8-i

CHAPTER 8. LIFE-CYCLE COST AND PAYBACK PERIOD ANALYSIS 

TABLE OF CONTENTS 

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

8.1.1 General Approach for Life-Cycle Cost and Payback Period Analysis................ 8-1 

8.1.2 Overview of Life-Cycle Cost and Payback Period Inputs................................... 8-3

8-5

8-9

8-11

8-11

8-16

8-18

8-19

8-20

8-21

8-21

8-22

8-23

8-23

8-24

8-27

8-31

8-31

8-32

8-33

8-33

8-35

8-37

8-40

8-42

8-47

8-7

8-8

8.2 LIFE-CYCLE COST INPUTS ........................................................................................ 

8.2.2 Total Installed Cost Inputs................................................................................... 

8.2.2.1 Baseline Manufacturer Selling Price ........................................................... 

8.2.2.2 Manufacturer Selling Price Increases for Higher-Efficiency Products........ 

8.2.3 Operating Cost Inputs........................................................................................ 

8.2.3.1 Annual Energy Consumption....................................................................... 

8.2.3.2 Energy Prices............................................................................................... 

8.2.3.3 Energy Price Trends..................................................................................... 

8.2.3.4 Repair and Maintenance Costs..................................................................... 

8.2.3.5 Motor Lifetime............................................................................................. 

8.2.4 The Weibull Distribution ................................................................................... 

8.2.5 Capacitor-Start Mechanical and Application Lifetimes .................................... 

8.2.6 Polyphase Mechanical and Application Lifetimes ............................................ 

8.2.6.1 Discount Rates............................................................................................. 

From rulemaking on distribution transformer standards ............................................... 

8.2.6.2 Effective Date of Standard........................................................................... 

8.2.7 Product Energy Efficiency in the Base Case ..................................................... 

8.3 PAYBACK PERIOD INPUTS...................................................................................... 

8.4 LIFE-CYCLE COST AND PAYBACK PERIOD RESULTS FOR 

REPRESENTATIVE PRODUCT CLASSES ............................................................... 

8.4.1 Polyphase Motors............................................................................................... 

8.4.2 Capacitor-Start Induction-Run Motors.............................................................. 

8.4.3 Capacitor-Start Capacitor-Run Motors.............................................................. 

8.5 LIFE CYCLE COSTS FOR ALL PRODUCT CLASSES ............................................ 

8.6 LIFE-CYCLE COST SENSITIVITY CALCULATIONS ............................................ 

8.7 REBUTTABLE PAYBACK PERIOD.......................................................................... 

LIST OF TABLES 

Table 8.1.1 Application Shares by Equipment Class.............................................................. 8-2 

Table 8.1.2 Shares of Motor Owner Type by Application...................................................... 8-2 

Table 8.2.1 Inputs for Life-Cycle Cost and Payback Period Analysis: Polyphase 

Motors.................................................................................................................. 

Table 8.2.2 Inputs for Life-Cycle Cost and Payback Period Analysis: Capacitor-Start 

Induction-Run Motors.......................................................................................... 

EERE-2007-BT-STD-0007 COMMENT 33
8-ii

Table 8.2.3 Inputs for Life-Cycle Cost and Payback Period Analysis: Capacitor-Start 

Capacitor-Run Motors ......................................................................................... 8-9

8-10

8-11

8-12

8-12

8-13

8-13

8-14

8-14

8-15

8-15

8-16

8-16

8-17

8-19

8-26

8-27

8-28

8-29

8-29

8-30

Table 8.2.24 Shares and Interest or Return Rates Used for Household Debt and Equity 

Types.................................................................................................................. 8-31 

8-32

8-35

8-37

Table 8.2.4 Inputs for Total Installed Cost ........................................................................... 

Table 8.2.5 Engineering Baseline Manufacturer Selling Price............................................. 

Table 8.2.6 Polyphase Motors: Manufacturer Selling Price Increases, 1 Horsepower......... 

Table 8.2.7 Capacitor-Start Induction-Run Motors: Manufacturer Selling Price 

Increases, 0.5 Horsepower................................................................................. 

Table 8.2.8 Capacitor-Start Capacitor-Run Motors: Manufacturer Selling Price 

Increases, 0.75 Horsepower............................................................................... 

Table 8.2.9 Markups for Small Electric Motors................................................................... 

Table 8.2.10 Polyphase Motors (1 hp): Consumer Equipment Prices, Shipping Costs, 

Installation Costs, and Total Installed Costs for Motors that are Not SpaceConstrained ........................................................................................................ 

Table 8.2.11 Polyphase Motors (1 hp): Consumer Equipment Prices, Shipping Costs, 

Installation Costs, and Total Installed Costs for Motors that are SpaceConstrained ........................................................................................................ 

