10B-i

APPENDIX 10B. NATIONAL NET PRESENT VALUE OF CONSUMER BENEFITS 

USING ALTERNATIVE EQUIPMENT PRICE FORECASTS

TABLE OF CONTENTS

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

10B.2 ALTERNATIVE BEVERAGE VENDING MACHINE PRICE TREND 

SCENARIOS ...............................................................................................................10B-1

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

10B.2.2 Low Price Decline Scenario.............................................................................10B-2

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

10B.3 NET PRESENT VALUE RESULTS USING ALTERNATIVE EQUIPMENT 

PRICE TRENDS..........................................................................................................10B-4

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 Equipment Class A Refrigerated Beverage 

Vending Machines (billion 2013$)............................................................10B-5

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

Discounted at 7 Percent, for Equipment Class A Refrigerated Beverage 

Vending Machines (billion 2013$)............................................................10B-5

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

Discounted at 3 Percent, for Equipment Class B Refrigerated Beverage 

Vending Machines (billion 2013$)............................................................10B-6

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

Discounted at 7 Percent, for Equipment Class B Refrigerated Beverage 

Vending Machines (billion 2013$)............................................................10B-6

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

Discounted at 3 Percent, for Equipment Class Combination 

Refrigerated Beverage Vending Machines (million 2013$)......................10B-7

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

Discounted at 7 Percent, for Equipment Class Combination 

Refrigerated Beverage Vending Machines (million 2013$)......................10B-8

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

Discounted at 3 Percent, for Equipment Class A Refrigerated Beverage 

Vending Machines (billion 2013$)............................................................10B-8

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

Discounted at 7 Percent, for Equipment Class A Refrigerated Beverage 

Vending Machines (billion 2012$)............................................................10B-9

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

Discounted at 3 Percent, for Equipment Class B Refrigerated Beverage 

Vending Machines (billion 2013$)............................................................10B-9
10B-ii

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

Discounted at 7 Percent, for Equipment Class B Refrigerated Beverage 

Vending Machines (billion 2013$)..........................................................10B-10

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

Discounted at 3 Percent, for Equipment Class Combination 

Refrigerated Beverage Vending Machines (million 2013$)....................10B-11

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

Discounted at 7 Percent, Equipment Class Combination Refrigerated 

Beverage Vending Machines (million 2013$).........................................10B-12

Table 10B.3.13 Comparison of Total NPV of Equipment Class A Refrigerated 

Beverage Vending Machines for Alternative Product Price Forecast .....10B-12

Table 10B.3.14 Comparison of Total NPV of Equipment Class B Refrigerated 

Beverage Vending Machines for Alternative Product Price Forecast .....10B-13

Table 10B.3.15 Comparison of Total NPV of Equipment Class Combination 

Refrigerated Beverage Vending Machines for Alternative Product 

Price Forecast...........................................................................................10B-14

LIST OF FIGURES

Figure 10B.2.1 Deflated Automatic Merchandising Machines PPI versus Year, with 

Exponential Fit from 1967 to 1995............................................................10B-2

Figure 10B.2.2 Deflated Automatic Merchandising Machines PPI versus Year, with 

Exponential Fit from 1996 to 2013............................................................10B-3

Figure 10B.2.3 Refrigerated Beverage Vending Machine Price Forecast Indexes ............10B-4
10B-1

APPENDIX 10B. NATIONAL NET PRESENT VALUE OF CONSUMER BENEFITS 

USING ALTERNATIVE EQUIPMENT PRICE FORECASTS

10B.1 INTRODUCTION

The net present value (NPV) results presented in chapter 10 reflect a default price trend 

based on an exponential fit to the prices of refrigerated beverage vending machines during the 

period of 1967-2013. The U.S. Department of Energy (DOE) obtained historical producer price 

index (PPI) data for “automatic merchandising machines, excluding parts” from the Bureau of 

Labor Statistics, which is the most disaggregated industry including refrigerated beverage 

vending machine manufacturing. DOE applied an annual price decline rate of 1.48 percent to 

project the prices of refrigerated beverage vending machines sold in each year in the forecast 

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

NPV results. In order to investigate the impact of different equipment price forecasts on the 

customer NPV for the considered ELs for refrigerated beverage vending machines, DOE also 

considered two alternative price trends for the sensitivity analysis: (1) high price decline 

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

used to derive these two alternative price trends and compares NPV results for both scenarios 

with the default price trend. 

10B.2 ALTERNATIVE BEVERAGE VENDING MACHINE PRICE TREND 

SCENARIOS

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

dividing the automatic merchandising machines PPI series into two time segments where one has 

a steeper price decline and the other has a shallower price decline. The high price decline 

scenario is based on an exponential fit to the PPI data for automatic merchandising machines

from 1967 to 1995. The low price decline scenario is based on an exponential fit to the same PPI 

data from 1996 to 2013. 

