CHAPTER 10. NATIONAL IMPACT ANALYSIS

TABLE OF CONTENTS

10.1 INTRODUCTION ......................................................................................................... 10-1

10.1.1 Alternative Scenarios......................................................................................... 10-1

10.2 FORECASTED EFFICIENCIES FOR BASE AND STANDARDS CASES .............. 10-1

10.2.1 Base Case Efficiencies....................................................................................... 10-2

10.2.1.1 Standards Case Efficiencies..................................................................... 10-3

10.3 NATIONAL ENERGY SAVINGS ............................................................................... 10-6

10.3.1 Definition ........................................................................................................... 10-6

10.3.2 Inputs.................................................................................................................. 10-7

10.3.2.1 Shipments................................................................................................. 10-7

10.3.2.2 Equipment Stock ...................................................................................... 10-8

10.3.2.3 Annual Energy Consumption per Unit..................................................... 10-8

10.3.2.4 National Annual Energy Consumption .................................................. 10-10

10.3.2.5 Site-to-Primary Energy Conversion Factors.......................................... 10-10

10.3.2.6 Full-Fuel-Cycle Energy Factors............................................................. 10-11

10.4 NET PRESENT VALUE............................................................................................. 10-11

10.4.1 Definition ......................................................................................................... 10-11

10.4.2 Inputs................................................................................................................ 10-13

10.4.2.1 Average Annual Installed Price.............................................................. 10-13

10.4.2.2 Annual Operating Cost Savings per Unit............................................... 10-15

10.4.2.3 Total Annual Increases in Equipment Cost............................................ 10-15

10.4.2.4 Total Annual Savings in Operating Cost................................................ 10-16

10.4.2.5 Discount Factor ...................................................................................... 10-16

10.4.2.6 Present Value of Costs ........................................................................... 10-16

10.4.2.7 Present Value of Savings........................................................................ 10-17

10.5 NATIONAL ENERGY SAVINGS AND NET PRESENT VALUE RESULTS........ 10-17

10.5.1 Summary of Inputs........................................................................................... 10-17

10.5.2 Annual Costs and Savings ............................................................................... 10-18

10.5.3 National Energy Savings Results by Energy Efficiency Level ....................... 10-19

10.5.4 Customer Net Present Value Results by Energy Efficiency Level.................. 10-21

10-i
LIST OF TABLES

Table 10.2.1 Base Case Estimated and Forecast Efficiency Level Market Share 

Distributions for Equipment Class A Refrigerated Beverage Vending 

Machines...................................................................................................... 10-2

Table 10.2.2 Base Case Estimated and Forecast Efficiency Level Market Share 

Distributions for Equipment Class B Refrigerated Beverage Vending 

Machines...................................................................................................... 10-3

Table 10.2.3 Equipment Class A HFC: Efficiency Level Market Share Distributions 

for Standards Cases...................................................................................... 10-4

Table 10.2.4 Equipment Class A CO2: Efficiency Level Market Share Distributions 

for Standards Cases...................................................................................... 10-4

Table 10.2.5 Equipment Class B HFC: Efficiency Level Market Share Distributions 

for Standards Cases...................................................................................... 10-5

Table 10.2.6 Equipment Class B CO2: Efficiency Level Market Share Distributions 

for Standards Cases...................................................................................... 10-5

Table 10.2.7 Combination B HFC Efficiency Level Market Share Distributions for 

Standards Cases ........................................................................................... 10-6

Table 10.3.1 Equipment Class A Refrigerated Beverage Vending Machines: 

Shipment-Weighted Average Annual Energy Use for Base and 

Standards Cases ........................................................................................... 10-8

Table 10.3.2 Equipment Class B Refrigerated Beverage Vending Machines: 

Shipment-Weighted Average Annual Energy Use for Base and 

Standards Cases ........................................................................................... 10-9

Table 10.3.3 Equipment Class Combination Refrigerated Beverage Vending 

Machines: Shipment-Weighted Average Annual Energy Use for Base 

and Standards Cases................................................................................... 10-10

Table 10.4.1 Refrigerated Beverage Vending Machines: Weighted Average 

Installed Price for Base and Standards Cases............................................ 10-14

Table 10.5.1 Inputs to Calculation of National Energy Savings and Net Present 

Value .......................................................................................................... 10-18

Table 10.5.2 Equipment Class A: Cumulative NES Full-Fuel-Cycle Results (quads)... 10-20

Table 10.5.3 Equipment Class B: Cumulative NES Full-Fuel-Cycle Results (quads)... 10-20

Table 10.5.4 Equipment Class Combo A and Combo B: Cumulative NES Full-FuelCycle Results (10-3 quads) ......................................................................... 10-21

Table 10.5.5 Cumulative Net Present Value of Customer Benefits for Equipment 

Class A Refrigerated Beverage Vending Machines, 3-Percent Discount 

Rate ............................................................................................................ 10-22

Table 10.5.6 Cumulative Net Present Value of Customer Benefits for Equipment 

Class A Refrigerated Beverage Vending Machines, 7-Percent Discount 

Rate ............................................................................................................ 10-22

Table 10.5.7 Cumulative Net Present Value of Customer Benefits for Equipment 

Class B Refrigerated Beverage Vending Machines, 3-Percent Discount 

Rate ............................................................................................................ 10-23

Table 10.5.8 Cumulative Net Present Value of Customer Benefits for Equipment 

Class B Refrigerated Beverage Vending Machines, 7-Percent Discount 

Rate ............................................................................................................ 10-23

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Table 10.5.9 Cumulative Net Present Value of Customer Benefits for Equipment 

Class Combination Refrigerated Beverage Vending Machines, 3-

Percent Discount Rate................................................................................ 10-24

Table 10.5.10 Cumulative Net Present Value of Customer Benefits for Equipment 

Class Combination Refrigerated Beverage Vending Machines, 7-

Percent Discount Rate................................................................................ 10-25

LIST OF FIGURES

Figure 10.5.1 Non-Discounted Annual Increases in Installed Cost and Savings in 

Operating Cost for Equipment Class A HFC Refrigerated Beverage 

Vending Machines at Efficiency Level 5................................................... 10-19

10-iii
CHAPTER 10. NATIONAL IMPACT ANALYSIS

10.1 INTRODUCTION

This chapter describes the method the U.S. Department of Energy (DOE) used to conduct 

a national impacts analysis (NIA) of each standard level for refrigerated beverage vending 

machines (BVMs). DOE evaluated the following impacts: (1) national energy savings (NES) 

attributable to each possible standard, (2) monetary value of those energy savings to customers 

of the considered equipment, (3) increased total installed cost of the equipment because of 

standards, and (4) net present value (NPV) of energy savings (the difference between the value 

of energy savings and increased total installed cost). 