Table 8.2.12 Capacitor-Start Induction-Run Motors (0.5 hp): Consumer Equipment 

Prices, Shipping Costs, Installation Costs, and Total Installed Costs for 

Motors that are Not Space-Constrained............................................................. 

Table 8.2.13 Capacitor-Start Induction-Run Motors (0.5 hp): Consumer Equipment 

Prices, Shipping Costs, Installation Costs, and Total Installed Costs for 

Motors that are Space-Constrained.................................................................... 

Table 8.2.14 Capacitor-Start Capacitor-Run Motors (0.75 hp): Consumer Equipment 

Prices, Shipping Costs, Installation Costs, and Total Installed Costs for 

Motors that are Not Space-Constrained............................................................. 

Table 8.2.15 Capacitor-Start Capacitor-Run Motors (0.75 hp): Consumer Equipment 

Prices, Shipping Costs, Installation Costs, and Total Installed Costs for 

Motors that are Space-Constrained.................................................................... 

Table 8.2.16 Inputs for Operating Cost................................................................................... 

Table 8.2.17 Average Annual Electricity Use by Efficiency Level for Small Electric 

Motors................................................................................................................ 

Table 8.2.18 Adjusted Real Discount Rates for Updated Values of Rf and ERP.................... 

Table 8.2.19 Weighted Average Cost of Capital for Sectors that Purchase Small Electric 

Motors................................................................................................................ 

Table 8.2.20 Average Shares of Considered Household Debt and Equity Types .................. 

Table 8.2.21 Average Nominal Interest Rates for Household Debt Classes (percent)........... 

Table 8.2.22 Average Real Effective Interest Rates for Household Debt Classes 

(percent)............................................................................................................. 

Table 8.2.23 Average Nominal and Real Interest Rates for Household Equity Types........... 

Table 8.2.25 Product Energy Efficiency in the Base Case ..................................................... 

Table 8.4.1 Polyphase Motors: Life-Cycle Cost and Payback Period Results..................... 

Table 8.4.2 Capacitor-Start Induction-Run Motors: Life-Cycle Cost and Payback 

Period Results.................................................................................................... 

EERE-2007-BT-STD-0007 COMMENT 33
8-iii

Table 8.4.3 Capacitor-Start Capacitor-Run Motors: Life-Cycle Cost and Payback 

Period Results.................................................................................................... 8-40

8-41

8-41

8-42

8-42

8-43

8-44

8-45

8-46

8-47

8-48

8-48

8-5

8-20

8-21

8-34

8-34

8-36

8-36

8-38

Table 8.5.1 Parameters for Motor Purchase Cost Model...................................................... 

Table 8.5.2 Polyphase Motor Consumer Cost Scaling Factors............................................. 

Table 8.5.3 CSIR Motor Consumer Cost Scaling Factors.................................................... 

Table 8.5.4 CSCR Motor Consumer Cost Scaling Factors................................................... 

Table 8.6.1 Polyphase Small Electric Motors: Life-Cycle Cost and Payback Period 

Sensitivity Results for a Shipments-weighted Distribution of Motor 

Capacities and Poles for Purchase Year 2030 and with 100% Power Factor 

Costs Included.................................................................................................... 

Table 8.6.2 Capacitor-Start Induction-Run Small Electric Motors: Life-Cycle Cost and 

Payback Period Sensitivity Results for a Shipments-Weighted Distribution 

of Motor Capacities and Poles for Purchase Year 2030 and with 100% 

Power Factor Costs Included ............................................................................. 

Table 8.6.3 Capacitor-Start Capacitor-Run Small Electric Motors: Life-Cycle Cost and 

Payback Period Sensitivity Results for a Shipments-weighted Distribution 

of Motor Capacities and Poles for Purchase Year 2030 and with 100% 

Power Factor Costs Included ............................................................................. 

Table 8.6.4 Capacitor-Start Small Electric Motors: Life-Cycle Cost and Payback 

Period Sensitivity Results for a Space-Constrained 0.5 hp, 4-pole CSCR 

Motor Customer with a CSIR Motor Baseline .................................................. 

Table 8.6.5 Capacitor-Start Induction-Run Motors: Shipment-Weighted Life-Cycle 

Cost and Payback Period Results for a 4-Pole One-Half Horsepower 

Motor with Switching to CSCR......................................................................... 

Table 8.7.1 Rebuttable Presumption Payback for Polyphase Motors................................... 

Table 8.7.2 Rebuttable Presumption Payback for Capacitor-Start Motors........................... 

LIST OF FIGURES 

Figure 8.1.1 Flow Diagram of Inputs for the Determination of Life-Cycle Cost and 

Payback Period..................................................................................................... 

Figure 8.2.1 Electricity Price (2007$/kWh) Distributions..................................................... 

Figure 8.2.2 Industrial Electricity Price Trends..................................................................... 

