8-i

LIFE-CYCLE COST AND PAYBACK PERIOD ANALYSIS

TABLE OF CONTENTS

8.1 INTRODUCTION ........................................................................................................... 8-1

8.1.1 General Approach to Analysis......................................................................................... 8-1

8.1.2 Overview of Inputs to Analysis ....................................................................................... 8-2

8.1.3 Replacement or New-Owner Market............................................................................... 8-5

8.2 INPUTS TO LIFE-CYCLE COST.................................................................................. 8-6

8.2.1 Inputs to Total Installed Cost........................................................................................... 8-6

8.2.1.2 Baseline Manufacturer Cost........................................................................... 8-8

8.2.1.3 Efficiency-Level Manufacturer Cost Increases ............................................. 8-8

8.2.1.4 Overall Markup.............................................................................................. 8-8

8.2.1.5 Installation Cost ............................................................................................. 8-9

8.2.2 Forecasting Future Product Prices................................................................................... 8-9

8.2.3 Total Installed Cost........................................................................................................ 8-11

8.2.4 Inputs to Operating Cost ................................................................................................ 8-11

8.2.4.1 Annual Energy Consumption....................................................................... 8-13

8.2.4.2 Energy Prices............................................................................................... 8-13

8.2.4.3 Energy Price Trends..................................................................................... 8-15

8.2.4.4 Repair and Maintenance Costs..................................................................... 8-16

8.2.5 Product Lifetime ............................................................................................................ 8-17

8.2.6 Discount Rates............................................................................................................... 8-18

8.2.6.1 Residential Purchases................................................................................... 8-18

8.2.6.2 Commercial Purchases................................................................................. 8-23

8.2.7 Effective Date of Potential Standard.............................................................................. 8-27

8.2.8 Product Energy Efficiency in the Base Case ................................................................. 8-28

8.3 INPUTS TO PAYBACK PERIOD................................................................................ 8-28

8.4 RESULTS OF LIFE-CYCLE COST AND PAYBACK PERIOD ANALYSIS........... 8-29

8.4.1 Base case Distributions of Life-Cycle Cost................................................................... 8-32

8.4.2 Distributions of Life-Cycle Costs at Higher Efficiency Levels..................................... 8-34

LIST OF TABLES

Table 8.1.1 Summary of Inputs to LCC and PBP Analysis.................................................... 8-5

Table 8.2.1 Inputs to Total Installed Cost............................................................................... 8-7

Table 8.2.2 Portable ACs: Baseline Manufacturer Cost ......................................................... 8-8

Table 8.2.3 Portable ACs: Overall Markups........................................................................... 8-9

Table 8.2.4 Portable ACs: Total Installed Costs in 2019...................................................... 8-11

Table 8.2.5 Inputs to Operating Costs................................................................................... 8-12

Table 8.2.6 Average Annual Energy Use by Efficiency Level for Residential and 

Commercial Applications .................................................................................. 8-13
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Table 8.2.7 Average Residential Electricity Prices in 2012 ................................................. 8-14

Table 8.2.8 Average Commercial Electricity Prices............................................................. 8-15

Table 8.2.9 Lifetime Parameters for Portable ACs............................................................... 8-17

Table 8.2.10 Income Groups................................................................................................... 8-18

Table 8.2.11 Types of Household Debt and Equity by Income Group................................... 8-20

Table 8.2.12 Real Effective Mortgage Interest Rates............................................................. 8-21

Table 8.2.13 Average Real Effective Interest Rates for Household Debt, %......................... 8-21

Table 8.2.14 Average Nominal and Real Rates of Return for Household Equity .................. 8-22

Table 8.2.15 Average Real Effective Discount Rate .............................................................. 8-23

Table 8.2.16 Risk-Free Rates and Equity Risk Premiums, 2004–2013.................................. 8-25

Table 8.2.17 Weighted-Average Cost of Capital for Sectors that Purchase Portable ACs..... 8-26

Table 8.2.18 Weighted-Average Cost of Capital for Small Businesses that Purchase 

Portable ACs...................................................................................................... 8-27

Table 8.2.19 Portable ACs: Base case Market Shares in 2014 ............................................... 8-28

Table 8.4.1 Summary of LCC and PBP Results by Efficiency Level, All Sectors............... 8-30

Table 8.4.2 Summary of Life-Cycle Cost Savings, All Sectors ........................................... 8-31

Table 8.4.3 Summary of LCC and PBP Results by Efficiency Level, Residential 

Settings............................................................................................................... 8-31

Table 8.4.4 Summary of Life-Cycle Cost Savings, Residential Settings ............................. 8-31

Table 8.4.5 Summary of LCC and PBP Results by Efficiency Level, Commercial 

Settings............................................................................................................... 8-31

Table 8.4.6 Summary of Life-Cycle Cost Savings, Commercial Settings............................ 8-32

LIST OF FIGURES

Figure 8.1.1 Flow Diagram of Inputs and Outputs for LCC and PBP ..................................... 8-4

Figure 8.2.1 Nominal and Deflated PPI Series for Small Electric Household Appliances 

from 1983 to 2013.............................................................................................. 8-10

Figure 8.2.2 Residential and Commercial Electricity Price Trends from AEO 2014 

Reference Case................................................................................................... 8-16

Figure 8.4.1 Base case Distribution of LCCs, Residential Settings....................................... 8-33

Figure 8.4.2 Base case Distribution of LCCs, Commercial Settings ..................................... 8-33

Figure 8.4.3 Distribution of LCC Savings for Efficiency Level 1, Residential Settings....... 8-34

Figure 8.4.4 Distribution of LCC Savings for Efficiency Level 1, Commercial Settings ..... 8-35

Figure 8.4.5 Range of Average LCC Savings, Residential Settings...................................... 8-36

Figure 8.4.6 Range of Average LCC Savings, Commercial Settings .................................... 8-36
8-1

CHAPTER 8 LIFE-CYCLE COST AND PAYBACK PERIOD ANALYSIS

8.1 INTRODUCTION

This chapter describes the U.S. Department of Energy’s (DOE’s) method for analyzing 

the economic impacts of potential energy efficiency standards on individual consumers of 

portable air conditioners (ACs). The effects of standards on individual consumers include a 

change in operating expense (usually a decrease) and a change in purchase price (usually an 

increase). This chapter describes three metrics DOE used to determine the effect of standards on 

individual consumers.

 Life-cycle cost (LCC) is the total consumer expense during the lifetime of an appliance, 

including purchase expense and operating costs (including energy expenditures). DOE 

discounts future operating costs to the time of purchase and sums them over the lifetime 

of the product.

 Payback period (PBP) measures the amount of time it takes a consumer to recover the 

assumed higher purchase price of a more energy efficient product through lower 

operating costs.

 Rebuttable payback period is a special case of the PBP. Whereas LCC is estimated for 

a range of inputs that reflect real-world conditions, rebuttable payback period is based on 

laboratory conditions, specifically the DOE test procedure.

Inputs to the LCC and PBP calculations are described in sections 8.2 and 8.3, 

respectively, of this chapter. Results of the analysis are presented in section 8.4. Key variables 

and calculations are presented for each metric. The calculations discussed here are illustrated 

with a Microsoft Excel spreadsheet available on the DOE’s rulemaking website at 

(http://www.eere.energy.gov/buildings/appliance_standards/). Details and instructions for using 

the spreadsheets are provided in appendix 8-A. 

8.1.1 General Approach to Analysis

Because each portable AC installation is unique, DOE incorporates variability and 

uncertainty into the LCC calculations for a broad sample of purchasers. The results indicate the 

number of installations that experience various economic impacts. The LCC analysis employs 

Monte Carlo simulations and probability distributions to explicitly model both the uncertainty 

and the variability in the model’s inputs (see appendix 8-B). In addition to using probability 

distributions to characterize several of the inputs to the analysis, DOE developed a sample of 

individual households that use portable ACs. By developing household samples, DOE was able 

to perform the LCC calculations to account for the variability in energy consumption and/or 
8-2

energy price associated with each household. DOE also developed a sample of commercial 

buildings that use portable ACs.

As described in chapter 7, DOE used the DOE Energy Information Administration 

(EIA)’s 2009 Residential Energy Consumption Survey (RECS 2009) to develop household 

samples for portable ACs based on households that use room ACs.