10B.2.1 High Price Decline Scenario 

For the high price decline scenario, DOE used an inflation-adjusted automatic 

merchandising machines PPI spanning the time period of 1967-1995 from the Bureau of Labor 

Statistics (BLS) to fit an exponential model with year as the explanatory variable.a The PPI 

during this period of time showed 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 inflationadjusted (deflated) price index for automatic merchandising machines 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:

 a Series ID PCU33331833331811; http://www.bls.gov/ppi/
10B-2

Y = a ∙ ebX

where Y is the automatic merchandising machines 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 1967 to 1995. See Figure 10B.2.1.

Figure 10B.2.1 Deflated Automatic Merchandising Machines PPI versus Year, with

Exponential Fit from 1967 to 1995

The regression performed as an exponential trend line fit results in an R-square of 0.99, 

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

Y = 1.906 × 1014 ∙ e(−0.0164)X

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

1, to project equipment 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 Low Price Decline Scenario

A similar approach was applied for the low price decline scenario as for the high price 

decline scenario. DOE used the inflation-adjusted automatic merchandising machines PPI 

spanning the time period of 1996-2013 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 shallower downward trend, 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 inflation-adjusted (deflated) price index for 

automatic merchandising machines was calculated by dividing the PPI series by the Gross 
10B-3

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 automatic merchandising machines 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 1996 to 2013. See Figure 10B.2.2.

Figure 10B.2.2 Deflated Automatic Merchandising Machines PPI versus Year, with 

Exponential Fit from 1996 to 2013

The regression performed as an exponential trend line fit results in an R-square of 0.91,

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

Y = 2.405 × 10(11) ∙ e(−0.0130)X

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

1, to project equipment 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 10B.2.1 shows the summary of the average annual rates of change for the 

equipment price index in each scenario. Figure 10B.2.3 shows the resulting price trends

projected from 2013 to 2050.
10B-4

Table 10B.2.1 Price Trend Sensitivities

Sensitivity Price Trend Average Annual Rate 

of Change %

Default Price 

Scenario

Exponential Fit using PPI data from 1967 to 

2013 -1.48

High Price Decline 

Scenario

Exponential Fit using PPI data from 1967 to 

1995 -1.63

Low Price Decline 

Scenario

Exponential Fit using PPI data from 1996 to 

2013 -1.29

Figure 10B.2.3 Refrigerated Beverage Vending Machine Price Forecast Indexes

10B.3 NET PRESENT VALUE RESULTS USING ALTERNATIVE 

EQUIPMENT PRICE TRENDS

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

equipment class considered for refrigerated beverage vending machines. 
10B-5

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

Discounted at 3 Percent, for Equipment Class A Refrigerated Beverage 

Vending Machines (billion 2013$)

Efficiency 

Level A HFC A CO2 Total

Billion 2013$

1 0.0017 0.0017 0.0034

2 0.0196 0.0194 0.0390

3 0.0438 0.0429 0.0868

4 0.0675 0.0634 0.1309

5 0.0880 0.0835 0.1715

6 0.0766 0.0490 0.1256

7 0.0331 0.0092 0.0423

8 -0.0093 -0.0298 -0.0390

9 -0.0342 -0.0374 -0.0716

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

Discounted at 7 Percent, for Equipment Class A Refrigerated Beverage 

Vending Machines (billion 2013$)

Efficiency 

Level A HFC A CO2 Total

Billion 2013$

1 0.0007 0.0007 0.0014

2 0.0079 0.0078 0.0157

3 0.0175 0.0169 0.0344

4 0.0256 0.0234 0.0491

5 0.0318 0.0294 0.0611

6 0.0207 0.0060 0.0268

7 -0.0074 -0.0200 -0.0274

8 -0.0348 -0.0454 -0.0802

9 -0.0509 -0.0504 -0.1013
10B-6

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

Discounted at 3 Percent, for Equipment Class B Refrigerated Beverage 

Vending Machines (billion 2013$)

Efficiency 

Level B HFC B CO2 Total

Billion 2013$

1 0.0025 0.0025 0.0049

2 0.0049 0.0049 0.0098

3 0.0106 0.0106 0.0212

4 0.0281 0.0280 0.0561

5 0.0479 0.0475 0.0954

6 0.0688 0.0678 0.1366

7 0.0834 0.0799 0.1633

8 0.0969 0.0719 0.1688

9 0.0282 0.0022 0.0303

10 -0.0505 -0.0692 -0.1197

11 -0.0665 -0.0665

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

Discounted at 7 Percent, for Equipment Class B Refrigerated Beverage 

Vending Machines (billion 2013$)