Figure 8.4.1 Polyphase Motors: Distribution of Life-Cycle Cost Savings for Efficiency 

Level 5 ............................................................................................................... 

Figure 8.4.2 Polyphase Motors: Distribution of Payback Periods for Efficiency Level 5..... 

Figure 8.4.3 Capacitor-Start Induction-Run Motors: Distribution of Life-Cycle Cost 

Savings for Efficiency Level 7 ......................................................................... 

Figure 8.4.4 Capacitor-Start Induction-Run Motors: Distribution of Payback Periods 

for Efficiency Level 7 ....................................................................................... 

Figure 8.4.5 Capacitor-Start Capacitor-Run Motors: Distribution of Life-Cycle Cost 

Savings for Efficiency Level 3 .......................................................................... 

EERE-2007-BT-STD-0007 COMMENT 33
8-iv

Figure 8.4.6 Capacitor-Start Capacitor-Run Motors: Distribution of Payback Periods 

for Efficiency Level 3 ....................................................................................... 8-39

EERE-2007-BT-STD-0007 COMMENT 33
8-1 

CHAPTER 8. LIFE-CYCLE COST AND PAYBACK PERIOD ANALYSIS 

8.1 INTRODUCTION 

 This chapter describes the Department of Energy (DOE)’s methodology for analyzing the 

economic impacts of possible energy efficiency standards on individual end users. The effect of 

standards on individual end users includes a change in operating expense (usually decreased) and 

a change in purchase price (usually increased). This chapter describes three metrics DOE used to 

determine the effect of standards on individual end users: 

• Life-cycle cost (LCC) is the total consumer expense over 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 equipment. 

• Payback period (PBP) is the change in purchase expense due to an increased efficiency 

standard divided by the change in annual operating expense that results from the 

standard. It represents the number of years it will take the user to recover the increased 

purchase expense through decreased operating expenses. 

• Rebuttable payback period is a special case of the PBP. Where LCC and PBP are 

estimated over a range of inputs reflecting actual conditions, rebuttable payback period is 

based on laboratory conditions, specifically DOE test procedure inputs. 

 Inputs to the LCC and PBP are discussed in sections 8.2 and 8.3, respectively, of this 

chapter. Results for the LCC and PBP are presented in section 8.4. The rebuttable PBP is 

discussed in section 8.5. Key variables and calculations are presented for each metric. DOE 

performed the calculations discussed here using a Microsoft Excel spreadsheet which is 

accessible on the Internet (http://www.eere.energy.gov/buildings/appliance_standards/). 

8.1.1 General Approach for Life-Cycle Cost and Payback Period Analysis 

 Recognizing that several inputs to the determination of consumer LCC and PBP are 

either variable or uncertain, DOE conducted the LCC and PBP analysis by modeling both the 

uncertainty and variability in the inputs using Monte Carlo simulation and probability 

distributions. DOE developed LCC and PBP spreadsheet models incorporating both Monte Carlo 

simulation and probability distributions by using a Microsoft Excel spreadsheet combined with 

Crystal Ball (a commercially available add-in program). 

 In addition to characterizing several of the inputs to the analysis with probability 

distributions, DOE also developed a sample of end-use applications for the equipment. These 

end-use applications determine the use profile of the motor and the economic characteristics of 

EERE-2007-BT-STD-0007 COMMENT 33
8-2 

the motor owner. Table 8.1.1 shows the market shares of each application for each equipment 

class. 

Table 8.1.1 Application Shares by Equipment Class 

Equipment Class 

No. Application Polyphase CSIR CSCR 

1 Air and gas compressors 17.3% 14.9% 14.9% 

2 Conveyors 13.3% 11.9% 11.9% 

3 General industrial machinery 11.3% 12.5% 12.5% 

4 Industrial and commercial fans and blowers 7.3% 6.9% 6.9% 

5 Pumps and pumping equipment 50.7% 53.7% 53.7% 

TOTAL 100% 100% 100% 

 In each Monte Carlo iteration, for each equipment class, one of the applications is 

identified by sampling a distribution of applications for that equipment class. The selected 

application determines the number of operating hours per year as well as the motor loading. The 

operating hours and the motor loading for the application are used in the energy use calculation 

(see Chapter 6). 

 There is also a distribution of owner types (by sector) associated with each application 

(Table 8.1.2). The sector to which the application belongs determines the energy price and 

discount rate used in the LCC calculation in each simulation. 

