on the “chained price index—industrial equipment” 

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

includes SPVUs. 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. 

10B.2.3 Summary

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

price index in each scenario. Figure 10B.2.2 shows the resulting price trends.

Table 10B.2.1 Price Trend Sensitivities

Sensitivity Price Trend Average Annual rate of 

change %

Medium (Default) Constant Price Projection 0.00

Low Price Scenario AEO2013-- “chained price index—

industrial equipment”

-0.26

High Price Scenario Exponential Fit using data from 2001 to 

2012

1.54

10B-3
Figure 10B.2.2 SPVU Price Forecast Indexes

10B.3 NPV RESULTS BY ALTERNATIVE PRICE TREND SCENARIO

Table 10B.3.1. Summary of Cumulative Net Present Value for SPVUs: Low Price Scenario

(Seven Percent Discount Rate) 

Equipment Class Net Present Value (Billion 2013$)

TSL 1 TSL 2 TSL 3 TSL 4

SPVAC <65,000 Btu/h 1 Phase 0.03 0.02 (0.24) (0.43)

SPVAC <65,000 Btu/h 3 Phase 0.01 0.01 (0.11) (0.19)

SPVHP <65,000 Btu/h 1 Phase 0.03 0.07 0.02 (0.07)

SPVHP <65,000 Btu/h 3 Phase 0.01 0.03 0.01 (0.03)

All Classes 0.09 0.13 (0.32) (0.73)

* Numbers in parentheses indicate negative NPV.

Table 10B.3.2. Summary of Cumulative Net Present Value for SPVUs: Low Price Scenario

(Three Percent Discount Rate) 

Equipment Class Net Present Value (Billion 2013$)

TSL 1 TSL 2 TSL 3 TSL 4

SPVAC <65,000 Btu/h 1 Phase 0.10 0.11 (0.39) (0.66)

SPVAC <65,000 Btu/h 3 Phase 0.04 0.05 (0.17) (0.30)

SPVHP <65,000 Btu/h 1 Phase 0.09 0.22 0.12 (0.01)

SPVHP <65,000 Btu/h 3 Phase 0.04 0.10 0.06 (0.01)

All Classes 0.28 0.48 (0.39) (0.98)

* Numbers in parentheses indicate negative NPV.

0.000

0.200

0.400

0.600

0.800

1.000

1.200

1.400

1.600

1.800

201320162019202220252028203120342037204020432046

Constant Price

Index_Default

Exponential Fit using

PPI deflated with GDP

(2001-2012)_ High

Price Case

AEO 2013_Low Price

Case

10B-4
Table 10B.3.3. Summary of Cumulative Net Present Value for SPVUs: High Price Scenario

(Seven Percent Discount Rate) 

Equipment Class Net Present Value (Billion 2013$)

TSL 1 TSL 2 TSL 3 TSL 4

SPVAC <65,000 Btu/h 1 Phase 0.01 (0.06) (0.46) (0.70)

SPVAC <65,000 Btu/h 3 Phase 0.00 (0.03) (0.21) (0.31)

SPVHP <65,000 Btu/h 1 Phase 0.02 0.04 (0.08) (0.19)

SPVHP <65,000 Btu/h 3 Phase 0.01 0.02 (0.04) (0.09)

All Classes 0.04 (0.03) (0.78) (1.28)

* Numbers in parentheses indicate negative NPV.

Table 10B.3.4. Summary of Cumulative Net Present Value for SPVUs: High Price Scenario

(Three Percent Discount Rate) 

Equipment Class Net Present Value (Billion 2013$)

TSL 1 TSL 2 TSL 3 TSL 4

SPVAC <65,000 Btu/h 1 Phase 0.04 (0.08) (0.92) (1.27)

SPVAC <65,000 Btu/h 3 Phase 0.02 (0.03) (0.41) (0.57)

SPVHP <65,000 Btu/h 1 Phase 0.07 0.15 (0.10) (0.27)

SPVHP <65,000 Btu/h 3 Phase 0.03 0.07 (0.05) (0.12)

All Classes 0.15 0.11 (1.48) (2.23)

* Numbers in parentheses indicate negative NPV.

10B-5
REFERENCES 

1. Margaret Taylor and K. Sydny Fujita. Accounting for Technological Change in Regulatory 

Impact Analyses: The Learning Curve Technique. Lawrence Berkeley National Laboratory, 

Berkeley, CA. April 2013.

10B-6