Efficiency 

Level B HFC B CO2 Total

Billion 2013$

1 0.0010 0.0010 0.0020

2 0.0020 0.0020 0.0040

3 0.0043 0.0043 0.0086

4 0.0115 0.0114 0.0228

5 0.0194 0.0191 0.0385

6 0.0272 0.0267 0.0540

7 0.0315 0.0296 0.0611

8 0.0343 0.0209 0.0552

9 -0.0076 -0.0214 -0.0290

10 -0.0545 -0.0641 -0.1186

11 -0.0640 -0.0640
10B-7

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

Discounted at 3 Percent, for Equipment Class Combination Refrigerated 

Beverage Vending Machines (million 2013$)

Efficiency 

Level

Combo A 

HFC

Combo A 

CO2

Combo B 

HFC

Combo B 

CO2

Total

Million 2013$

1 2.21 2.20 1.73 1.72 7.86

2 4.41 4.38 3.44 3.42 15.65

3 6.55 6.48 5.12 5.08 23.23

4 8.66 8.57 6.70 6.65 30.58

5 9.71 9.62 7.44 7.37 34.13

6 10.76 10.66 7.89 7.83 37.13

7 11.80 11.68 7.98 8.00 39.46

8 12.73 12.60 5.50 5.75 36.58

9 13.16 12.97 26.14

10 10.53 10.48 21.02

11 9.96 9.94 19.90
10B-8

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

Discounted at 7 Percent, for Equipment Class Combination Refrigerated 

Beverage Vending Machines (million 2013$)

Efficiency 

Level

Combo A 

HFC

Combo A 

CO2

Combo B 

HFC

Combo B 

CO2

Total

Million 2013$

1 0.90 0.89 0.71 0.70 3.21

2 1.80 1.77 1.41 1.39 6.37

3 2.66 2.62 2.08 2.06 9.42

4 3.50 3.45 2.71 2.68 12.34

5 3.92 3.87 3.00 2.95 13.74

6 4.34 4.28 3.12 3.09 14.84

7 4.76 4.69 3.06 3.07 15.58

8 5.12 5.04 1.65 1.78 13.59

9 5.20 5.09 10.29

10 3.64 3.62 7.26

11 3.31 3.31 6.62

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

Discounted at 3 Percent, for Equipment Class A Refrigerated Beverage 

Vending Machines (billion 2013$)

Efficiency 

Level A HFC A CO2 Total

Billion 2013$

1 0.0017 0.0017 0.0034

2 0.0196 0.0195 0.0391

3 0.0441 0.0432 0.0872

4 0.0683 0.0645 0.1328

5 0.0898 0.0856 0.1754

6 0.0812 0.0551 0.1362

7 0.0421 0.0195 0.0616

8 0.0041 -0.0153 -0.0112

9 -0.0183 -0.0222 -0.0405
10B-9

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

Discounted at 7 Percent, for Equipment Class A Refrigerated Beverage 

Vending Machines (billion 2012$)

Efficiency 

Level A HFC A CO2 Total

Billion 2013$

1 0.0007 0.0007 0.0014

2 0.0079 0.0078 0.0157

3 0.0176 0.0171 0.0346

4 0.0260 0.0239 0.0500

5 0.0326 0.0303 0.0629

6 0.0229 0.0088 0.0317

7 -0.0032 -0.0153 -0.0185

8 -0.0286 -0.0387 -0.0673

9 -0.0435 -0.0433 -0.0868

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

Discounted at 3 Percent, for Equipment Class B Refrigerated Beverage 

Vending Machines (billion 2013$)

Efficiency 

Level B HFC B CO2 Total

Billion 2013$

1 0.0025 0.0025 0.0049

2 0.0049 0.0049 0.0098

3 0.0106 0.0106 0.0212

4 0.0282 0.0280 0.0562

5 0.0480 0.0476 0.0956

6 0.0691 0.0683 0.1374

7 0.0845 0.0812 0.1657

8 0.0992 0.0756 0.1748

9 0.0364 0.0118 0.0482

10 -0.0359 -0.0536 -0.0895

11 -0.0506 -0.0506
10B-10

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

Discounted at 7 Percent, for Equipment Class B Refrigerated Beverage 

Vending Machines (billion 2013$)

Efficiency 

Level B HFC B CO2 Total

Billion 2013$

1 0.0010 0.0010 0.0020

2 0.0020 0.0020 0.0040

3 0.0043 0.0043 0.0086

4 0.0115 0.0114 0.0229

5 0.0194 0.0192 0.0386

6 0.0274 0.0269 0.0543

7 0.0320 0.0302 0.0622

8 0.0354 0.0226 0.0580

9 -0.0038 -0.0169 -0.0207

10 -0.0477 -0.0569 -0.1046

11 -0.0566 -0.0566
10B-11

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

Discounted at 3 Percent, for Equipment Class Combination Refrigerated 

Beverage Vending Machines (million 2013$)