Table 8.1.2 Shares of Motor Owner Type by Application 

Motor Owner Type (%) 

No. Application Industrial Commercial Agricultural Residential

1 Air and gas compressors 40% 40% 10% 10% 

2 Conveyors and packaging equipment 40% 50% 10% 0% 

3 General industrial machinery 50% 40% 10% 0% 

4 Industrial and commercial fans and blowers 50% 50% 0% 0% 

5 Pumps and pumping equipment 40% 35% 20% 5% 

 DOE used Energy Information Administration (EIA) data on electricity prices in 2006 for 

different customer classes (which is accessible on the Internet at 

http://www.eia.doe.gov/cneaf/electricity/page/eia861.html) to establish the variability in energy 

pricing. DOE used data from the literature on motor loading and motor application 

characteristics to estimate the variability of annual energy use. Due to the large range of 

applications and motor use characteristics considered in the LCC and PBP analysis, the range of 

annual energy use and energy prices can be quite large. Thus, although the annual energy use and 

EERE-2007-BT-STD-0007 COMMENT 33
8-3 

energy pricing are not uncertain for any particular application, their variability across all 

applications contributes to the range of LCCs and PBPs calculated for any particular standard 

level. 

 Results presented at the end of this chapter are based on 10,000 samples per Monte Carlo 

simulation run. DOE displays the LCC and PBP results as distributions of impacts compared to 

the base case without standards. 

8.1.2 Overview of Life-Cycle Cost and Payback Period Inputs 

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

establishing the initial expense, otherwise known as the total installed cost, and (2) inputs for 

calculating the operating cost. 

 The primary inputs for establishing the total installed cost are: 

• Baseline manufacturer selling price: The price at which the manufacturer sells the 

baseline equipment, which includes the costs incurred by the manufacturer to produce 

equipment meeting existing standards. 

• Manufacturer selling price increases: The change in manufacturer selling price 

associated with producing equipment to meet a particular standard level. 

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

manufacturer cost to a consumer equipment price. The markups and sale tax are 

described in detail in Chapter 7, Markups for Equipment Price Determination. 

• Installation cost: The cost to the consumer of installing the equipment. The installation 

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

consumer equipment price. The installation cost includes labor, overhead, and any 

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

equipment price plus the installation cost. 

 The primary inputs for calculating the operating cost are: 

• Equipment energy consumption and reactive power: The equipment energy consumption 

is the site energy use associated with operating the equipment. Reactive power is power 

that is reflected back to the electrical system by a change in the phase of alternating 

current power. Chapter 6, Energy Use Characterization, details how DOE determined the 

equipment energy consumption based on various data sources. 

• Equipment efficiency: The equipment efficiency dictates the energy consumption 

associated with standard-level equipment (i.e., equipment with efficiencies greater than 

baseline equipment). Chapter 6, Energy Use Characterization, details how energy and 

reactive power change with increasing equipment efficiency and how equipment 

efficiency relates to actual equipment energy use. 

EERE-2007-BT-STD-0007 COMMENT 33
8-4 

• Energy prices: Energy prices are the prices paid by end users for energy (i.e., electricity). 

DOE determined current energy prices based on data from the DOE-EIA. 

• Energy price trends: DOE used the EIA Annual Energy Outlook 2009 (AEO2009) to 

forecast energy prices into the future. For the results presented in this chapter, DOE used 

the American Recovery and Reinvestent Act case of AEO2009 (DOE’s reference case) to 

forecast future energy prices. 

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

components that have failed. Maintenance costs are associated with maintaining the 

operation of the equipment. 

• Lifetime: The age at which the equipment is retired from service. 

• Discount rate: The rate at which DOE discounted future expenditures to establish their 

present value. 

 Figure 8.1.1 graphically depicts the relationships between the installed cost and operating 

cost inputs for the calculation of the LCC and PBP. In the figure below, the yellow boxes 

indicate the inputs, the green boxes indicate intermediate outputs, and the blue boxes indicate the 

final outputs (the LCC and PBP). 

EERE-2007-BT-STD-0007 COMMENT 33
Figure 8.1.1 Flow Diagram of Inputs for the Determination of Life-Cycle Cost 

and Payback Period 

8.2 LIFE-CYCLE COST INPUTS 

 Life-cycle cost is the total customer expense over the life of a piece of equipment, 

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 equipment. 

DOE defines LCC by the following equation: 

( ) ∑= +

+=

N

t

t

t

r

OC ICLCC

1 1

Where: 

LCC = life-cycle cost in dollars, 

8-5 

EERE-2007-BT-STD-0007 COMMENT 33
8-6 

IC = total installed cost in dollars, 

∑ = sum over the 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 and PBP analysis in 2008, DOE 

expresses dollar values in 2008$. 

 Tables 8.1.1 through 8.1.3 summarize the input values that DOE used to calculate the 

LCC and PBP for the three equipment classes of small electric motors: polyphase, capacitor-start 

induction-run (CSIR), and capacitor-start capacitor-run (CSCR) respectively. Each table 

summarizes the total installed cost inputs and the operating cost inputs including the lifetime, 

discount rate, and energy price trends. DOE characterized all of the total cost inputs with singlepoint values, but characterized several of the operating cost inputs with probability distributions 

that capture the input’s uncertainty and/or variability. For those inputs characterized with 

probability distributions, the values provided in the following tables are the average or typical 

values. Also listed in the following tables is the chapter of the technical support document (TSD) 

where more detailed information on the inputs can be found. The sections following the tables 

discuss total installed cost, operating cost, lifetime, and discount rate. 