DOE determined both the NES and NPV for all the efficiency levels (ELs) considered for 

refrigerated beverage vending machines. DOE performed all calculations for the considered 

equipment using a Microsoft Excel spreadsheet model, which is accessible on the Internet 

(http://www1.eere.energy.gov/buildings/appliance_standards/rulemaking.aspx/ruleid/73). The 

spreadsheets combine the calculations for determining the NES and NPV for each considered 

equipment class with input from the appropriate shipments model. Details and instructions for 

using the NIA model are provided in appendix 10-A. 

Chapter 9 provides a detailed description of the shipments models that DOE used to 

forecast future purchases of the considered equipment. Chapter 9 includes a description of the 

sensitivity of shipments to total installed cost and operating cost, and how DOE captured those 

sensitivities within the NIA model. 

In its preliminary analysis, DOE studied three different equipment classes in detail as 

described in chapter 3, Market and Technology Assessment. To estimate the national impacts of 

potential standards for the equipment considered in this rulemaking, DOE applied the equipment

cost and annual energy consumption estimation to each equipment class considered in this 

analysis.

10.1.1 Alternative Scenarios

The results in this chapter were calculated using selected inputs from the Reference case 

in the Energy Information Administration’s (EIA’s) Annual Energy Outlook 2014 (AEO2014).1

DOE also calculated NIA results using inputs from the High Economic Growth case and the Low 

Economic Growth case in AEO2014. These results can be viewed in the NIA spreadsheet by 

selecting the high or low growth economic scenario.

10.2 FORECASTED EFFICIENCIES FOR BASE AND STANDARDS CASES 

A key factor in estimating NES and NPV is the trend in energy efficiency forecasted for 

the base case (without amended standards) and each of the standards cases. In calculating the 

NES, per-unit annual energy consumption is a direct function of equipment efficiency. For the 

NPV, two inputs depend on efficiency. The first input, the per-unit total installed cost, is a direct 

function of efficiency. The per-unit annual operating cost, because it is a function of the per-unit 

10-1
annual consumption, is indirectly dependent on equipment efficiency. This section describes the 

method DOE used to forecast the energy efficiency distribution of the considered equipment 

under the base case and each of the potential standards cases. 

10.2.1 Base Case Efficiencies

The base case market share distribution of ELs in the compliance year is discussed in 

chapter 8, and shown in the tables below. DOE assumed that the distribution would remain the 

same for all years in the shipments forecast period.

Table 10.2.1 Base Case Estimated and Forecast Efficiency Level Market Share 

Distributions for Equipment Class A Refrigerated Beverage Vending 

Machines

Market Shares (%)

Efficiency Level HFC CO2

0 4.67 4.67

1 45.26 45.26

2 21.46 21.46

3 21.46 21.46

4 7.15 7.15

5 0.00 0.00

6 0.00 0.00

7 0.00 0.00

8 0.00 0.00

9 0.00 0.00

10-2
Table 10.2.2 Base Case Estimated and Forecast Efficiency Level Market Share 

Distributions for Equipment Class B Refrigerated Beverage Vending 

Machines

Market Shares (%)

Efficiency Level HFC CO2

0 5.83 5.83

1 0.00 0.00

2 7.75 7.75

3 28.29 28.29

4 7.75 7.75

5 11.63 11.63

6 3.88 3.88

7 15.50 15.50

8 11.63 11.63

9 0.00 0.00

10 3.88 7.75

11 3.88

For combination refrigerated beverage vending machines there is currently no standard 

and no ENERGY STAR specification; therefore, there is less incentive for manufacturers to 

make these machines exhibit a high level of energy efficiency. DOE therefore assumes 100

percent of the market will be at the minimum efficiency level in the base case. 

10.2.1.1 Standards Case Efficiencies

Table 10.2.3 through Table 10.2.6 show the efficiency distributions that DOE used for 

equipment class A and B refrigerated beverage vending machines under each standards case. The 

tables include the shipment-weighted energy use factor (SWEUF) associated with each standards 

case. In the absence of other data, DOE assumed that the standard case distribution of efficiency 

levels remains static in the future.

10-3
Table 10.2.3 Equipment Class A HFC: Efficiency Level Market Share Distributions for 

Standards Cases

Efficiency 

Level

Energy 

Use 

Factor

Market Share (%)

Base 

Case

Standard at Efficiency Level:

1 2 3 4 5 6 7 8 9

EL0 1.00 4.7 - - - - - - - - -

EL1 0.95 45.3 49.9 - - - - - - - -

EL2 0.90 21.5 21.5 71.4 - - - - - - -

EL3 0.85 21.5 21.5 21.5 92.8 - - - - - -

EL4 0.80 7.2 7.2 7.2 7.2 100.0 - - - - -

EL5 0.75 0.0 0.0 0.0 0.0 0.0 100.0 - - - -

EL6 0.70 0.0 0.0 0.0 0.0 0.0 0.0 100.0 - - -

EL7 0.65 0.0 0.0 0.0 0.0 0.0 0.0 0.0 100.0 - -

EL8 0.60 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 100.0 -

EL9 0.57 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 100.0

SWEUF 0.909 0.907 0.882 0.846 0.800 0.750 0.700 0.650 0.600 0.570

Table 10.2.4 Equipment Class A CO2: Efficiency Level Market Share Distributions for 

Standards Cases

Efficiency 

Level

Energy 

Use 

Factor

Market Share

Base 

Case

Standard at Efficiency Level:

1 2 3 4 5 6 7 8 9

EL0 1.00 4.7 - - - - - - - - -

EL1 0.95 45.3 49.9 - - - - - - - -

EL2 0.90 21.5 21.5 71.4 - - - - - - -

EL3 0.85 21.5 21.5 21.5 92.8 - - - - - -

EL4 0.80 7.2 7.2 7.2 7.2 100.0 - - - - -

EL5 0.75 0.0 0.0 0.0 0.0 0.0 100.0 - - - -

EL6 0.70 0.0 0.0 0.0 0.0 0.0 0.0 100.0 - - -

EL7 0.65 0.0 0.0 0.0 0.0 0.0 0.0 0.0 100.0 - -

EL8 0.60 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 100.0 -

EL9 0.59 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 100.0

SWEUF 0.909 0.907 0.882 0.846 0.800 0.750 0.700 0.650 0.600 0.590

10-4
Table 10.2.5 Equipment Class B HFC: Efficiency Level Market Share Distributions for 

Standards Cases

Efficiency 

Level

Energy 

Use 

Factor

Market Share

Base 

Case

Standard at Efficiency Level:

1 2 3 4 5 6 7 8 9 10 11

EL0 1.00 5.8 - - - - - - - - - - -

EL1 0.95 0.0 5.8 - - - - - - - - - -

EL2 0.90 7.8 7.8 13.6 - - - - - - - - -

EL3 0.85 28.3 28.3 28.3 41.9 - - - - - - - -

EL4 0.80 7.8 7.8 7.8 7.8 49.6 - - - - - - -

EL5 0.75 11.6 11.6 11.6 11.6 11.6 61.3 - - - - - -

EL6 0.70 3.9 3.9 3.9 3.9 3.9 3.9 65.1 - - - - -

EL7 0.65 15.5 15.5 15.5 15.5 15.5 15.5 15.5 80.6 - - - -

EL8 0.60 11.6 11.6 11.6 11.6 11.6 11.6 11.6 11.6 92.3 - - -

EL9 0.55 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 92.3 - -

EL10 0.50 3.9 3.9 3.9 3.9 3.9 3.9 3.9 3.9 3.9 3.9 96.1 -

EL11 0.49 3.9 3.9 3.9 3.9 3.9 3.9 3.9 3.9 3.9 3.9 3.9 100.0

SWEUF 0.754 0.751 0.748 0.741 0.720 0.695 0.665 0.632 0.592 0.546 0.500 0.490

Table 10.2.6 Equipment Class B CO2: Efficiency Level Market Share Distributions for

Standards Cases

Efficiency 

Level

Energy 

Use 

Factor

Market Share

Base 

Case

Standard at Efficiency Level:

1 2 3 4 5 6 7 8 9 10

EL0 1.00 5.8 - - - - - - - - - -

EL1 0.95 0.0 5.8 - - - - - - - - -

EL2 0.90 7.8 7.8 13.6 - - - - - - - -

EL3 0.85 28.3 28.3 28.3 41.9 - - - - - - -

EL4 0.80 7.8 7.8 7.8 7.8 49.6 - - - - - -

EL5 0.75 11.6 11.6 11.6 11.6 11.6 61.3 - - - - -

EL6 0.70 3.9 3.9 3.9 3.9 3.9 3.9 65.1 - - - -

EL7 0.65 15.5 15.5 15.5 15.5 15.5 15.5 15.5 80.6 - - -

EL8 0.60 11.6 11.6 11.6 11.6 11.6 11.6 11.6 11.6 92.3 - -

EL9 0.55 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 92.3 -

EL10 0.50 7.8 7.8 7.8 7.8 7.8 7.8 7.8 7.8 7.8 7.8 100.0

SWEUF 0.754 0.751 0.748 0.741 0.721 0.696 0.665 0.633 0.592 0.546 0.500

10-5
For all four types of combination refrigerated beverage vending machines, the market is 

assumed to be 100% at the standards case level. See Table 10.2.7 for an example. 

Table 10.2.7 Combination B HFC Efficiency Level Market Share Distributions for 

Standards Cases

Efficiency 

Level

Energy 

Use 

Factor

Market Share

Base 

Case

Standard at Efficiency Level:

1 2 3 4 5 6 7 8

EL0 1.00 100.0 - - - - - - - -

EL1 0.90 0.0 100.0 - - - - - - -

EL2 0.80 0.0 0.0 100.0 - - - - - -

EL3 0.70 0.0 0.0 0.0 100.0 - - - - -

EL4 0.60 0.0 0.0 0.0 0.0 100.0 - - - -

EL5 0.55 0.0 0.0 0.0 0.0 0.0 100.0 - - -

EL6 0.50 0.0 0.0 0.0 0.0 0.0 0.0 100.0 - -

EL7 0.45 0.0 0.0 0.0 0.0 0.0 0.0 0.0 100.0 -

EL8 0.41 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 100.0

SWEUF 1.000 0.900 0.800 0.700 0.600 0.550 0.500 0.450 0.410

10.3 NATIONAL ENERGY SAVINGS

DOE calculated the national energy savings associated with the difference between the 

base case and the case associated with each potential standard for the BVM equipment

considered herein. DOE calculated cumulative energy savings throughout the forecast period, 

which extends from 2019 to 2048. DOE used full-fuel-cycle (FFC) energy factors to estimate 

national energy savings; see section 10.3.2.6.

10.3.1 Definition 

The following equation shows that DOE calculated annual NES as the difference between 

two projections: a base case (without amended standards) and a standards case. Positive values 

of NES represent energy savings (that is, national annual energy consumption (AEC) under a 

standard is less than in the base case).

STD

_

BASE NESy = AEC AEC

Cumulative energy savings are the sum of annual national energy savings throughout the 

forecast period, which extends over the lifetime of equipment shipped in 2019-2048. Since the 

analysis includes lifetimes of up to 30 years, the evaluation period for cumulative energy savings 

spans 2019-2078.

10-6
DOE calculated the national annual site energy consumption by multiplying the number 

or stock of each equipment class (by vintage) by its unit energy consumption (UEC; also by 

vintage). The calculation of national annual energy consumption is represented by the following 

equation.

y = ∑ V ×UECV AEC STOCK

DOE defined the quantities for the two previous expressions as follows.

AEC = national annual energy consumption each year in quadrillion British thermal units 

(quads), summed over vintages of the equipment stock, STOCKV,

NES = annual national energy savings (quads),

STOCKV = stock of equipment (millions of units) of vintage V that survive in the year 

for which DOE calculated annual energy consumption,

UECV = annual energy consumption per equipment in kilowatt-hours (kWh),

V = year in which the equipment was purchased as a new unit, and 

y = year in the forecast.