1 The EIA constructed RECS

2009, which consists of 12,083 housing units, to be representative of the household population of 

the United States. DOE was able to assign a unique annual energy use and/or energy price to 

each household in the sample. The large sample of households considered in the analysis

provides wide ranges of annual energy use and energy prices. (The ranges in energy 

consumption are presented in chapter 7.) The variability in annual energy use and/or energy 

pricing across households contributes to the range of LCCs calculated for any particular 

efficiency level. DOE also used the EIA’s 2003 Commercial Buildings Energy Consumption 

Survey (CEBCS 2003) to develop a sample of commercial buildings that use portable ACs, again 

based on buildings that use room ACs. The EIA constructed the 2003 CBECS, which consists of 

5,215 commercial buildings, to be representative of commercial buildings throughout the United 

States. DOE utilized CBECS 2003 as it did RECS 2009 to develop a broad sample of buildings 

that use portable ACs and to establish the variability of annual energy use and energy prices. 

DOE displays LCC results as distributions of effects for various efficiency levels 

compared to base case conditions. Results, presented in section 8.4, were derived from 10,000 

samples for each Monte Carlo simulation run. To illustrate the implications of the analysis, DOE 

generated frequency charts that depict the variation in LCC for each efficiency level considered

for potential standards for portable ACs.

8.1.2 Overview of Inputs to Analysis

DOE categorizes inputs to the LCC and PBP analysis as: (1) inputs for establishing the 

purchase expense, otherwise known as total installed cost, and (2) inputs for calculating 

operating costs.

Following are the primary inputs for establishing the total installed cost.

 Baseline manufacturer cost: The costs incurred by the manufacturer to produce 

products that meet current minimum efficiency standards, if any. 

 Efficiency-level manufacturer cost increase: The change in manufacturer cost

associated with producing products to meet a particular efficiency level.

 Markups and sales tax: The markups and sales tax associated with converting the 

manufacturer cost to a consumer product cost.
8-3

 Installation cost: The cost to the consumer of installing the product. The installation 

cost represents all costs required to install the product other than the marked-up 

consumer product cost. The installation cost includes labor, overhead, and any 

miscellaneous materials and parts. Thus, the total installed cost equals the consumer 

product cost plus the installation cost. 

Following are the primary inputs for calculating the operating cost.

 Product energy consumption: The product energy consumption is the site energy use 

associated with operating the product.

 Product efficiency: The product efficiency dictates the energy consumption associated 

with products that have efficiencies greater than the baseline efficiency.

 Energy prices: Energy prices are the prices paid by consumers for energy (e.g., 

electricity or gas).

 Energy price trends: DOE used the EIA Annual Energy Outlook 2014 (AEO 2014) to 

forecast future energy prices for the results presented in this chapter.

 Repair and maintenance costs: Repair costs are associated with repairing or replacing 

components that fail. Maintenance costs are associated with maintaining the operation 

of the product.

 Lifetime: The age at which the product is retired from service. 

 Discount rate: The rate at which DOE discounts future expenditures to establish their 

present value. 

The data inputs to PBP are the average total installed cost (product cost and installation 

cost) to the consumer plus the average annual (first-year) operating costs for each efficiency

level. The inputs to operating costs are the annual energy cost, the annual repair cost, and the 

annual maintenance cost. Because the PBP represents a simple payback, the energy price is 

required only for the year in which a potential energy conservation standard is estimated to take 

effect. The energy price DOE uses in the PBP calculation is the price projected for that year. 

Figure 8.1.1 depicts the relationships among the inputs to installed cost and operating 

cost for the calculating a product’s LCC and PBP. In the figure, the yellow boxes indicate inputs, 

the green boxes indicate intermediate outputs, and the blue boxes indicate final outputs (the LCC 

and PBP).
8-4

Figure 8.1.1 Flow Diagram of Inputs and Outputs for LCC and 

PBP

Table 8.1.1 summarizes the input values that DOE used to calculate the LCC and PBP for 

portable ACs. The table summarizes the inputs to total installed cost and operating costs,

including the product lifetime, discount rate, and energy price trends. DOE used single-point 

values to characterize all the inputs to total cost, but characterized several inputs to operating 

cost using probability distributions that capture the input’s uncertainty and/or variability. For 

those inputs characterized using probability distributions, the values provided in Table 8.1.1 are 

average or typical values.

Baseline

Manufacturer

Cost

Std-Level

Manufacturer

Cost

Manufacturer

Markup

Retailer or

Distributor

Markup

Sales Tax

Installation

Cost

 Energy

Consumption

Equipment

Price

Lifetime

Operating

Expense

Annual Energy

Expense

Lifetime Repair and

Maintenance

Cost

Discount Rate

Energy Price

Trends

Annual

Operating

Expense

Payback

Period

Life-Cycle

Cost

Energy Prices

Total Installed

Cost
8-5

Table 8.1.1 Summary of Inputs to LCC and PBP Analysis

Input Average or Typical Value Characterization

Baseline 

manufacturer cost 

(2013$)

$291.30 Single-point value

Efficiency-level

manufacturer cost 

increase (2013$)

EL 1 = $4.09

Single- point value

EL 2 = $4.67

EL 3 = $5.26

EL 4 = $47.76

Manufacturer 

markup 1.42 Single- point value

Retailer markup Baseline = 1.36

Incremental = 1.11 Single- point value

Sales tax 7.10% Variable based on 

region

Baseline 

installation cost 

(2013$)

$0.00 Single- point value

Annual energy use

Baseline residential use = 724 kWh Variable based on 

Baseline commercial use = 1713 kWh usage

2019 average 

energy prices 

(2013$)

Residential = 12.5 c/kWh Variable based on 

Commercial = 11.0 c/kWh region

2019 marginal 

energy prices 

(2013$)

Residential = 12.0 c/kWh Variable based on 

Commercial =12.2 c/kWh region

Annual baseline 

maintenance costs $0.00 Single-point value

Lifetime 10.5 years Weibull distribution

Discount rate

Mean Residential = 4.7% Custom distribution 

based on purchaser 

sample

Mean Commercial = 8.1%

Energy price trend AEO 2014 Reference case Time series

8.1.3 Replacement or New-Owner Market

The LCC and PBP analysis uses separate values for replacement products and for 

products purchased by consumers who have not owned a portable AC previously (first-time 

owners) or are buying an additional unit. The type of application affects some variables, such as

markups, installation costs, and discount rates. The derivation of the appropriate values for new 

owners or replacement applications is described in chapter 6 for markups and in this chapter for 
8-6

installation costs and discount rates. For portable ACs, DOE assumed that there would be no

builder-installed products in newly constructed homes or commercial buildings.

8.2 INPUTS TO LIFE-CYCLE COST

The LCC is the total consumer expense during the life of an appliance, including 

purchase expense and operating costs (including energy expenditures). DOE discounts future 

operating costs to the time of purchase and sums them over the lifetime of the product. DOE 

defines LCC by the following equation.

   

 

N

t

t

t

r

OC LCC IC

1 1

Where:

LCC = life-cycle cost in dollars,

IC = total installed cost in dollars,

∑ = sum over product lifetime, from year 1 to year N,

N = lifetime of appliance in years,

OC = operating cost in dollars, 

r = discount rate, and

t = year for which operating cost is being determined.

Because DOE gathered most of its data for the LCC in 2013, DOE expresses dollar 

values in 2013$. 

8.2.1 Inputs to Total Installed Cost

DOE defines the total installed cost using the following equation.

IC CPC  INST

Where:

CPC = consumer product cost (i.e., consumer cost for the product only), and 

INST = installation cost (the consumer cost to install the product).

The product cost depends on how the consumer purchases the product. As discussed in 

chapter 6, Markups for Product Price Determination, DOE defines markups and sales taxes to 

convert manufacturing costs into consumer product costs. Table 8.2.1 summarizes the inputs for 

determining total installed cost.
8-7

Table 8.2.1 Inputs to Total Installed Cost

Baseline manufacturer cost

Efficiency-level manufacturer cost increase

Markups

Sales tax (part of markups)

Installation cost

The baseline manufacturer cost is the cost incurred by the manufacturer to produce 

products that meet current minimum efficiency standards, if any. Efficiency-level manufacturer 

cost increase is the change in manufacturer cost associated with producing products at a higher

efficiency level. Markups and sales tax convert the manufacturer cost to a consumer product

cost. The installation cost represents all costs to the consumer for installing the product, other 

than the marked-up consumer product cost. The installation cost includes labor, overhead, and 

any miscellaneous materials and parts. DOE calculated the total installed cost for baseline 

products using the following equation.