EERE-2007-BT-STD-0007 COMMENT 33
8-7 

Table 8.2.1 Inputs for Life-Cycle Cost and Payback Period Analysis: Polyphase Motors 

Input Average or Typical Value Characterization 

TSD Chapter 

Reference 

Total Installed Cost Inputs 

Baseline Manufacturer 

Selling Price 

77.15% = $97.74 Single-Point Value 5 

Manufacturer Selling 

Price 

78.7% = $103.81 

80.0% = $107.01 

81.6% = $112.88 

82.5% = $117.01 

85.2% = $150.86 - $229.84 

86.7% = $184.73 - $236.20 

88.3% = $324.66 - $1,770.27 

Price varies with efficiency level 

and whether or not application is 

space-constrained. DOE estimates 

20% of applications may be spaceconstrained 

5 

Distribution and OEM 

Markups 

Baseline = 2.33 

Incremental = 1.71 

Shipping Cost = $0.50/pound 

Point Value for each distribution 

chain with 20% variance added 7 

Sales Tax 1.0684 Point Value 7 

Installation Cost $252.90 Point Value 8 

Operating Cost Inputs 

Duty cycle 2665 hours/year 

Full distribution ranging from 50 

to 8760 hours per year and with 

distribution varying with 

application 

6 

Annual Energy Use Baseline use* = 1763 kWh Variability based on usage 6 

Reactive Power Baseline = 0.94 kilovolt-amperes 

reactive 

Variability based on usage, load 

and power factor 6 

Energy Prices 

(Marginal) 

Electric Energy = 7.6 ¢/kWh Variability based on application 

owner types 8 

Repair and Maintenance 

Costs No cost increase with efficiency No cost increase with efficiency 8 

Lifetime 9 years Distribution based in part on 

annual hours of operation 8 

Discount Rate 5.87% Variability based on application 

owner types 8 

Energy Price Trend AEO 2009 American Recovery 

and Reinvestment Act Case 

Two sensitivities: 

High & Low Energy Price Cases 8 

* Annual use provided for market baseline product only. Annual use decreases with increased product efficiency. 

EERE-2007-BT-STD-0007 COMMENT 33
8-8 

Table 8.2.2 Inputs for Life-Cycle Cost and Payback Period Analysis: Capacitor-Start 

Induction-Run Motors 

Input Average or Typical Value Characterization 

TSD Chapter 

Reference 

Total Installed Cost Inputs 

Baseline Manufacturer 

Selling Price 

57.7% = $91.04 Single-Point Value 5 

Manufacturer Selling 

Price 

59.5% = $95.62 

62.0% = $98.54 

64.2% = $99.78 

68.5% = $107.19 – 114.57 

71.2% = $118.98 

73.0% = $132.16 - $182.28 

77.0% = $150.70 - $1,204.30 

Price varies with efficiency level 

and whether or not application is 

space-constrained. DOE estimates 

20% of applications may be spaceconstrained 

5 

Distribution and OEM 

Markups 

Baseline = 2.33 

Incremental = 1.71 

Shipping Cost = $0.50/pound 

Point Value for each distribution 

chain, with 20% variance added 7 

Sales Tax 1.0684 Point Value 7 

Installation Cost $252.90 Point Value 8 

Operating Cost Inputs 

Usage 2627 hours/year 

Full distribution ranging from 50 

to 8760 hours per year and with 

distribution varying with 

application 

6 

Annual Energy Use Baseline use* = 1277 kWh Variability based on usage 6 

Reactive Power Baseline = 0.88 kilovolt-amperes 

reactive 

Variability based on usage, load 

and power factor 6 

Energy Prices Electric Energy = 7.6 ¢/kWh Variability based on application 

owner types 8 

Repair and Maintenance 

Costs No cost increase with efficiency No cost increase with efficiency 8 

Lifetime 7 years Distribution based in part on 

annual hours of operation 8 

Discount Rate 5.86% Variability based on application 

owner types 8 

Energy Price Trend AEO 2009 American Recovery 

and Reinvestment Act Case 

Two sensitivities: 

High & Low Energy Price Cases 8 

* Annual use provided for market baseline product only. Annual use decreases with increased product efficiency. 