Electricity consumption is converted from site energy to source energy (quads) by 

applying a time-dependent conversion factor.

The stock of equipment depends on annual shipments and the equipment lifetime. As 

described in chapter 9, DOE projected shipments under the base case and the standards cases. 

DOE projected that in some instances shipments under the standards cases would be lower than 

under the base case, because DOE believes that the higher purchase cost of more-efficient 

equipment would cause some customers to forego purchasing new equipment. 

To avoid including savings attributable to shipments displaced because of standards, 

DOE used the projected standards-case shipments and, in turn, the standards-case stock, to 

calculate the annual energy consumption for the base case. 

10.3.2 Inputs 

The inputs to the calculation of NES are:

• shipments;

• equipment stock (STOCKV);

• annual energy consumption per unit (UEC);

• national annual energy consumption (AEC); and

• site-to-source conversion factor (src_conv).

10.3.2.1 Shipments

DOE forecasted shipments of each considered equipment class under the base case and 

all standards cases. Several factors affect forecasted shipments, including purchase cost,

10-7
operating cost, and profitability. As noted earlier, the increased cost of more-efficient equipment

causes some customers to forego buying the equipment. Consequently, in some instances 

shipments forecasted under the standards cases are lower than under the base case. The method 

DOE used to calculate and generate the shipments forecasts for each considered equipment class 

is described in detail in chapter 9, Shipments Analysis.

10.3.2.2 Equipment Stock

The equipment stock in a given year is the number of each type of equipment shipped 

from earlier years that survive in that year. The NIA model tracks the number of units shipped 

each year. DOE assumes that refrigerated beverage vending machines have an increasing 

probability of retiring as they age. The probability of survival as a function of years since

purchase is the survival function. Chapter 8 provides additional details on the survival functions 

that DOE used.

10.3.2.3 Annual Energy Consumption per Unit

DOE used the SWEUFs presented in section 10.2 for the base case and standards cases, 

along with the data on annual energy consumption presented in chapters 7 and 8, to estimate the 

shipment-weighted average annual per-unit energy consumption under the base and each 

standards case. The average annual per-unit energy consumption for each equipment category is 

shown in the tables below.

Table 10.3.1 Equipment Class A Refrigerated Beverage Vending Machines: ShipmentWeighted Average Annual Energy Use for Base and Standards Cases

Standard at Efficiency Level:

0 1 2 3 4 5 6 7 8 9

Equipment Class A (Total)

SWEUF 0.909 0.907 0.882 0.846 0.800 0.750 0.700 0.650 0.600 0.579

Avg. energy 

use (kWh)

1,387 1,383 1,345 1,291 1,220 1,144 1,067 991 915 883 

A HFC

SWEUF 0.909 0.907 0.882 0.846 0.800 0.750 0.700 0.650 0.600 0.570

Avg. energy 

use (kWh)

1,387 1,383 1,345 1,291 1,220 1,144 1,067 991 915 869 

A CO2

SWEUF 0.909 0.907 0.882 0.846 0.800 0.750 0.700 0.650 0.600 0.590

Avg. energy 

use (kWh)

1,387 1,383 1,345 1,291 1,220 1,144 1,067 991 915 900 

SWEUF = shipment-weighted energy use factor

10-8
Table 10.3.2 Equipment Class B Refrigerated Beverage Vending Machines: ShipmentWeighted Average Annual Energy Use for Base and Standards Cases

Standard at Efficiency Level

0 1 2 3 4 5 6 7 8 9 10 11

Equipment Class B (Total)

SWEUF 0.754 0.751 0.748 0.741 0.720 0.696 0.665 0.632 0.592 0.546 0.500 0.490

Avg. energy 

use (kWh)

1,294 1,289 1,284 1,273 1,237 1,194 1,142 1,086 1,016 937 858 

841

B HFC

SWEUF 0.754 0.751 0.748 0.741 0.720 0.695 0.665 0.632 0.592 0.546 0.500 0.490

Avg. energy 

use (kWh)

1,294 1,289 1,284 1,272 1,236 1,194 1,141 1,085 1,016 937 858 841 

B CO2

SWEUF 0.754 0.751 0.748 0.741 0.721 0.696 0.665 0.633 0.592 0.546 0.500

Avg. energy 

use (kWh)

1,295 1,290 1,285 1,273 1,237 1,194 1,142 1,086 1,017 938 858 

SWEUF = shipment-weighted energy use factor

10-9
Table 10.3.3 Equipment Class Combination Refrigerated Beverage Vending Machines: 

Shipment-Weighted Average Annual Energy Use for Base and Standards 

Cases

Standard at Efficiency Level

0 1 2 3 4 5 6 7 8 9 10 11

Equipment Class Combination (Total)

SWEUF 1.000 0.900 0.800 0.700 0.600 0.550 0.500 0.450 0.405 0.350 0.300 0.290

Avg. energy 

use (kWh) 1970 1773 1576 1379 1182 1084 985 887 797 778 667 644

Combo A HFC

SWEUF 1.000 0.900 0.800 0.700 0.600 0.550 0.500 0.450 0.400 0.350 0.300 0.290

Avg. energy 

use (kWh) 2222 2000 1778 1556 1333 1222 1111 1000 889 778 667 644

Combo A CO2

SWEUF 1.000 0.900 0.800 0.700 0.600 0.550 0.500 0.450 0.400 0.350 0.300 0.290

Avg. energy 

use (kWh) 2222 2000 1778 1556 1333 1222 1111 1000 889 778 667 644

Combo B HFC

SWEUF 1.000 0.900 0.800 0.700 0.600 0.550 0.500 0.450 0.410

Avg. energy 

use (kWh) 1718 1546 1374 1203 1031 945 859 773 704

Combo B CO2

SWEUF 1.000 0.900 0.800 0.700 0.600 0.550 0.500 0.450 0.410

Avg. energy 

use (kWh) 1718 1546 1374 1203 1031 945 859 773 704

SWEUF = shipment-weighted energy use factor

10.3.2.4 National Annual Energy Consumption

The national AEC is the product of the annual energy consumption per unit and the 

number of units of each vintage. This method of calculation accounts for differences in unit 

energy consumption from year to year. In determining national annual energy consumption, 

DOE first calculated annual energy consumption at the site, then applied a conversion factor and 

a full-fuel-cycle energy factor, described in section 10.3.2.5 and section 10.3.2.6, to calculate 

primary energy consumption. 