MFG OVERALL BASE BASE

BASE BASE BASE

COST MU INST

IC CPC INST

  

 

_

Where:

ICBASE = baseline total installed cost,

CPCBASE = consumer product cost for baseline model, 

INSTBASE = baseline installation cost,

COSTMFG = manufacturer cost for baseline model, and

MUOVERALL_BASE = overall baseline markup (product of manufacturer markup, baseline 

retailer and/or distributor markup, and sales tax).

DOE calculated the total installed cost for products at higher efficiency levels using the 

following equation.

   

   

  BASE MFG OVERALL INCR EL

BASE BASE EL EL

BASE EL BASE EL

EL EL EL

IC COST MU INST

CPC INST CPC INST

CPC CPC INST INST

IC CPC INST

     

     

     

 

_

Where:

ICEL = total installed cost for higher-efficiency product,

CPCEL = consumer product cost for higher-efficiency product, 
8-8

INSTEL = installation cost for higher-efficiency product,

CPCBASE = consumer product cost for baseline product, 

ΔCPCEL = change in product cost for higher-efficiency product,

INSTBASE = baseline installation cost,

ΔINSTEL = change in installation cost for higher-efficiency product,

ICBASE = baseline total installed cost,

ΔCOSTMFG = change in manufacturer cost for higher-efficiency product, and

MUOVERALL_INCR = incremental overall markup (product of manufacturer markup, 

incremental retailer or distributor markup, and sales tax for higherefficiency product).

The rest of this section provides information about each of the above input variables that 

DOE used to calculate the total installed cost of portable ACs.

8.2.1.2 Baseline Manufacturer Cost

DOE developed the baseline manufacturer costs for portable ACs as described in chapter 

5, Engineering Analysis. Table 8.2.2 shows the manufacturer cost for a baseline model that 

performs at a cooling energy efficiency ratio (EERcm) of 2.08.

Table 8.2.2 Portable ACs: Baseline Manufacturer Cost

Baseline 

EERcm

Manufacturer Cost

2013$

2.08 291

8.2.1.3 Efficiency-Level Manufacturer Cost Increases

DOE used a reverse-engineering analysis to develop manufacturer cost increases 

associated with increases in efficiency levels for portable ACs. Refer to chapter 5, Engineering 

Analysis, for details.

8.2.1.4 Overall Markup

The overall markup on a product is determined by multiplying the manufacturer and 

retailer markups and the sales tax together to arrive at a single markup value. Table 8.2.3 shows 

the overall baseline and incremental markups for portable ACs. Incremental markups are those 

that apply to products at higher efficiency levels manufactured under a potential energy 

efficiency standard. Refer to chapter 6 for details.
8-9

Table 8.2.3 Portable ACs: Overall Markups

Markup Baseline Markup Incremental Markup

Manufacturer 1.42

Retailer 1.36 1.11

Sales Tax 1.07

Overall 2.07 1.69

8.2.1.5 Installation Cost

The cost of installation covers all labor and material costs associated with installing a 

portable AC in a residence or business enterprise. DOE’s research indicates that installation cost 

for a portable AC is independent of efficiency. DOE assumed an installation cost of $0 for all 

efficiency levels. 

8.2.2 Forecasting Future Product Prices

Historical price data for certain appliances and equipment that have been subject to 

energy conservation standards indicate that the assumption of constant real prices and costs may 

overestimate long-term trends in appliance and equipment prices. Economic literature and 

historical data suggest that the real costs of products may trend downward over time based on

“learning” or “experience” curves. According to the experience curve approach, the real cost of 

production is related to the cumulative production or “experience” with a product. An extensive 

literature describes the learning or experience curve phenomenon, which typically is based on 

observations in the manufacturing sector. Desroches et al. (2013)1and Weiss et al. (2010)2

summarize the data and literature available to DOE that are relevant to forecasting prices for 

certain appliances and equipment.

Typically, DOE uses historical shipments data to estimate cumulative shipments

(production). The historical shipments data for portable ACs are, however, too limited to 

construct robust cumulative production estimates for portable ACs. Therefore, DOE decided to 

use the most representative Producer Price Index (PPI) series for portable ACs to fit to an 

exponential model having year as the explanatory variable. In this case, the exponential function 

takes the form of:

Y = a ∙ e

bX

where Y is the proxy for portable AC price, X is the time variable, a is the constant, and b is the 

slope parameter of the time variable. 

To derive the exponential parameters for portable ACs, DOE obtained historical PPI data 

for “small electric household appliances, except fans” from the Bureau of Labor Statistics for 
8-10

1983 to 2013.3 Although this PPI series encompass more than portable ACs, no PPI data specific 

to portable ACs were available. The PPI data reflect nominal prices, adjusted for changes in 

product quality. DOE calculated an inflation-adjusted (deflated) price index by dividing the PPI 

series by the Gross Domestic Product Chained Price Index. The deflated price index is presented 

in 2013 dollar. Error! Reference source not found. presents the nominal and inflation-adjusted 

PPI trends for portable ACs from 1983 to 2013.

Figure 8.2.1 Nominal and Deflated PPI Series for Small Electric 

Household Appliances from 1983 to 2013

For portable ACs, the regression performed as an exponential trend line fit results in an 

R-square of 0.99, which indicates a superior fit to the data. The fit results in a 1.99-percent 

annual rate of price decline. The final estimated exponential function for portable ACs is:

Y = 3.743 × 1017 ∙ e

(−0.0201)X

Based on the fitted regressions, DOE derived a price factor index for portable ACs for 

each future year in the analysis period (2019–2048). For the LCC and PBP analysis, DOE 
8-11

renormalized the price factor index, setting 2013 equal to 1, to estimate the price of portable ACs 

in 2019, the expected year of any new energy efficiency standard for portable ACs. In 2019, the 

price factor is 0.886.

8.2.3 Total Installed Cost 

The total installed cost is the sum of the consumer product cost and installation cost. 

Error! Reference source not found. presents the total installed costs in 2019 for the portable

ACs in the residential and commercial sectors, accounting for the effects of the learning curve. 

Costs are presented at the baseline level and each efficiency level identified in chapter 5. Slight 

differences in installed cost between the residential and commercial sectors for a given efficiency 

level reflect the different geographic distributions of installations and, hence, different sales tax 

distributions. 

Table 8.2.4 Portable ACs: Total Installed Costs in 2019 

Efficiency 

Level EERcm

Residential Total 

Installed Cost

2013$

Commercial Total 

Installed Cost

2013$

Baseline 2.08 534 534

1 3.53 540 540

2 4.32 541 541

3 5.28 542 542

4 5.82 605 605

8.2.4 Inputs to Operating Cost 

DOE defines a product’s operating cost (OC) using the following equation.

OC  EC  RC  MC

Where:

EC = energy expenditure associated with operating the product, 

RC = repair cost associated with component failure, and 

MC = cost for maintaining product operation.

Table 8.2.5 shows the inputs for determining the annual operating costs and their 

discounted value throughout a product’s lifetime.
8-12

Table 8.2.5 Inputs to Operating Costs

Annual energy consumption

Energy prices and price trends

Repair and maintenance costs

The annual energy consumption is the site energy use associated with operating the 

product. The annual energy consumption changes with product efficiency. Energy prices are the 

prices paid by consumers for energy (e.g., electricity or gas). Multiplying the annual energy 

consumption by the energy price yields the annual energy cost. Repair costs are associated with 

repairing or replacing components that fail. Maintenance costs are associated with maintaining 

the operation of the product. DOE used energy price trends to forecast energy prices into the 

future and to establish the present value of lifetime energy costs.

DOE calculated the annual operating cost for baseline products using the following 

equation.

OCBASE  AECBASE  PRICEENERGY  RCBASE  MCBASE ( )

Where:

OCBASE = operating cost for baseline product,

AECBASE = annual energy consumption for baseline product, 

PRICEENERGY = energy price,

RCBASE = repair cost associated with component failure for baseline product, 

and

MCBASE = cost for maintaining baseline product.

DOE calculated the annual operating cost for higher-efficiency products using the 

following equation.