Efficiency 

Level

Combo A 

HFC

Combo A 

CO2

Combo B 

HFC

Combo B 

CO2

Total

Million 2013$

1 2.22 2.20 1.73 1.72 7.87

2 4.42 4.38 3.45 3.42 15.67

3 6.56 6.49 5.12 5.09 23.26

4 8.67 8.59 6.71 6.66 30.64

5 9.73 9.64 7.46 7.39 34.22

6 10.78 10.69 7.93 7.87 37.27

7 11.83 11.72 8.07 8.08 39.70

8 12.77 12.65 5.76 5.99 37.18

9 13.24 13.06 26.30

10 10.83 10.78 21.61

11 10.30 10.28 20.58
10B-12

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

Discounted at 7 Percent, Equipment Class Combination Refrigerated 

Beverage Vending Machines (million 2013$)

Efficiency 

Level

Combo A 

HFC

Combo A 

CO2

Combo B 

HFC

Combo B 

CO2

Total

Million 2013$

1 0.90 0.89 0.71 0.70 3.21

2 1.80 1.78 1.41 1.39 6.38

3 2.66 2.62 2.09 2.06 9.43

4 3.51 3.46 2.72 2.69 12.38

5 3.93 3.88 3.01 2.97 13.78

6 4.35 4.30 3.15 3.11 14.91

7 4.77 4.71 3.10 3.11 15.69

8 5.14 5.06 1.77 1.90 13.86

9 5.24 5.13 10.37

10 3.78 3.75 7.54

11 3.47 3.46 6.93

Table 10B.3.13 Comparison of Total NPV of Equipment Class A Refrigerated Beverage 

Vending Machines 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$

1 0.0034 0.0014 0.0034 0.0014 0.0034 0.0014

2 0.0391 0.0157 0.0390 0.0157 0.0391 0.0157

3 0.0870 0.0345 0.0868 0.0344 0.0872 0.0346

4 0.1320 0.0496 0.1309 0.0491 0.1328 0.0500

5 0.1737 0.0622 0.1715 0.0611 0.1754 0.0629

6 0.1318 0.0296 0.1256 0.0268 0.1362 0.0317

7 0.0535 -0.0223 0.0423 -0.0274 0.0616 -0.0185

8 -0.0229 -0.0727 -0.0390 -0.0802 -0.0112 -0.0673

9 -0.0535 -0.0929 -0.0716 -0.1013 -0.0405 -0.0868
10B-13

Table 10B.3.14 Comparison of Total NPV of Equipment Class B Refrigerated Beverage 

Vending Machines 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$

1 0.0049 0.0020 0.0049 0.0020 0.0049 0.0020

2 0.0098 0.0040 0.0098 0.0040 0.0098 0.0040

3 0.0212 0.0086 0.0212 0.0086 0.0212 0.0086

4 0.0561 0.0229 0.0561 0.0228 0.0562 0.0229

5 0.0955 0.0386 0.0954 0.0385 0.0956 0.0386

6 0.1371 0.0542 0.1366 0.0540 0.1374 0.0543

7 0.1647 0.0618 0.1633 0.0611 0.1657 0.0622

8 0.1723 0.0569 0.1688 0.0552 0.1748 0.0580

9 0.0407 -0.0242 0.0303 -0.0290 0.0482 -0.0207

10 -0.1022 -0.1105 -0.1197 -0.1186 -0.0895 -0.1046

11 -0.0572 -0.0597 -0.0665 -0.0640 -0.0506 -0.0566
10B-14

Table 10B.3.15 Comparison of Total NPV of Equipment Class Combination Refrigerated 

Beverage Vending Machines 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%

Million 2013$

1 7.87 3.21 7.86 3.21 7.87 3.21

2 15.66 6.37 15.65 6.37 15.67 6.38

3 23.25 9.43 23.23 9.42 23.26 9.43

4 30.62 12.36 30.58 12.34 30.64 12.38

5 34.18 13.77 34.13 13.74 34.22 13.78

6 37.21 14.88 37.13 14.84 37.27 14.91

7 39.60 15.64 39.46 15.58 39.70 15.69

8 36.93 13.75 36.58 13.59 37.18 13.86

9 26.23 10.34 26.14 10.29 26.30 10.37

10 21.36 7.42 21.02 7.26 21.61 7.54

11 20.29 6.80 19.90 6.62 20.58 6.93