10.3.2.5 Site-to-Primary Energy Conversion Factors

In determining national annual energy consumption, DOE initially calculated the annual 

energy consumption at the site (for electricity, the energy in kWh consumed at the 

establishment). It then used site energy consumption to calculate primary (source) energy 

10-10
consumption by applying a conversion factor to account for losses associated with the 

generation, transmission, and distribution of electricity. The conversion factor is a multiplicative 

factor used to convert site energy consumption into primary or source energy consumption, 

expressed in quads (quadrillion Btu). DOE used annual conversion factors based on the version 

of the National Energy Modeling System (NEMS)a that corresponds to AEO2014. The factors 

are marginal values, which represent the response of the system to an incremental decrease in 

consumption. For electricity, the conversion factors change over time in response to projected 

changes in generation sources (i.e., the types of power plants projected to provide electricity to 

the Nation). The values derived from the AEO2014 NEMS end in 2040. DOE assumed that 

conversion factors remain at the 2040 values throughout the rest of the forecast.

10.3.2.6 Full-Fuel-Cycle Energy Factors

The full-fuel-cycle (FFC) measures point-of-use (site) energy; the energy losses 

associated with generation, transmission, and distribution of electricity; and the energy 

consumed in extracting, processing, and transporting or distributing primary fuels. To calculate 

the FFC by incorporating the energy consumed in extracting, processing, and transporting or 

distributing primary fuels, referred to as upstream activities, DOE developed FFC multipliers 

using the data and projections generated by the NEMS used for AEO 2013. The AEO 2013

provides extensive information about the energy system, including projections of future oil, 

natural gas, and coal supplies; energy use for oil and gas field and refinery operations; and fuel 

consumption and emissions related to electric power production. This information can help 

define a set of parameters that represents the energy intensity of energy production. 

10.4 NET PRESENT VALUE

DOE calculated the NPV of the increased product cost and reduced operating cost 

associated with the difference between the base case and each potential standards case for the 

considered refrigerated beverage vending machine equipment classes. 

10.4.1 Definition

The NPV is the value in the present of a time-series of costs and savings. The NPV is 

described by the equation:

NPV PVS PVC _ =

a For more information on NEMS, please refer to the U.S. Department of Energy, Energy Information 

Administration documentation. A useful summary is National Energy Modeling System: An Overview 2000, 

DOE/EIA-0581(2000), March 2000. EIA approves use of the name NEMS to describe only an official version of 

the model without any modification to code or data. Because this analysis entails some minor code modifications 

and the model is run under various policy scenarios that are variations on EIA assumptions, DOE refers to the model 

by the name NEMS-BT (BT is DOE’s Building Technologies Program, under whose aegis this work has been 

performed). NEMS-BT was previously called NEMS-BRS.

10-11

 
Where:

PVS = present value of savings in operating cost, and 

PVC = present value of increased total product cost to customers. 

DOE determined the PVS and PVC according to the following expressions.

PVS = ∑OCSy× DFy

PVC = ∑TICy× DFy

Where:

OCS = total annual savings in operating cost each year summed over vintages of the 

equipment stock, STOCKV,

TIC = total annual increases in product cost each year summed over years of the 

equipment shipments, SHIPy,

DF = discount factor in each year, and 

y = year in the forecast.

DOE calculated the total annual customer savings in operating cost by multiplying the 

number or stock of a given equipment class (by vintage) by its per-unit operating cost savings 

(also by vintage). DOE calculated the total annual increases in customer equipment cost by 

multiplying the number of shipments of the given equipment class (by vintage) by its per-unit 

increase in customer equipment cost (also by vintage). The calculation of total annual operating 

cost savings and total annual equipment cost increases is represented by the following equations.

OCSy = ∑STOCKV ×UOCSV

TICy = ∑SHIPy ×UTICy

Where:

STOCKV = stock of equipment of vintage V that survive in the year for which DOE 

calculated annual energy consumption,

UOCSV = annual per-unit savings in operating cost,

V = year in which the equipment was purchased as a new unit,

SHIPy = shipments of equipment in year y, and

UTICy = annual per-unit increase in installed equipment cost in year y.

DOE determined the total increased equipment cost for each year from the effective date 

of a potential standard (2019) to 2048. It determined the present value of operating cost savings 

for each year from the effective date of the standard to the year when all units purchased by 2048

have been retired. DOE calculated costs and savings as the difference between a standards case 

and a base case without amended standards.

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DOE developed a discount factor from the national discount rate and the number of years 

between the present (i.e., year to which the sum is being discounted) and the year in which the

costs and savings occur. The NPV is the sum over time of the discounted net savings.

10.4.2 Inputs

The inputs to calculation of the NPV are: 

• average annual equipment cost;

• average annual savings in operating cost;

• total annual increases in equipment cost;

• total annual savings in operating cost; 

• discount factor;

• present value of costs; and

• present value of savings.

The increase in total annual equipment cost is equal to the annual change in the average 

annual equipment cost (difference between base case and standards case) multiplied by the 

shipments forecasted in the standards case. As with the calculation of the NES, DOE did not 

calculate total annual equipment costs using base-case shipments. To avoid including savings 

due to displaced shipments (by customers deciding not to buy higher-cost equipment), DOE used 

the standards-case projection of shipments and, in turn, the standards-case stock, to calculate 

equipment costs. 

The total annual savings in operating cost are equal to the change in annual operating cost 

(difference between base case and standards case) per unit multiplied by the shipments

forecasted in the standards case. 

10.4.2.1 Average Annual Installed Price

The average annual installed price is directly dependent on efficiency. DOE therefore 

used the efficiency distributions presented in section 10.2.1.1 for the base case and each 

standards case, along with the equipment costs at various ELs (presented in chapter 8), to 

estimate the weighted-average annual installed price under the base and standards cases. The 

average annual installed price for each equipment category is shown in Table 10.4.1.