EERE-2007-BT-STD-0007 COMMENT 33
Table 8.2.3 Inputs for Life-Cycle Cost and Payback Period Analysis: Capacitor-Start 

Capacitor-Run Motors 

Input Average or Typical Value Characterization 

TSD Chapter 

Reference 

Total Installed Cost Inputs 

Baseline Manufacturer 

Selling Price 

71.0% = $110.82 (engineering) Single-Point Value 5 

Manufacturer Selling 

Price 

74.3% = $116.06 

78.3% = $128.60 - $136.22 

80.3% = $133.71 - $141.49 

81.6% = $142.23 - $145.27 

82.7% = $149.23 - $152.88 

83.7% = $162.90 - $237.53 

85.4% = $172.75 - $245.36 

87.3% = $353.50 - $1,778.48 

Price curve using power law 

interpolation to determine price 

increase relative to engineering 

baseline 

5 

Distribution and OEM 

Markups 

Baseline = 2.33 

Incremental = 1.71 

Shipping Cost = $0.50/pound 

Point Value for each distribution 

chain, with 20% variance added 7 

Sales Tax 1.0684 Single-Point Value 7 

Installation Cost $252.90 Single-Point Value 8 

Operating Cost Inputs 

Usage 2627 hours/year 

Variability determined from 

distribution of applications. Usage 

ranges from 50 to 8760 hours/year 

6 

Annual Energy Use Baseline use* = 1451 kWh Variability based on usage 6 

Reactive Power Baseline = 0.82 kilovolt-amperes 

reactive 

Variability based on usage, load 

and power factor 6 

Energy Prices Electricity = 7.6 ¢/kWh Variability based on application 

owner types 8 

Repair and Maintenance 

Costs No cost increase with efficiency No cost increase with efficiency 8 

Lifetime 7 years Distribution based in part on 

annual hours of operation 8 

Discount Rate 5.86% Variability based on application 

owner types 8 

Energy Price Trend AEO 2009 American Recovery 

and Reinvestment Act Case 

Two sensitivities: 

High & Low Energy Price Cases 8 

* Annual use provided for market baseline product only. Annual use decreases with increased product efficiency. 

8.2.2 Total Installed Cost Inputs 

DOE defines the total installed cost, IC, using the following equation: 

= EQPIC + INST

8-9 

Where: 

EERE-2007-BT-STD-0007 COMMENT 33
EQP = equipment price (i.e., customer cost for the equipment only), expressed in 

dollars, and 

INST = installation cost or the customer price to install equipment (i.e., the cost for 

labor and materials), also in dollars. 

 The equipment price is based on how the customer (end user) purchases the equipment. 

As discussed in Chapter 7, Markups for Equipment Price Determination, DOE defined markups 

and sales taxes for converting manufacturing selling prices into customer equipment prices. 

 Table 8.2.4 summarizes the inputs for the determination of total installed cost. 

Table 8.2.4 Inputs for Total Installed Cost 

Baseline Manufacturer Selling Price 

Manufacturer Selling Price Increase 

Markups and Sales Tax 

Installation Cost 

The baseline manufacturer selling price is the price charged by the manufacturer to 

produce equipment for the current market. Manufacturer selling price increase is the change in 

manufacturer price associated with producing equipment at a standard level. Markups and sales 

tax convert the manufacturer selling price to a consumer equipment price. The installation cost is 

the cost to the consumer of installing the equipment and represents all costs required to install the 

equipment other than the marked-up consumer equipment price. The installation cost includes 

labor, overhead, and any miscellaneous materials and parts. Thus, the total installed cost equals 

the consumer equipment price plus the installation cost. DOE calculated the total installed cost 

for baseline products based on the following equation: 

MFG OVERALL BASE BASE

BASE BASE BASE

MSP MU INST

IC EQP INST

×= +

= +

_

Where: 

ICBASE = baseline total installed cost, 

EQPBASE = consumer equipment price for baseline models, 

INSTBASE = baseline installation and shipping cost, 

MSPMFG = manufacturer selling price for baseline models, and 

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

retailer or distributor markup, and sales tax). 

 DOE calculated the total installed cost for standard-level products based on the following 

equation: 

8-10 

EERE-2007-BT-STD-0007 COMMENT 33
8-11 

)

)

here: 

ICSTD = standard-level total installed cost, 

dard-level models, 

seline models, 

for standard-level models, 

 = g price for standard-level models, and 

The remainder of this section provides information about each of the above input 

ariabl

8.2.2.1 Baseline Manufacturer Selling Price 

 selling price (MSP) that 

SP 

able 8.2.5 Engineering Baseline Manufacturer Selling Price 

seline MSP (2008$) 

( ) (

( ) (

( ) BASE MFG OVERALL INCR STD

BASE BASE STD STD

BASE STD BASE STD

STD STD STD

IC MSP MU INST

EQP INST EQP INST

EQP EQP INST INST

IC EQP INST

×Δ+= Δ+

= + Δ+Δ+

= +Δ+ Δ+

+=

_

W

EQPSTD = consumer equipment price for stan

INSTSTD = standard-level installation cost, 

EQPBASE = consumer equipment price for ba

ΔEQPSTD = change in equipment price for standard-level models, 

INSTBASE = baseline installation and shipping cost, 

ΔINSTSTD = change in installation and shipping cost 

ICBASE = baseline total installed cost, 

ΔMSPMFG change in manufacturer sellin

MUOVERALL_INCR = incremental overall markup (product of manufacturer markup, 

incremental retailer or distributor markup, and sales tax). 

v es that DOE used to calculate the total installed cost for small electric motors. 