OCEL AECEL  PRICEENERGY  RCEL  MCEL ( )

Where:

OCEL = operating cost for higher-efficiency product,

AECEL = annual energy consumption for higher-efficiency product, 

PRICEENERGY = energy price,

RCEL = repair cost associated with component failure for higher-efficiency 

product, and

MCEL = cost for maintaining higher-efficiency product.
8-13

The rest of this section provides information about each of the above input variables that 

DOE used to calculate the operating costs for portable ACs. 

8.2.4.1 Annual Energy Consumption

As described in chapter 7, Energy Use Characterization, and in section 8.1.1 of this 

chapter, DOE used from RECS 2009 and CBECS 2003 to develop a sample of individual 

households and commercial buildings that have portable ACs. DOE performed the LCC

calculation for each household and commercial enterprise in its samples to account for the 

variability in both energy use and energy price. Table 8.2.6 provides the average annual energy 

consumption by efficiency level for portable ACs in residential and commercial applications.

Table 8.2.6 Average Annual Energy Use by Efficiency Level for Residential and 

Commercial Applications

Efficiency 

Level EERcm

Residential

Energy Use

kWh

Commercial

Energy Use

kWh

Baseline 2.08 724 1,713

1 3.53 525 1,411

2 4.32 473 1,330

3 5.28 434 1,274

4 5.82 400 1,173

8.2.4.2 Energy Prices

DOE derived average monthly energy prices for various geographic areas in the United 

States using the latest data from the EIA and monthly energy price factors that DOE developed. 

DOE then assigned an appropriate energy price to each household and commercial building in 

the samples, depending on building type (residential or commercial) and geographic location.

Average Electricity Prices. DOE derived annual electricity prices for 2012 from EIA 

Form 826 data.4 The EIA Form 826 data include energy prices by state. DOE calculated annual 

electricity prices for each RECS or CBECS region by averaging monthly energy prices by state 

to obtain state electricity prices. For regions having more than one state, DOE weighted each 

state’s average price by its number of households in 2012. Table 8.2.7 and Table 8.2.8 show the 

electricity prices by region for residential and commercial sectors, respectively (see appendix 8-

C for more details).
8-14

Table 8.2.7 Average Residential Electricity Prices in 2012

RECS Region 2013$/kWh

Connecticut, Maine, New 

Hampshire, Rhode Island, Vermont 0.165 

Massachusetts 0.151 

New York 0.178 

New Jersey 0.160 

Pennsylvania 0.129 

Illinois 0.117 

Indiana, Ohio 0.115 

Michigan 0.143 

Wisconsin 0.134 

Iowa, Minnesota, North Dakota, 

South Dakota 0.111 

Kansas, Nebraska 0.109 

Missouri 0.102 

Virginia 0.113 

Delaware, District of Columbia, 

Maryland 0.131 

Georgia 0.112 

North Carolina, South Carolina 0.114 

Florida 0.116 

Alabama, Kentucky, Mississippi 0.106 

Tennessee 0.103 

Arkansas, Louisiana, Oklahoma 0.091 

Texas 0.111 

Colorado 0.116 

Idaho, Montana, Utah, Wyoming 0.097 

Arizona 0.113 

Nevada, New Mexico 0.118 

California 0.155 

Oregon, Washington 0.091 

Alaska 0.182 

Hawaii 0.379 

West Virginia 0.100 

U.S. Average 0.120 
8-15

Table 8.2.8 Average Commercial Electricity Prices

Census Division 2013$/kWh

New England 0.139

Middle Atlantic 0.130

East North Central 0.096

West North Central 0.086

South Atlantic 0.095

East South Central 0.100

West South Central 0.081

Mountain 0.091

Pacific 0.129

U.S. Average 0.105

Monthly Electricity Prices. Portable ACs are used during the warm months of the year. 

As described in chapter 7, DOE assigned each household and commercial enterprise to a NOAA 

weather station. After matching the household or enterprise to a weather station, DOE utilized 

the monthly data for cooling-degree days from the corresponding weather station to estimate the 

relative fraction of cooling-degree days by month (see appendix 7A for more details). DOE 

divided the number of cooling-degree days in each month by the total number of cooling-degree 

days in the year for the corresponding weather station. DOE assumed the relative fraction of 

cooling-degree days by month reflects the appropriate weighting of electricity usage by month. 

In conducting the LCC analysis for portable ACs, DOE used monthly electricity prices 

because electricity tariffs show seasonal variation in many areas of the country. To determine 

monthly electricity prices, DOE developed monthly price factors for electricity based on longterm price data. See appendix 8C for a description of DOE’s method for developing price 

factors. DOE multiplied the annual prices shown in the previous tables by the monthly price 

factors to derive prices for each month.

Marginal Electricity Prices. Monthly electricity prices were adjusted by applying

seasonal marginal price factors to determine monthly marginal electricity prices. The marginal 

energy prices were used to determine the cost to the consumer of the variations in energy 

consumed. For a detailed discussion of the development of marginal energy price factors and for 

a comparison to other data and methods, see appendix 8C.

8.2.4.3 Energy Price Trends

DOE used price forecasts in the EIA’s Annual Energy Outlook 20145 (AEO 2014) to 

estimate future trends in electricity prices for the residential and commercial sectors. To arrive at 

prices in future years, DOE multiplied the average prices described in the preceding section by 

the forecast of annual average price changes in AEO 2014. To estimate the trend after 2040, 

DOE followed past guidelines provided by the EIA to the Federal Energy Management Program, 

applying the average rate of change during 2025–2040 to future prices. DOE calculated LCC 
8-16

and PBP using the Reference Case in AEO 2014. Figure 8.2.2 shows residential and commercial 

electricity price trends.

Figure 8.2.2 Residential and Commercial Electricity Price 

Trends from AEO 2014 Reference Case

8.2.4.4 Repair and Maintenance Costs

The maintenance cost is the cost of regular scheduled product maintenance. The repair 

cost is the cost to repair a product when it fails. Typically, small incremental changes in product

efficiency incur no, or only very small, changes in repair and maintenance costs compared to

baseline products. For portable ACs, DOE found no data about repair frequencies. DOE assumed 

that repair frequencies are low and do not increase for higher-capacity or higher-efficiency units. 

Because repair and maintenance costs to not increase with efficiency level, DOE assumed a cost 

of $0 for all efficiency levels.
8-17

8.2.5 Product Lifetime

The product lifetime is the age at which a product is retired from service. Rather than use 

a single average value for the lifetime of portable ACs, DOE developed a lifetime distribution to 

characterize the probability a portable AC will be retired from service at a given age. This 

section describes the survival function DOE developed for its analysis.

DOE assumed that the probability function for the annual survival of portable ACs would 

take the form of a Weibull distribution. A Weibull distribution is a probability distribution 

commonly used to measure failure rates.aIts form is similar to an exponential distribution, which 

models a fixed failure rate, except that a Weibull distribution allows for a failure rate that 

changes over time in a specific fashion. The cumulative Weibull distribution takes the form:

e

x

P x

















 



( ) 

for x > θ and

P(x) = 1 for x ≤ θ

Where:

P(x) = probability that the appliance is still in use at age x,

x = age of appliance in years,

α = scale parameter, which would be the decay length in an exponential 

distribution,

β = shape parameter, which determines the way in which the failure rate changes 

through time, and

θ = delay parameter, which allows for a delay before any failures occur.

When β = 1, the failure rate is constant over time, giving the distribution the form of a 

cumulative exponential distribution. In the case of appliances, β commonly is greater than 1, 

reflecting an increasing failure rate as appliances age. DOE estimated a delay parameter of θ = 1

year, based on the typical manufacturer warranty period for portable ACs. Based on values for 

room ACs, DOE assumed a maximum lifetime of 20 years and an average lifetime of 10.47

years, then solved for the scale and shape parameters.

6 Table 8.2.9 shows the lifetime parameters 

for portable ACs. See appendix 8D for more details.

Table 8.2.9 Lifetime Parameters for Portable ACs

Value Weibull Parameters

Minimum

(years) 

Average

(years)

Maximum

(years)

Maximum

Percentile (%)

Alpha 

(scale)

Beta 

(shape)

3 10.47 20 99 10.66 2.64

 

a For reference on the Weibull distribution, see sections 1.3.6.6.8 and 8.4.1.3 of the NIST/SEMATECH e-Handbook 

of Statistical Methods, <www.itl.nist.gov/div898/handbook/>.
8-18

8.2.6 Discount Rates

The discount rate is the rate at which DOE discounts future consumer expenditures to 

establish their present value. DOE derived discount rates for the LCC from estimates of the 

finance cost of purchasing household appliances. Following financial theory, the finance cost of 

raising funds to purchase appliances can be interpreted as (1) the financial cost of any debt 

incurred to purchase products, or (2) the opportunity cost of any equity used to purchase 

products. The opportunity cost of funds may include interest payments on debt and lost interest 

returns on assets. DOE considers both possibilities. DOE also estimated discount rates for 

purchasers of portable ACs in the commercial sector.