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Table 10.4.1 Refrigerated Beverage Vending Machines: Weighted Average Installed

Price for Base and Standards Cases

Standard at Efficiency Level

0 1 2 3 4 5 6 7 8 9 10 11

Equipment Class A (Total)

SWEUF 0.909 0.907 0.882 0.846 0.800 0.750 0.700 0.650 0.600 0.579

Avg. Installed 

Price (2013$)

2,438 2,438 2,441 2,450 2,489 2,541 2,723 2,965 3,208 3,309 

A HFC

SWEUF 0.909 0.907 0.882 0.846 0.800 0.750 0.700 0.650 0.600 0.570

Avg. Installed 

Price (2013$)

2,401 2,401 2,404 2,412 2,447 2,499 2,647 2,894 3,141 3,289 

A CO2

SWEUF 0.909 0.907 0.882 0.846 0.800 0.750 0.700 0.650 0.600 0.590

Avg. Installed 

Price (2013$)

2,479 2,480 2,483 2,493 2,536 2,590 2,809 3,047 3,285 3,333 

Equipment Class B (Total)

SWEUF 0.754 0.751 0.748 0.741 0.720 0.696 0.665 0.632 0.592 0.546 0.500 0.490

Avg. Installed 

Price (2013$)

2,200 2,200 2,200 2,200 2,201 2,206 2,222 2,265 2,358 2,688 3,046 3050

B HFC

SWEUF 0.754 0.751 0.748 0.741 0.720 0.695 0.665 0.632 0.592 0.546 0.500 0.490

Avg. Installed 

Price (2013$)

2,157 2,157 2,157 2,157 2,158 2,162 2,178 2,218 2,280 2,607 2,974 3,050 

B CO2

SWEUF 0.754 0.751 0.748 0.741 0.721 0.696 0.665 0.633 0.592 0.546 0.500

Avg. Installed 

Price (2013$)

2,249 2,249 2,249 2,250 2,251 2,255 2,272 2,319 2,447 2,781 3,129 

Equipment Class Combination (Total)

SWEUF 1.000 0.900 0.800 0.700 0.600 0.550 0.500 0.450 0.405 0.350 0.300 0.290

Avg. Installed 

Price (2013$) 2071 2074 2079 2093 2115 2131 2167 2229 2463 2482 3013 3123

Combo A HFC

SWEUF 1.000 0.900 0.800 0.700 0.600 0.550 0.500 0.450 0.400 0.350 0.300 0.290

Avg. Installed 

Price (2013$) 2230 2235 2242 2259 2280 2290 2301 2313 2342 2445 2984 3096

Combo A CO2

SWEUF 1.000 0.900 0.800 0.700 0.600 0.550 0.500 0.450 0.400 0.350 0.300 0.290

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Avg. Installed 

Price (2013$) 2288 2293 2302 2321 2342 2353 2364 2378 2407 2519 3041 3150

Combo B HFC

SWEUF 1.000 0.900 0.800 0.700 0.600 0.550 0.500 0.450 0.410

Avg. Installed 

Price (2013$) 1854 1855 1858 1868 1891 1910 1973 2088 2543

Combo B CO2

SWEUF 1.000 0.900 0.800 0.700 0.600 0.550 0.500 0.450 0.410

Avg. Installed 

Price (2013$) 1911 1912 1915 1926 1949 1971 2032 2135 2561

SWEUF = shipment-weighted energy use factor

As discussed in chapter 8, examination of historical price data for certain appliances and 

equipment that have been subject to energy conservation standards indicates that the assumption 

of constant real prices and costs may, in many cases, over-estimate long-term appliance and 

equipment price trends.

For this preliminary analysis for refrigerated beverage vending machines, DOE applied 

the default equipment price trend based on an exponential fit function derived using historical 

data on refrigeration equipment Producer Price Index (PPI) (described in chapter 8) to project the 

prices of refrigerated beverage vending machines sold in each year in the forecast period (2019-

2048). DOE applied the same price factors to project prices for each equipment class at each 

considered EL. The average annual rate of price decline in the default case is 1.48 percent.

To investigate the impact of different equipment price projections on the customer net 

present value (NPV) for different efficiency levels, DOE also considered two alternative price 

trends. Details on how these alternative price trends were developed are documented in appendix 

10-B which also presents the results of the sensitivity analysis.

10.4.2.2 Annual Operating Cost Savings per Unit

The average annual operating cost includes the costs for energy, repair, and maintenance. 

As described in chapter 8, DOE assumed that repair and maintenance costs were lower at 

increased efficiency levels in some equipment classes (specifically, B and Combination). 

Therefore, for all the considered equipment, DOE determined the per-unit annual savings in 

operating cost based on the savings in energy costs plus repair and maintenance costs attributable 

to a standard. DOE determined the per-unit annual savings in energy cost by multiplying the perunit annual savings in energy consumption developed for each equipment class by the 

appropriate energy price. As described in chapter 8, DOE forecasted energy prices based on 

projected average annual price changes in EIA’s AEO2014. 

10.4.2.3 Total Annual Increases in Equipment Cost 

The total annual increase in equipment cost for any given standards case is the product of 

the average cost increase per unit due to the standard and the number of units of each vintage 

10-15
shipped. This method accounts for differences in equipment cost from year to year. The equation 

for determining the total annual increase in equipment cost for a given standards case, which was 

shown in section 10.4.1, is repeated here.

TICy = ∑SHIPy ×UTICy

As with the calculation of the NES, DOE did not calculate total annual equipment costs 

using base-case shipments. To avoid including savings due to displaced shipments (by customers

deciding not to buy higher-cost equipment), DOE used the standards-case projection of 

shipments and, in turn, the standards-case stock, to calculate equipment costs. 

10.4.2.4 Total Annual Savings in Operating Cost 

The total annual savings in operating cost for any given standards case is the product of 

the annual savings in operating cost per unit attributable to the standard and the number of units 

of each vintage. This method accounts for differences in annual savings in operating cost from 

year to year. The equation for determining the total annual savings in operating cost for a given 

standards case, which was presented in section 10.4.1, is repeated here. 