 The engineering analysis provides a baseline manufacturer

includes all manufacturer markups (see TSD chapter 5). Table 8.2.5 presents the baseline M

and the associated energy efficiency for each equipment class for the baseline models analyzed 

in the engineering analysis. 

T

Product Class Baseline Efficiency (%) Ba

Polyphase (1 hp) 77.15 $97.74 

CSIR (0.5 hp) 57.70 $91.04 

CSCR (0.75 hp) 71.00 $110.82 

8.2.2.2 Manufacturer Selling Price Increases for Higher-Efficiency Products 

els 

for sma

DOE determined the MSP increases associated with increases in energy efficiency lev

ll electric motors in the engineering analysis (see TSD chapter 5). Tables 8.2.6 through 

8.2.8 present the MSP along with the associated energy efficiency for each equipment category.

EERE-2007-BT-STD-0007 COMMENT 33
8-12 

Table 8.2.6 Polyphase Motors: Manufacturer Selling Price Increases, 1 Horsepower 

Energy Efficiency 

Level 

Efficiency 

(%) 

Not Space-Constrained 

Standard-Level 

MSP (2008$) 

Space-Constrained 

Standard-Level 

MSP (2008$) 

Baseline 77.15 $97.74 $97.74 

1 78.70 $103.81 $103.81 

2 80.00 $107.01 $107.01 

3 81.60 $112.88 $112.88 

4 82.50 $117.01 $117.01 

5 85.20 $150.86 $229.84 

6 86.70 $184.73 $236.20 

7 88.30 $324.66 $1,770.27 

Table 8.2.7 Capacitor-Start Induction-Run Motors: Manufacturer Selling Price 

Increases, 0.5 Horsepower 

Energy Efficiency 

Level 

Efficiency 

(%) 

Not Space-Constrained 

Standard-Level 

MSP (2008$) 

Space-Constrained 

Standard-Level 

MSP (2008$) 

Baseline 57.70 $91.04 $91.04 

1 59.50 $95.62 $95.62 

2 62.00 $98.54 $98.54 

3 64.20 $99.78 $99.78 

4 68.50 $107.19 $114.57 

5 71.20 $118.98 $118.98 

6 73.00 $132.16 $182.28 

7 77.00 $150.70 $1,204.30 

EERE-2007-BT-STD-0007 COMMENT 33
8-13 

Table 8.2.8 Capacitor-Start Capacitor-Run Motors: Manufacturer Selling Price 

Increases, 0.75 Horsepower 

Energy Efficiency 

Level 

Efficiency 

(%) 

Not Space-Constrained 

Standard-Level 

MSP (2008$) 

Space-Constrained 

Standard-Level 

MSP (2008$) 

Baseline 71.00 $110.82 $110.82 

1 74.30 $116.06 $116.06 

2 78.30 $128.60 $136.22 

3 80.30 $133.71 $141.49 

4 81.60 $142.23 $145.27 

5 82.70 $149.23 $152.88 

6 83.70 $162.90 $237.53 

7 85.40 $172.75 $245.36 

8 87.30 $353.50 $1,778.48 

 Table 8.2.9 shows the baseline and incremental markups estimated for each point in the 

small motor supply chain. The overall baseline and incremental markups shown are weighted 

averages based on the share of shipments in each distribution channel. Refer to TSD chapter 7 

for details. 

Table 8.2.9 Markups for Small Electric Motors 

Point in Supply Chain Baseline Incremental 

Wholesale 1.10 1.04 

OEM 1.35 1.27 

Retail and Post-OEM 1.43 1.18 

Contractor/Installer 1.10 1.10 

Sales Tax 1.0684 

Overall* 2.49 1.83 

* Weighted average of the three distribution channels. 

 DOE derived installation costs for small electric motors from data in the RS Means 

Electrical Cost Data, 2008.

1

 The average cost estimated by DOE is $253. Since DOE found no 

information to indicate differences in installation costs among motor applications, it used the 

same installation cost for each equipment class. While DOE did find evidence of increasing 

installation costs with increasing motor size for medium motors in the RS Means data, DOE 

found no evidence that installation costs would be impacted with increased motor energy 

efficiency levels for small electric motors. 