8.2.6.1 Residential Purchases

DOE believes that few if any portable ACs are installed by builders in new homes.

Therefore, DOE evaluated the costs associated with consumers purchasing portable ACs 

themselves. DOE used publicly available data (the Federal Reserve Board’s Survey of Consumer 

Finances

7

[SCF]) to estimate a consumer’s opportunity cost of funds for purchasing a portable 

AC. A discount rate is applied in the LCC to future energy cost savings and non-energy 

operations and maintenance costs in order to present the estimated net LCC and LCC savings. 

DOE notes that the discount rate used in the LCC analysis is distinct from an implicit discount 

rate, because it is not used to model consumer purchase decisions. 

DOE estimates individual distributions of discount rates for six income groups, divided 

based on income percentile as reported in the Federal Reserve Board’s SCF.

7 The groups reflect 

the fact that low and high income consumers tend to have substantially different proportions of 

debt and asset types and tend to face different interest rates on debts and assets. Table 8.2.10 lists 

the income groups DOE identified. Summaries of debts, assets, and discount rates presented in 

this chapter are averages across the entire population.

Table 8.2.10 Income Groups

Income Group Percentile of Income

1 1

st to 20th

2 21st to 40th

3 41st to 60th

4 61st to 80th

5 81st to 90th

6 91th to 99th

Sources: Federal Reserve Board. Survey of Consumer Finances (SCF) for 1995, 1998, 2001, 2004, 2007, and 2010.

Debt and Asset Classes. DOE’s approach to approximating a consumer’s opportunity 

cost of funds involved identifying all relevant household debt or asset classes’. The approach 

assumes that, when future expenditures are required or future savings accumulate, consumers are 

likely to draw from or add to their collection of debt and asset holdings approximately in 

proportion to their current holdings. DOE has included several previously excluded debt types 
8-19

(vehicle and education loans, mortgages, and all forms of home equity loan) in order to better 

account for all the borrowing options available to consumers.

DOE uses the average percentage of total debt plus equity and the associated interest rate 

of each asset and debt type to calculate a weighted-average discount rate for each SCF 

household. The household-level discount rates then are aggregated to develop distributions of 

discount rates for each of the six income groups. Note that in the past DOE aggregated asset and 

debt types among households by summing the dollar values across all households and then 

calculating percentages. Weighting by dollar value gave disproportionate influence to the

percentages and rates of assets and debts of higher-income consumers. DOE has shifted to a 

household-level weighting to more accurately reflect the average consumer in each income 

group.

DOE estimated the average percentages of each type of debt and equity using data from 

the Federal Reserve Board’s SCF for 1995, 1998, 2001, 2004, 2007, and 2010.7, b DOE derived 

the household-weighted mean percentages of each source of financing throughout the 5 years 

surveyed. Table 8.2.11 lists the percentages of each type of household debt and equity used by 

each of the six income groups identified. DOE posits that these long-term averages are most 

appropriate for use in its analysis. 

 

b Although two older versions of the SCF are available (1989 and 1992), those surveys are not used in this analysis 

because they do not provide all the necessary types of data (e.g., credit card interest rates). DOE believes that the 

15-year span covered by the five surveys adequately represent recent debt and equity percentages and interest rates.
8-20

Table 8.2.11 Types of Household Debt and Equity by Income Group

 Type of Debt or Equity

Income Group

1 2 3 4 5 6

Debt %

Mortgage 18.9 24.1 33.1 38.1 39.3 25.0

Home equity loan 3.1 3.3 2.6 3.6 4.5 7.2

Credit card 15.3 13.0 11.8 8.7 6.0 2.7

Other installment loan 25.1 20.6 17.3 13.2 9.6 4.7

Other residential loan 0.7 0.6 0.6 0.7 1.0 1.2

Other line of credit 1.6 1.5 1.3 1.5 2.1 1.8

Equity %

Savings account 18.5 16.0 12.7 10.6 10.4 7.9

Money market account 3.6 4.5 4.0 4.5 5.0 8.6

Certificate of deposit 7.0 7.8 5.5 5.0 4.4 4.2

Savings bond 1.8 1.7 1.9 2.2 1.7 1.1

Bonds 0.2 0.4 0.5 0.7 0.8 3.8

Stocks 2.3 3.1 4.4 5.7 7.6 15.8

Mutual funds 2.1 3.5 4.3 5.7 7.6 15.9

Total 100.0 100.0 100.0 100.0 100.0 100.0

Sources: Federal Reserve Board. Survey of Consumer Finances (SCF) for 1995, 1998, 2001, 2004, 2007, and 2010.

Interest Rates for Types of Debt. DOE’s source for interest rates for mortgages, loans, 

credit cards, and lines of credit was the Federal Reserve Board’s SCF for 1995, 1998, 2001, 

2004, 2007, and 2010,7 which associates an interest rate with each type of debt for each 

household in the SCF. In calculating effective interest rates for home equity loans and 

mortgages, DOE accounted for the fact that interest on both is tax deductible (see Table 8.2.12). 

The effective rate corresponds to the interest rate after deduction of mortgage interest for income 

tax purposes and after adjusting for inflation (using the Fisher formula).c For example, a 6-

percent nominal mortgage rate has an effective rate of 4.5 percent for a household paying taxes 

at a 25-percent marginal rate. When adjusted for an inflation rate of 2 percent, the effective real 

rate becomes 2.45 percent.8

 

c The Fisher formula is given by: Real Interest Rate = [(1 + Nominal Interest Rate) / (1 + Inflation Rate)] – 1.
8-21

Table 8.2.12 Real Effective Mortgage Interest Rates

Year Mortgage Interest Rates in Selected Years %

Average 

Nominal Interest 

Rate

Inflation 

Rate9

Applicable 

Marginal Tax 

Rate10

Average Real Effective 

Interest Rate

1995 8.2 2.83 24.2 3.3

1998 7.9 1.56 25.0 4.3

2001 7.6 2.85 24.2 2.8

2004 6.2 2.66 20.9 2.2

2007 6.3 2.85 20.6 2.1

2010 5.7 1.64 20.0 2.9

Table 8.2.13 shows the household-weighted average effective real rates for various types 

of household debt. Because the interest rate for each type of debt reflects economic conditions 

throughout numerous years and various phases of economic growth and recession, DOE expects 

them to be representative of rates in effect in 2019, the expected date of compliance for any new 

standard for portable ACs.

Table 8.2.13 Average Real Effective Interest Rates for Household Debt, %

 Type of Debt

Income Group

1 2 3 4 5 6

Mortgage 6.6 6.2 6.1 5.2 5.0 4.0

Home equity loan 7.0 6.9 6.7 5.9 5.7 4.3

Credit card 15.2 15.0 14.5 14.2 14.0 14.5

Other installment 

loan 10.8 10.3 9.9 9.4 8.7 8.6

Other residential loan 9.8 10.2 8.9 8.2 7.7 7.4

Other line of credit 9.1 10.9 9.6 8.8 7.4 6.1

Sources: Federal Reserve Board. Survey of Consumer Finances (SCF) for 1995, 1998, 2001, 2004, 2007, and 2010.

Interest Rates for Types of Assets. No rate data are available from the SCF for classes of 

assets, so DOE derived interest rates from various sources of national historical data (1983–

2013). The interest rates associated with certificates of deposit,11 savings bonds,12 and bonds 

(AAA corporate bonds)13 were collected from Federal Reserve Board time-series data. Rates on 

money market accounts came from Cost of Savings Index data.14 Rates on savings accounts were 

estimated as one-half the rate for money market accounts, based on recent differentials between 
8-22

the return on the two types of assets. The rates for stocks are the annual returns on the Standard 

and Poor’s.15 Rates for mutual funds are a weighted average of the stock rates (two-thirds 

weight) and bond rates (one-third weight) in each year. DOE assumed rates on checking 

accounts to be zero.

DOE adjusted the nominal rates to real rates using the annual inflation rate for each year. 

