APPENDIX 10-B. NIA SENSITIVITY ANALYSIS FOR

ALTERNATIVE PRODUCT PRICE TREND SCENARIOS

TABLE OF CONTENTS

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

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

10-B.2.1 Exponential Fit Approach (High Price Scenario)....................................................1

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

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

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

LIST OF TABLES

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

Table 10-B.3.1 Summary of Cumulative Net Present Value for PTAC and PTHP: 

Decreasing Price Scenario (Seven Percent Discount Rate)...............................4

Table 10-B.3.2 Summary of Cumulative Net Present Value for PTAC and PTHP: 

Decreasing Price Scenario (Three Percent Discount Rate)................................5

Table 10-B.3.3 Summary of Cumulative Net Present Value for PTACs and PTHPs: 

Increasing Price Scenario (Seven Percent Discount Rate) ................................5

Table 10-B.3.4 Summary of Cumulative Net Present Value for PTACs and PTHPs: 

Increasing Price Scenario (Three Percent Discount Rate).................................5

LIST OF FIGURES

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

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

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

ALTERNATIVE PRODUCT PRICE TREND SCENARIOS

10-B.1INTRODUCTION

The U.S. Department of Energy (DOE) used a constant price assumption for the default 

forecast in the national impact analysis (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 trial standard levels (TSLs) for packaged terminal air conditioners (PTACs), 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 equipment, there are insufficient data to apply a

price-based 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 equipment in question to derive alternative price trends for 

sensitivity analysis. This approach was used for PTAC.

10-B.2ALTERNATIVE PTAC PRICE TREND SCENARIOS

For PTAC, 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— industrial equipment” that was forecasted for the U.S. Energy Information 

Administration’s (EIA’s) Annual Energy Outlook 2013 (AEO2013). 

10-B.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 2001-2013 to fit an exponential model with year as the 

explanatory variable. DOE obtained historical PPI data all other miscellaneous refrigeration and 

air-conditioning equipment spanning the time period 2001-2013 from the Bureau of Labor 

10-B-1
Statistics’ (BLS).a The PPI data reflect nominal prices, adjusted for product quality changes. An 

inflation-adjusted (deflated) price index for all other miscellaneous refrigeration and airconditioning equipment was calculated by dividing the PPI series by the Gross Domestic Product 

Chained Price Index. The deflated price index is now presented in 2013 dollar values. In this 

case, the exponential function takes the form of:

Y = a ∙ ebX 

where Y is the all other miscellaneous refrigeration and air-conditioning equipment 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 PTAC price index versus year from 2001 to 2013. See Figure 10-B.2.1.

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

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:

Y = 8.12 × 10(−13) ∙ e0.0138X

a

 Series ID PCU3334153334159; http://www.bls.gov/ppi/

10-B-2

 
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.

10-B.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 AEO 2013 out to 2040. This index is the most disaggregated category that 

includes PTACs. To develop an inflation-adjusted index, DOE normalized the above index with 

the “chained price index—gross domestic product” forecasted for AEO 2013. To extend the price 

index beyond 2040, DOE used the average annual price growth rate in 2031 to 2040. 

10-B.2.3 Summary

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

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

Table 10-B.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”

-0.25

High Price Scenario Exponential Fit using data from 2001 to 

2013

1.39

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

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

Table 10-B.3.1 Summary of Cumulative Net Present Value for PTAC and PTHP: 

Decreasing Price Scenario (Seven Percent Discount Rate)

Equipment Class Net Present Value (Billion 2012$)

TSL 1 TSL 2 TSL 3 TSL 4 TSL 5

PTAC < 7,000 Btu/h 0.0 -0.4 -1.3 -2.2 -2.4

PTAC 7,000 - 15,000 Btu/h 0.2 -1.6 -7.5 -15.5 -17.5

PTAC > 15,000 Btu/h -0.4 -2.4 -5.6 -8.6 -9.2

PTHP < 7,000 Btu/h 0.2 0.4 0.4 0.3 0.3

PTHP 7,000 - 15,000 Btu/h 6.7 15.8 25.6 30.4 30.8

PTHP > 15,000 Btu/h 0.3 0.8 0.3 -0.7 -1.0

10-B-4
Table 10-B.3.2 Summary of Cumulative Net Present Value for PTAC and PTHP: 

Decreasing Price Scenario (Three Percent Discount Rate)

Equipment Class Net Present Value (Billion 2012$)

TSL 1 TSL 2 TSL 3 TSL 4 TSL 5

PTAC < 7,000 Btu/h 0.0 0.0 -0.3 -0.9 -1.0

PTAC 7,000 - 15,000 Btu/h 5.0 16.4 26.3 26.1 25.2

PTAC > 15,000 Btu/h 0.0 -2.2 -6.8 -10.6 -11.3

PTHP < 7,000 Btu/h 0.7 2.1 3.3 3.8 3.9

PTHP 7,000 - 15,000 Btu/h 19.0 54.1 96.7 119.2 121.9

PTHP > 15,000 Btu/h 1.2 4.0 5.5 5.3 5.1

All Classes 25.9 74.4 124.8 143.0 143.7

Table 10-B.3.3 Summary of Cumulative Net Present Value for PTACs and PTHPs: 

Increasing Price Scenario (Seven Percent Discount Rate)

Equipment Class

Net Present Value (Billion 2012$)

TSL 1 TSL 2 TSL 3 TSL 4 TSL 5

PTAC < 7,000 Btu/h 0.0 -1.0 -2.9 -4.4 -4.7

PTAC 7,000 - 15,000 Btu/h -2.6 -13.1 -32.2 -47.8 -50.7

PTAC > 15,000 Btu/h -1.1 -4.7 -9.7 -13.6 -14.3

PTHP < 7,000 Btu/h 0.0 -0.3 -0.9 -1.4 -1.5

PTHP 7,000 - 15,000 Btu/h 3.9 5.5 4.8 3.2 3.0

PTHP > 15,000 Btu/h -0.1 -0.8 -2.8 -4.6 -5.0

All Classes 0.1 -14.4 -43.7 -68.6 -73.2

Table 10-B.3.4 Summary of Cumulative Net Present Value for PTACs and PTHPs: 

Increasing Price Scenario (Three Percent Discount Rate)

Equipment Class Net Present Value (Billion 2012$)

TSL 1 TSL 2 TSL 3 TSL 4 TSL 5

PTAC < 7,000 Btu/h 0.0 -1.3 -3.8 -5.4 -5.7

PTAC 7,000 - 15,000 Btu/h -1.0 -9.0 -27.6 -41.3 -43.3

PTAC > 15,000 Btu/h -1.7 -7.6 -15.8 -21.2 -22.0

PTHP < 7,000 Btu/h 0.2 0.4 0.3 0.1 0.1

PTHP 7,000 - 15,000 Btu/h 12.7 30.6 49.5 60.9 62.6

PTHP > 15,000 Btu/h 0.3 0.4 -1.5 -3.2 -3.5

All Classes 10.5 13.6 1.0 -10.0 -11.7

10-B-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.

10-B-6