OCS = ∑STOCKV ×UOCSV

10.4.2.5 Discount Factor

DOE multiplied monetary values in future years by a discount factor to determine the

present value. The discount factor (DF) is described by the equation:

( y yp ) _

( r )

DF

1+

1 =

Where:

r = discount rate, 

y = year in which the monetary value exists, and 

yP = year in which the present value is being determined.

Although DOE used customer discount rates to determine the life-cycle cost of 

refrigerated beverage vending machines (chapter 8), it used national discount rates to calculate 

national NPV. DOE estimated NPV using both a 3-percent and a 7-percent real discount rate, in 

accordance with the Office of Management and Budget’s guidance to Federal agencies on the 

development of regulatory analysis, particularly section E therein: Identifying and Measuring 

Benefits and Costs.

2 DOE defined the present year as 2013.

10.4.2.6 Present Value of Costs

The present value of increased equipment costs is the annual total cost increase in each 

year (the difference between a standards case and the base case), discounted to the present, and 

summed throughout the period in which DOE is considering the installation of equipment (2019

10-16
through 2048). DOE calculated annual increases in installed cost as the difference in total 

equipment cost for new appliances purchased each year, multiplied by the shipments in the 

standards case.

10.4.2.7 Present Value of Savings

The present value of savings in operating cost is the annual savings on operating cost (the 

difference between the base case and a standards case), discounted to the present and summed 

from the effective date to the time when the last unit installed in 2048 is retired from service.

Savings are decreases in operating cost associated with the higher energy efficiency of 

equipment purchased in the standards case compared to the base case. Total annual savings in 

operating cost are the savings per unit multiplied by the number of units of each vintage that 

survive in a particular year. 

10.5 NATIONAL ENERGY SAVINGS AND NET PRESENT VALUE RESULTS 

The NIA model produces estimates of the NES and NPV attributable to a given 

efficiency level. The inputs to the NIA model were discussed in sections 10.3.2 (inputs to NES) 

and 10.4.2 (inputs to NPV). DOE generated the NES and NPV results using a Microsoft Excel 

spreadsheet, which is accessible on the Internet 

(http://www1.eere.energy.gov/buildings/appliance_standards/rulemaking.aspx/ruleid/73). Details 

regarding and instructions for using the spreadsheet are provided in appendix 10-A.

10.5.1 Summary of Inputs

Table 10.5.1 summarizes the inputs to the NIA model. 

10-17
Table 10.5.1 Inputs to Calculation of National Energy Savings and Net Present Value 

Input Description

Shipments Annual shipments from shipments model. (See chapter 9.)

Compliance date of standard 2019 

Base-case forecasted efficiencies See section 10.2.

Standards-case efficiencies See section 10.2.

Annual energy consumption per unit Annual weighted-average values are a function of SWEUF. 

(See section 10.3.2.3.)

Total installed cost per unit Annual weighted-average values are a function of the 

efficiency distribution. (See section 10.4.2.1.)

Energy cost per unit

Annual weighted-average values are a function of annual 

energy consumption per unit and energy prices. (See chapter 

8 for energy prices.)

Repair and maintenance costs per 

unit

Repair cost and maintenance costs vary with efficiency level

for some equipment classes. (See chapter 8.)

Forecast of energy prices

Energy prices: EIA AEO2014 forecasts (to 2040) and 

extrapolation thereafter. (See chapter 8.)

Site-to-source conversion factor

A time-series conversion factor that includes electric 

generation, transmission, and distribution losses. Conversion, 

which changes yearly, is generated by DOE-EIA’s NEMS* 

program.

Discount rates 3% and 7% real.

Present year Future expenses are discounted to 2013.

* Chapter 15, Utility Impact Analysis, provides more detail on the National Energy Modeling System (NEMS)

10.5.2 Annual Costs and Savings

Figure 10.5.1 illustrates the basic inputs to the calculation of NPV by showing the nondiscounted annual increases in equipment cost and annual savings in operating cost at the 

national level for efficiency level 5 for equipment class A subcategory HFC refrigerated 

beverage vending machines. The figure also shows the net savings, which is the difference 

between the savings and costs for each year. The annual increase in equipment cost is the total 

cost for equipment purchased each year in the forecast period. The annual savings in operating 

cost applies to equipment operating in each year. The NPV is the difference between the 

cumulative annual discounted savings and cumulative annual discounted costs. Figure 10.5.1

shows, as an example, non-discounted annual increases in installed cost and savings in operating 

cost for equipment class A subcategory HFC at efficiency level 5; DOE could create figures like 

Figure 10.5.1 for each of the considered efficiency levels for each equipment subcategory.

10-18
Figure 10.5.1 Non-Discounted Annual Increases in Installed Cost and Savings in Operating 

Cost for Equipment Class A HFC Refrigerated Beverage Vending Machines

at Efficiency Level 5

10.5.3 National Energy Savings Results by Energy Efficiency Level

This section provides the cumulative national energy savings that DOE calculated for 

each of the ELs analyzed for refrigerated beverage vending machines. Note that values in Table 

10.5.2 and Table 10.5.3 are in quads, whereas values in Table 10.5.4 are in 10-3 quads.

-4.0

-2.0

0.0

2.0

4.0

6.0

8.0

10.0

Million 2013$

Year

Operating Cost Savings

Increased Equipment

Cost

Net Savings

10-19
Table 10.5.2 Equipment Class A: Cumulative NES Full-Fuel-Cycle Results (quads)

Efficiency Level HFC CO2 Total

1 0.0003 0.0003 0.0007

2 0.0038 0.0038 0.0076

3 0.0088 0.0088 0.0176

4 0.0154 0.0153 0.0306

5 0.0223 0.0222 0.0446

6 0.0292 0.0290 0.0582

7 0.0358 0.0355 0.0713

8 0.0422 0.0420 0.0842

9 0.0460 0.0432 0.0892

Table 10.5.3 Equipment Class B: Cumulative NES Full-Fuel-Cycle Results (quads)

Efficiency Level HFC CO2 Total

1 0.0005 0.0005 0.0009

2 0.0009 0.0009 0.0018

3 0.0020 0.0020 0.0040

4 0.0053 0.0053 0.0106

5 0.0092 0.0092 0.0184

6 0.0141 0.0140 0.0281

7 0.0192 0.0191 0.0383

8 0.0255 0.0253 0.0509

9 0.0323 0.0320 0.0643

10 0.0387 0.0385 0.0773

11 0.0401 0.0401

10-20
Table 10.5.4 Equipment Class Combo A and Combo B: Cumulative NES Full-Fuel-Cycle 