Average nominal and real interest rates for the classes of household assets are listed in Table 

8.2.14. Because the interest and return rates for each type of asset reflect economic conditions 

throughout numerous years, DOE expects them to be representative of rates that may be in effect 

in 2019. For each asset type, DOE developed a distribution of rates, as shown in appendix 8-E.

Table 8.2.14 Average Nominal and Real Rates of Return for Household Equity 

Type of Equity Average Real 

Rate %

Savings account 1.0

Money market account 1.9 

Certificate of deposit 1.9 

Savings bonds 3.4 

Bonds 4.2 

Stocks 9.4 

Mutual fund 7.4 

Calculation and Summary of Consumer Discount Rates. Using the asset and debt data 

discussed above, DOE calculated distributions of discount rates for each income group. First, 

DOE calculated the discount rate for each consumer in each of the six years of the SCF, using 

the following formula.

DRi = ∑Sharei,j

j

× Ratei,j

Where:

DRi = discount rate for consumer i,

Sharei,j = percent of asset or debt type j for consumer i, and

Ratei,j = real interest rate or rate of return on asset or debt type j for consumer i.

After the real discount rate was estimated for each consumer, DOE compiled the 

distribution of discount rates in each SCF by income group by calculating the proportion of 

consumers whose discount rates fell into bins having 1-percent increments, ranging from 0 or 1 

percent to more than 30 percent. Giving equal weight to each SCF, DOE compiled a six-survey 

distribution of discount rates. 
8-23

Table 8.2.15 presents the average real effective discount rate and its standard deviation 

for each of the six income groups. To account for variations among households, DOE sampled a 

rate for each RECS household from the distributions for the appropriate income group. (RECS 

provides household income data). Appendix 8E presents the full probability distributions for 

each income group that DOE considered in the LCC analysis. 

Table 8.2.15 Average Real Effective Discount Rate

Income 

Group

Discount 

Rate %

1 4.85

2 5.12

3 4.75

4 4.04

5 3.80

6 3.57

Overall 

Average 4.49

8.2.6.2 Commercial Purchases

“Regular-Size” The commercial discount rate is the rate at which future operating costs 

are discounted to establish their present value in the LCC analysis. The discount rate value is 

applied in the LCC to future year energy costs and non-energy operations and maintenance costs 

to calculate the estimated net life-cycle cost of products of various efficiency levels and lifecycle cost savings as compared to the baseline for a representative sample of commercial end 

users.

DOE’s method views the purchase of a higher efficiency appliance as an investment that 

yields a stream of energy cost savings. DOE derives the discount rates for the LCC analysis by 

estimating the cost of capital for companies that purchase portable ACs. The weighted average 

cost of capital (WACC) is commonly used to estimate the present value of cash flows to be 

derived from a typical company project or investment. Most companies use both debt and equity 

capital to fund investments, so their cost of capital is the weighted average of the cost to the firm 

of equity and debt financing, as estimated from financial data for publicly traded firms in the 

sectors that purchase portable ACs.16

Damodaran Online, which is widely used as a source of information about debt and 

equity financing for most types of firms, was the primary source of data for this analysis.15

Detailed sectors included in the Damondaran Online database are assigned to the aggregate 

categories of retail, property management, medical, industrial, lodging, office, and other.

DOE estimated the cost of equity using the capital asset pricing model (CAPM).17 The 

CAPM assumes that the cost of equity (ke) for a particular company is proportional to the 
8-24

systematic risk that company faces, whereby high risk is associated with a high cost of equity 

and low risk is associated with a low cost of equity. The systematic risk facing a firm is 

determined by several variables: the risk coefficient of the firm (β), the expected return on riskfree assets (Rf), and the equity risk premium (ERP). The risk coefficient of the firm indicates the 

risk associated with that firm relative to the price variability in the stock market. The expected 

return on risk-free assets is defined by the yield on long-term government bonds. The ERP

represents the difference between the expected stock market return and the risk-free rate. The 

cost of equity financing is estimated using the following equation, in which the variables are 

defined as above.

k R  ERP e

f   

Where:

ke = cost of equity,

Rf = expected return on risk-free assets,

β = risk coefficient of the firm, and

ERP = equity risk premium.

Several parameters in the cost of capital equations can change substantially over time, so 

that the estimates can vary depending on the period for which data are selected and the details of 

the data-averaging method. DOE uses Federal Reserve methodologies for both the period and 

data to select for key parameters and for the averaging method. When applying the CAPM, the 

Federal Reserve uses a 40-year period for calculating discount rate averages, utilizes the gross 

domestic product price deflator for estimating inflation, and considers the best method for 

determining the risk-free rate as one where “the time horizon of the investor is matched with the 

term of the risk-free security.”

18

 

By taking a 40-year average of Federal Reserve data on annual nominal returns for 10-

year Treasury bills, DOE estimated the risk-free rates for 2004‒2013 (see Table 8.2.16).19 DOE 

also estimated the ERP by calculating the difference between the risk-free rate and stock market 

returns for the same period, as estimated using Damodaran Online data on the historical return to 

stocks.15
8-25

Table 8.2.16 Risk-Free Rates and Equity Risk Premiums, 2004–2013 

Year Risk-Free 

Rate %

ERP %

2004 7.10 3.25

2005 7.11 3.68

2006 7.10 3.49

2007 7.08 3.36

2008 7.01 2.40

2009 6.88 3.07

2010 6.74 3.23

2011 6.61 2.94

2012 6.41 3.99

2013 6.24 5.30

The cost of debt financing (kd) is the interest rate paid on money borrowed by a company. 

The cost of debt is estimated by adding a risk adjustment factor (Ra) to the risk-free rate. This 

risk adjustment factor depends on the variability of stock returns represented by standard 

deviations in stock prices. For firm i, the cost of debt financing is calculated as:

di Rf Rai k  

Where:

kd = cost of debt financing for firm, i,

Rf = expected return on risk-free assets, and

Rai = risk adjustment factor for firm, i. 

DOE estimated the weighted-average cost of capital for a firm using the following 

equation.

e e d wd WACC  k w  k 

Where:

WACC = weighted-average cost of capital,

we = proportion of equity financing, and

wd = proportion of debt financing.
8-26

By adjusting for inflation, DOE estimated the real weighted-average cost of capital, or 

discount rate, for each company in its sample of companies that have portable ACs. DOE then 

aggregated each company’s real WACC to estimate the discount rate for each type of ownership 

in the analysis of portable ACs in commercial settings. Table 8.2.17 shows the average WACC 

values for the major sectors that purchase portable ACs. Although WACC values for any sector 

may trend higher or lower over substantial periods, the values represent a cost of capital that is 

averaged over major business cycles. 

Table 8.2.17 Weighted-Average Cost of Capital for Sectors that Purchase Portable ACs

Sector Real Weighted-Average 

Cost of Capital %

Standard 

Deviation %

Retail 3.56 2.01

Medical 3.96 1.49

Hotels 6.23 2.37

Food service 3.73 2.20

Office 5.41 2.18

Education 2.46 2.21

Other 4.09 1.46

Small Business The Small Business Administration (SBA) defines a small business by its 

annual receipts or its number of employees. CWAF are used throughout the U.S. economy, so 

DOE did not assign a different distribution of CWAF applications or sectors of the economy to 

this subgroup.

The capital asset pricing model (CAPM) underestimates the cost of capital for small 

companies. In CAPM, the risk premium β is used to account for the higher returns associated 

with greater risk. However, for small companies, particularly very small companies, historic 

returns have been significantly higher than the CAPM equation predicts. This additional return 

can be accounted for by adding a size premium to the cost of equity for small firms:

ke Rf    ERP S

Where:

ke = cost of equity,

Rf = expected return on risk-free assets,

β = risk coefficient of the firm, 

ERP = equity risk premium, and

S

= size premium.
8-27

DOE obtained size premium data from Ibbotson Associates’ Stocks, Bonds, Bills, and 

Inflation 2009 Yearbook.

17

 For the period of 1926-2008, the average size premium for the smallest 

companies in all industries is 5.81 percent, implying that on average, historic performance of 

small companies has been 5.81 percent higher than the CAPM estimate of the small company 

cost of equity.

d

DOE calculated the real weighted average cost of capital using the cost of equity 

including a size premium for small companies instead of the CAPM cost of equity.17 Table 

8.2.18 presents DOE’s estimates of the discount rates for small companies. 

Table 8.2.18 Weighted-Average Cost of Capital for Small Businesses that Purchase 

Portable ACs

Sector Real Weighted-Average 

Cost of Capital %

Standard 

Deviation %

Retail 9.00 3.65

Medical 8.04 2.78

Hotels 8.11 3.16

Food service 8.35 3.39

Office 7.47 3.25

Education 2.46 2.21

Other 8.29 3.53

8.2.7 Effective Date of Potential Standard

The effective date is the future date when a potential energy efficiency standard becomes 

operative. Based on DOE’s implementation report for energy conservation standards activities 

submitted pursuant to Section 141 of the Energy Policy Act of 2005, a final rule for the portable 

ACs being considered for this standards rulemaking is scheduled for completion in August 

2016.

20 The effective date of any new energy efficiency standards for the products would be 3 

years after the final rule is published, or August 2019. DOE calculated the LCC for all 

consumers as if each would purchase a new portable AC in the year potential standards would 

take effect.

 

d

In this calculation, small companies are defined as companies with market capitalization of less than or equal to 

$218.53 million, the Ibbotson Associates’ definition of Decile 10 companies.
8-28

8.2.8 Product Energy Efficiency in the Base Case

To estimate the percentage of consumers who would be affected by a potential standard 

at any of the efficiency levels identified in chapter 5, DOE’s LCC analysis first considered the 

projected distribution of efficiencies for products that consumers purchase under the base case 

(the case without new energy efficiency standards). DOE refers to this distribution of product 

energy efficiencies as the base case efficiency distribution. Using the projected distribution of 

efficiencies for portable ACs, DOE randomly assigned a product efficiency to each household

and commercial user drawn from the RECS 2009 and CBECS 2003 data sets. If a consumer is 

assigned a product efficiency that is greater than or equal to the efficiency under consideration, 

the LCC calculation shows that the consumer would not be affected by that efficiency level. The 

energy efficiency distributions that DOE used in the LCC analysis are described below.

DOE counted the numbers of portable AC models available from online retailers to 

obtain the percentage of single-duct and dual-duct models. The single-duct models were 

allocated to the baseline efficiency level. The dual-duct models were split evenly between 

efficiency levels 1 and 2. DOE is unaware of any models on the market that exceed efficiency 

level 2. Table 8.2.19 shows the resulting base case efficiency distribution. DOE assumed that the 

residential and commercial sectors have the same base case efficiency distribution.

Table 8.2.19 Portable ACs: Base case Market Shares in 2014

Efficiency 

Level EERcm

Market 

Share %

Baseline 2.08 90.0

1 3.53 5.0

2 4.32 5.0

3 5.28 0.0

4 5.82 0.0

8.3 INPUTS TO PAYBACK PERIOD 

The payback period (PBP) is the amount of time, expressed in years, it takes a consumer

to recover the assumed higher purchase price of a more energy efficient product through lower 

operating costs. Payback periods can exceed the life of a product if the increased total installed 

cost of the more efficient product is not recovered quickly enough through reduced operating 

costs. Numerically, the PBP is the ratio of the increase in purchase cost (i.e., from a less efficient 

to a more efficient design) to the decrease in first-year annual operating expenditures. The 

equation for PBP is:

PBP =

∆IC

∆OC
8-29

Where:

PBP = payback period in years,

∆ IC = difference in the total installed cost between the more efficient product 

(efficiency levels 1, 2, 3, etc.) and the baseline product, and

∆OC = difference in first-year annual operating costs between the more efficient 

product and the baseline product.

The data inputs to PBP are the total installed cost of the product to the consumer for each 

efficiency level and the annual (first-year) operating costs for each efficiency level. As for the 

LCC, the inputs to the total installed cost are the product price and installation cost. The inputs to 

the operating costs are the annual energy and annual maintenance costs. The PBP uses the same 

inputs as does the LCC analysis, except that electricity price trends are not required. Because the 

PBP is a simple payback, the required electricity cost is only for the year in which a potential 

new efficiency standard would take effect—in this case, 2019.

DOE also calculates a rebuttable PBP, which is the time it takes the consumer to recover 

the assumed higher purchase cost of a more energy efficient product through lower energy costs. 

Numerically, the rebuttable PBP is the ratio of the increase in purchase cost (from a less efficient 

to a more efficient design) to the decrease in annual energy expenditures, which is the decrease

in first-year annual energy costs as calculated using the DOE test procedure. The calculation 

excludes repair and maintenance costs. Because there currently is no DOE test procedure for 

portable ACs—it is in development—DOE has not yet calculated the rebuttable PBP.

8.4 RESULTS OF LIFE-CYCLE COST AND PAYBACK PERIOD ANALYSIS

This section presents the LCC and PBP results for portable ACs. As discussed in section

8.1.1, DOE’s approach to conducting the LCC analysis relied on developing samples of 

consumers who use room ACs (as a stand-in for portable ACs). DOE characterized the 

uncertainty of many of the inputs to the analysis with probability distributions. DOE used a 

Monte Carlo simulation technique to calculate the average LCC and LCC savings for the 

consumers in the sample. The calculation of payback period uses average values rather than 

distributions. PBP is calculated by dividing the change in average installed cost by the change in 

average first-year operating cost for the baseline efficiency level and each higher efficiency level 

considered. 

DOE calculated LCC savings and PBPs relative to the base case products that it assigned 

to sample households. As noted in section 8.2.8, for some consumers DOE assigned a baseline 

product that is more efficient than some of the efficiency levels considered. For that reason, the 

average LCC impacts are not equal to the difference between the LCC of a specific efficiency 

level and the LCC of the baseline product.
8-30

LCC calculations were performed 10,000 times on the sample of consumers established 

for residential and commercial applications. Each LCC calculation was performed on a single 

consumer who was selected from the sample. The selection of a consumer was based on its 

weight (i.e., how representative a particular consumer is of other consumers in the distribution).

Each LCC calculation also sampled from the probability distributions that DOE developed to 

characterize many of the inputs to the analysis.

Based on the Monte Carlo simulations, DOE calculated the percent of consumers who 

would experience a net LCC cost for each efficiency level. DOE considered a consumer to

receive no impact at a given efficiency level if DOE assigned it a baseline product that operates 

at the same or higher efficiency than the level under consideration. The tables and figures 

presented below illustrate the range of LCC impacts among sample consumers of portable ACs.

Table 8.4.1 through Table 8.4.6 show the LCC and PBP results by efficiency level for 

portable ACs. The efficiency levels correspond to those identified in the engineering analysis

(chapter 5). The LCC results presented in Table 8.4.1 and Table 8.4.2 combine the results for 

residential and commercial users, which means that DOE had to assign an appropriate weight to 

the results for each type of user. DOE found no shipment data on portable ACs that give a 

breakdown between commercial and residential purchasers. DOE assumed that 99 percent of 

shipments are to the residential sector and 1 percent to the commercial sector. 

Table 8.4.1 Summary of LCC and PBP Results by Efficiency Level, All Sectors

Efficiency 

Level EERcm

Average Costs

2013$ Simple 

Payback

Installed years

Cost

First Year’s 

Operating Cost

Lifetime 

Operating Cost LCC

Baseline 2.08 534 101 866 1,399 --

1 3.53 540 73 621 1,161 0.21

2 4.32 541 65 558 1,098 0.19

3 5.28 542 59 509 1,051 0.19

4 5.82 605 54 464 1,069 1.51

Note: The average LCC, LCC savings, and simple PBP for each efficiency level are calculated assuming that all 

consumers use products having that EL. This assumption allows the results for each efficiency level to be 

compared under the same conditions. 
8-31

Table 8.4.2 Summary of Life-Cycle Cost Savings, All Sectors

Efficiency 

Level EERcm

Life-Cycle Cost Savings

% of Consumers Who

Experience Net Cost

Average Savings

2013$

1 3.53 32 213

2 4.32 34 272

3 5.28 36 319

4 5.82 37 301

Note: The LCC savings for each efficiency level are calculated relative to the base case efficiency distribution. The 

calculation includes households that experience zero LCC savings (no impact).