Results (10-3 quads)

Efficiency 

Level Combo-A HFC Combo-A CO2 Combo-B HFC Combo-B CO2 Total

1 0.417 0.416 0.323 0.321 1.477

2 0.835 0.831 0.645 0.642 2.954

3 1.252 1.247 0.968 0.964 4.430

4 1.669 1.662 1.290 1.285 5.907

5 1.878 1.870 1.452 1.446 6.646

6 2.087 2.078 1.613 1.606 7.384

7 2.296 2.286 1.774 1.767 8.123

8 2.504 2.494 1.867 1.865 8.730

9 2.713 2.701 5.414

10 2.893 2.881 5.774

11 2.920 2.909 5.829

10.5.4 Customer Net Present Value Results by Energy Efficiency Level

Table 10.5.5 through Table 10.5.10 show the cumulative NPV associated with each of the 

considered ELs for each refrigerated beverage vending machine equipment class. Results in

Table 10.5.5, Table 10.5.7, and Table 10.5.9 are shown as the discounted dollar values using a 

3% discount rate, and results in Table 10.5.6, Table 10.5.8, and Table 10.5.10 are shown as the 

discounted dollar value of the net savings using a 7% discount rate. Note that values in Table 

10.5.5 through Table 10.5.8 are in billion 2013 dollars, whereas values in Table 10.5.9 and Table 

10.5.10 are in million 2013 dollars.

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Table 10.5.5 Cumulative Net Present Value of Customer Benefits for Equipment Class A

Refrigerated Beverage Vending Machines, 3-Percent Discount Rate

Efficiency 

Level HFC CO2 Total

Billion 2013 dollars

1 0.0017 0.0017 0.0034

2 0.0196 0.0194 0.0391

3 0.0440 0.0431 0.0870

4 0.0680 0.0641 0.1320

5 0.0890 0.0847 0.1737

6 0.0793 0.0525 0.1318

7 0.0384 0.0151 0.0535

8 -0.0015 -0.0214 -0.0229

9 -0.0250 -0.0286 -0.0535

Table 10.5.6 Cumulative Net Present Value of Customer Benefits for Equipment Class A

Refrigerated Beverage Vending Machines, 7-Percent Discount Rate

Efficiency 

Level HFC CO2 Total

Billion 2013 dollars

1 0.0007 0.0007 0.0014

2 0.0079 0.0078 0.0157

3 0.0175 0.0170 0.0345

4 0.0259 0.0237 0.0496

5 0.0323 0.0299 0.0622

6 0.0220 0.0076 0.0296

7 -0.0050 -0.0173 -0.0223

8 -0.0312 -0.0415 -0.0727

9 -0.0466 -0.0463 -0.0929

10-22
Table 10.5.7 Cumulative Net Present Value of Customer Benefits for Equipment Class B 

Refrigerated Beverage Vending Machines, 3-Percent Discount Rate

Efficiency 

Level HFC CO2 Total

Billion 2013 dollars

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 0.0561

5 0.0479 0.0476 0.0955

6 0.0690 0.0681 0.1371

7 0.0840 0.0807 0.1647

8 0.0982 0.0741 0.1723

9 0.0329 0.0077 0.0407

10 -0.0420 -0.0601 -0.1022

11 -0.0572 -0.0572

Table 10.5.8 Cumulative Net Present Value of Customer Benefits for Equipment Class B 

Refrigerated Beverage Vending Machines, 7-Percent Discount Rate

Efficiency 

Level HFC CO2 Total

Billion 2013 dollars

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 0.0273 0.0268 0.0542

7 0.0318 0.0300 0.0618

8 0.0349 0.0219 0.0569

9 -0.0054 -0.0188 -0.0242

10 -0.0506 -0.0599 -0.1105

11 -0.0597 -0.0597

10-23
Table 10.5.9 Cumulative Net Present Value of Customer Benefits for Equipment Class 

Combination Refrigerated Beverage Vending Machines, 3-Percent Discount 

Rate

Efficiency 

Level Combo-A HFC Combo-A CO2

Combo-B 

HFC

Combo-B 

CO2

Total

Million 2013 dollars

1 2.22 2.20 1.73 1.72 7.87

2 4.41 4.38 3.44 3.42 15.66

3 6.56 6.49 5.12 5.08 23.25

4 8.67 8.59 6.71 6.66 30.62

5 9.72 9.63 7.45 7.38 34.18

6 10.77 10.68 7.91 7.85 37.21

7 11.82 11.70 8.03 8.05 39.60

8 12.76 12.63 5.65 5.89 36.93

9 13.21 13.02 26.23

10 10.71 10.66 21.36

11 10.16 10.14 20.29

10-24
Table 10.5.10 Cumulative Net Present Value of Customer Benefits for Equipment Class 

Combination Refrigerated Beverage Vending Machines, 7-Percent Discount 

Rate

Efficiency 

Level

Combo-A 

HFC

Combo-A 

CO2

Combo-B 

HFC

Combo-B 

CO2

Total

Million 2013 dollars

1 0.90 0.89 0.71 0.70 3.21

2 1.80 1.78 1.41 1.39 6.37

3 2.66 2.62 2.09 2.06 9.43

4 3.51 3.46 2.71 2.68 12.36

5 3.93 3.88 3.00 2.96 13.77

6 4.35 4.29 3.14 3.10 14.88

7 4.77 4.70 3.08 3.09 15.64

8 5.13 5.05 1.72 1.85 13.75

9 5.22 5.12 10.34

10 3.72 3.70 7.42

11 3.40 3.39 6.80

10-25
REFERENCES

1 Energy Information Administration. Annual Energy Outlook 2014 with Projections to 2040. 

April 2014. U.S. Department of Energy,Washington, DC.

2 Office of Management and Budget. OMB Circular A-4, Regulatory Analysis. 2003. OMB: 

Washington, D.C. September 17, 2003. 

<www.whitehouse.gov/omb/assets/omb/circulars/a004/a-4.pdf> 

10-26