Table 8.4.3 Summary of LCC and PBP Results by Efficiency Level, Residential Settings

Efficiency 

Level EERcm

Average Costs

2013$ Simple 

Payback

Installed years

Cost

First Year’s 

Operating Cost

Lifetime 

Operating Cost LCC

Baseline 2.08 534 101 861 1,394 --

1 3.53 540 72 617 1,156 0.21

2 4.32 541 64 553 1,094 0.19

3 5.28 542 59 505 1,046 0.19

4 5.82 605 53 461 1,066 1.52

Table 8.4.4 Summary of Life-Cycle Cost Savings, Residential Settings

Efficiency 

Level EERcm

Life-Cycle Cost Savings

% of Consumers Who

Experience Net Cost

Average Savings

2013$

1 3.53 32 212

2 4.32 34 271

3 5.28 35 319

4 5.82 37 300

Table 8.4.5 Summary of LCC and PBP Results by Efficiency Level, Commercial Settings

Efficiency 

Level EERcm

Average Costs

2013$

Simple 

Payback
8-32

Installed 

Cost

First Year’s 

Operating 

Cost

Lifetime 

Operating 

Cost

LCC

years

Baseline 2.08 534 190 1,351 1,884 --

1 3.53 540 150 1,066 1,606 0.15

2 4.32 541 139 9,90 1,531 0.14

3 5.28 542 131 938 1,480 0.13

4 5.82 605 117 836 1,441 0.98

Table 8.4.6 Summary of Life-Cycle Cost Savings, Commercial Settings

Efficiency 

Level EERcm

Life-Cycle Cost Savings

% of Consumers Who

Experience Net Cost

Average Savings

2013$

1 3.53 50 253

2 4.32 52 326

3 5.28 55 376

4 5.82 30 415

8.4.1 Base case Distributions of Life-Cycle Cost

Figure 8.4.1 shows the base case LCC distribution for portable ACs for residential 

consumers. The figure shows the full range of LCCs for the sample of portable ACs. Figure 8.4.2

shows the base case distributions of LLC for portable ACs in commercial settings.
8-33

Figure 8.4.1 Base case Distribution of LCCs, Residential Settings 

Figure 8.4.2 Base case Distribution of LCCs, Commercial 

Settings
8-34

8.4.2 Distributions of Life-Cycle Costs at Higher Efficiency Levels

Figure 8.4.3 and Figure 8.4.4 are frequency charts that show the distributions of LCC

savings at efficiency level 1 for portable ACs used in residential and commercial settings, 

respectively. DOE can generate frequency charts similar to those shown for every efficiency 

level.

Figure 8.4.3 Distribution of LCC Savings for Efficiency Level 1, 

Residential Settings
8-35

Figure 8.4.4 Distribution of LCC Savings for Efficiency Level 1, 

Commercial Settings

Figure 8.4.5 and Figure 8.4.6 show the range of LCC savings for the efficiency levels

considered for portable ACs in residential and commercial settings, respectively. For each 

efficiency level, the top and the bottom of the box indicate the 75th and 25th percentiles, 

respectively. The red line at the middle of the box indicates the median; 50 percent of households 

or establishments have life-cycle cost savings greater than this value. The “whiskers” at the 

bottom and the top of each box indicate the 5th and 95th percentiles. The red circle shows the 

average LCC savings for each efficiency level.
8-36

Figure 8.4.5 Range of Average LCC Savings, Residential Settings

Figure 8.4.6 Range of Average LCC Savings, Commercial 

Settings
8-37

REFERENCES

 

1 Desroches et al. (2013)“Incorporating Experience Curves in Appliances Standards 

Analysis”, Energy Policy. 2013. Vol. 52, pp. 402-416 (Last Accessed September 11, 

2014.) <http://dx.doi.org/10.1016/j.enpol.2012.09.066>

2 Weiss, M., H.M. Junginger, M.K. Patel, and K. Blok. 2010. A Review of Experience 

Curve Analyses for Energy Demand Technologies. Technological Forecasting & Social 

Change. Vol. 77: pp. 411–428.

3 U.S. Department of Labor Bureau of Labor Statistics. Producer Price Index for 1983–

2013. PPI series ID: PCU33521033521014. (Last accessed September 8, 2014.) 

<http://www.bls.gov/ppi/>

4 U.S. Department of Energy - Energy Information Administration, Form EIA-826 

Database Monthly Electric Utility Sales and Revenue Data, 2013.

<http://www.eia.doe.gov/cneaf/electricity/page/eia826.html>

5 U.S. Department of Energy-Energy Information Administration, Annual Energy Outlook 

2014 with Projections to 2040, 2014. Washington, DC. 

<http://www.eia.gov/forecasts/aeo/>

6 U.S. Department of Energy–Office of Energy Efficiency and Renewable Energy. Energy 

Conservation Program for Consumer Products: Energy Conservation Standards for 

Clothes Dryers and Room Air Conditioners; Final Rule. 10 CFR Part 430. Federal 

Register. August 19, 2011. Vol. 76, no.164: pp. 52854–52862. (Last accessed September 

8, 2014.) http://www.regulations.gov/#!documentDetail;D=EERE-2007-BT-STD-0010-

0067

7 The Federal Reserve Board. Survey of Consumer Finances (SCF). 1989, 1992, 1995, 

1998, 2001, 2004, 2007, 2010. 

<http://www.federalreserve.gov/pubs/oss/oss2/scfindex.html>

8 U.S. Department of Labor–Bureau of Labor Statistics. Bureau of Labor Statistics Data, 

Prices & Living Conditions. 2012. (Last accessed September 8, 2014.) 

<http://data.bls.gov>

9 The Federal Reserve Board, Federal Reserve Statistical Release, Selected Interest Rates, 

Historical Data, Instrument: Savings Bonds: 20-year, 

Frequency.<www.federalreserve.gov/releases/H15/data.htm>

10 The Federal Reserve Board, Federal Reserve Statistical Release, Selected Interest Rates, 

Historical Data, Instrument: Corporate bonds/Moody’s Seasoned AAA, Frequency: 

Annual, Description: Moody’s yield on seasoned corporate bonds—all industries, AAA. 
8-38

 

2013. (Last accessed September 8, 2014.) 

<www.federalreserve.gov/releases/H15/data.htm>

11 The Federal Reserve Board, Federal Reserve Statistical Release, Selected Interest Rates, 

Historical Data, Instrument: CDs (secondary market), Maturity: 6-month, Frequency: 

Annual, Description: Average rate on 6-month negotiable certificates of deposit 

(secondary market), quoted on an investment basis. 2013. (Last accessed September 8, 

2014.) <www.federalreserve.gov/releases/H15/data.htm>

12 The Federal Reserve Board, Federal Reserve Statistical Release, Selected Interest Rates, 

Historical Data, Instrument: Savings Bonds: 20-year, 

Frequency.<www.federalreserve.gov/releases/H15/data.htm>

13 The Federal Reserve Board, Federal Reserve Statistical Release, Selected Interest Rates, 

Historical Data, Instrument: Corporate bonds/Moody’s Seasoned AAA, Frequency: 

Annual, Description: Moody’s yield on seasoned corporate bonds—all industries, AAA. 

2013. (Last accessed September 8, 2014.)

14 Mortgage-X - Mortgage Information Service, Cost of Savings Index (COSI) Index 

History. 2013. (Last accessed September 8, 2014.) <http://mortgagex.com/general/indexes/default.asp>

15 Damodaran Online Data Page. The Data Page: Historical Returns on Stocks, Bonds and 

Bills - United States, 2013. Damodaran. (Last accessed September 8, 2014).

16 Modigliani, F. and M. Miller, The Cost of Capital, Corporation Finance and the Theory 

of Investment. American Economic Review, 1958. June: pp. 261-297

17 Ibbotson Associates, SBBI Valuation Edition 2009 Yearbook. 2009. Chicago, IL.

18 Federal Reserve Board, Federal Reserve Bank Services Private Sector Adjustment 

Factor, 2005, 2005. Washington, D.C. (Last accessed September 8, 2014.) 

<http://www.federalreserve.gov/boarddocs/Press/other/2005/20051012/attachment.pdf>

19 Federal Reserve Board, H.15 Historical Data Selected Interest Rates, 2013. (Last 

accessed September 8, 2014.) <http://www.federalreserve.gov/releases/H15/data.htm>

20 U.S. Department of Energy, Implementation Report: Energy Conservation Standards 

Activities: Submitted Pursuant to Section 141 of the Energy Policy Act of 2005, 2006. 

<http://www1.eere.energy.gov/buildings/appliance_standards/pdfs/implementation_repor

t_0806.pdf >