Total Installed Cost: The total installed cost is the sum of the end user equipment price 

and the installation cost. Refer back to section 8.2.1 to see the equations that DOE used to 

EERE-2007-BT-STD-0007 COMMENT 33
8-14 

calculate the total installed cost for various energy efficiency levels. Tables 8.2.10 through 8.2.15 

present the end user equipment price, installation costs, shipping and total installed costs for each 

small motor equipment class for both the space-constrained and the not space-constrained cases. 

Table 8.2.10 Polyphase Motors (1 hp): Consumer Equipment Prices, Shipping Costs, 

Installation Costs, and Total Installed Costs for Motors that are Not SpaceConstrained 

Energy 

Efficiency Level 

Efficiency 

(%) 

Equipment Price 

(2008$) 

Shipping Cost 

(2008$) 

Installation 

Cost 

(2008$) 

Total Installed 

Cost 

(2008$) 

Baseline 77.15 $243.28 $15.62 $252.90 $511.80 

1 78.70 $254.38 $16.82 $252.90 $524.10 

2 80.00 $260.24 $17.93 $252.90 $531.06 

3 81.60 $270.98 $18.59 $252.90 $542.47 

4 82.50 $278.53 $19.31 $252.90 $550.74 

5 85.20 $340.47 $22.55 $252.90 $615.92 

6 86.70 $402.44 $25.36 $252.90 $680.70 

7 88.30 $658.47 $27.45 $252.90 $938.83 

Table 8.2.11 Polyphase Motors (1 hp): Consumer Equipment Prices, Shipping Costs, 

Installation Costs, and Total Installed Costs for Motors that are SpaceConstrained 

Energy 

Efficiency Level 

Efficiency 

(%) 

Equipment Price 

(2008$) 

Shipping Cost 

(2008$) 

Installation 

Cost 

(2008$) 

Total Installed 

Cost 

(2008$) 

Baseline 77.15 $243.28 $15.62 $252.90 $511.80 

1 78.70 $254.38 $16.82 $252.90 $524.10 

2 80.00 $260.24 $17.93 $252.90 $531.06 

3 81.60 $270.98 $18.59 $252.90 $542.47 

4 82.50 $278.53 $19.31 $252.90 $550.74 

5 85.20 $484.98 $19.22 $252.90 $757.11 

6 86.70 $496.62 $19.61 $252.90 $769.13 

7 88.30 $3,303.54 $19.61 $252.90 $3,576.05 

EERE-2007-BT-STD-0007 COMMENT 33
8-15 

Table 8.2.12 Capacitor-Start Induction-Run Motors (0.5 hp): Consumer Equipment 

Prices, Shipping Costs, Installation Costs, and Total Installed Costs for 

Motors that are Not Space-Constrained 

Energy 

Efficiency Level 

Efficiency 

(%) 

Equipment Price 

(2008$) 

Shipping Cost 

(2008$) 

Installation 

Cost 

(2008$) 

Total Installed 

Cost 

(2008$) 

Baseline 57.70 $226.59 $10.90 $252.90 $490.38 

1 59.50 $234.98 $11.40 $252.90 $499.28 

2 62.00 $240.32 $11.90 $252.90 $505.12 

3 64.20 $242.59 $12.25 $252.90 $507.74 

4 68.50 $256.14 $14.23 $252.90 $523.28 

5 71.20 $277.71 $12.87 $252.90 $543.48 

6 73.00 $301.83 $15.62 $252.90 $570.35 

7 77.00 $335.75 $18.48 $252.90 $607.13 

Table 8.2.13 Capacitor-Start Induction-Run Motors (0.5 hp): Consumer Equipment 

Prices, Shipping Costs, Installation Costs, and Total Installed Costs for 

Motors that are Space-Constrained 

Energy 

Efficiency Level 

Efficiency 

(%) 

Equipment Price 

(2008$) 

Shipping Cost 

(2008$) 

Installation 

Cost 

(2008$) 

Total Installed 

Cost 

(2008$) 

Baseline 57.70 $226.59 $10.90 $252.90 $490.38 

1 59.50 $234.98 $11.40 $252.90 $499.28 

2 62.00 $240.32 $11.90 $252.90 $505.12 

3 64.20 $242.59 $12.25 $252.90 $507.74 

4 68.50 $269.65 $12.57 $252.90 $535.11 

5 71.20 $277.71 $12.87 $252.90 $543.48 

6 73.00 $393.53 $12.93 $252.90 $659.36 

7 77.00 $2,263.55 $12.87 $252.90 $2,529.32 

EERE-2007-BT-STD-0007 COMMENT 33
Table 8.2.14 Capacitor-Start Capacitor-Run Motors (0.75 hp): Consumer Equipment 

Prices, Shipping Costs, Installation Costs, and Total Installed Costs for 

Motors that are Not Space-Constrained 

Energy 

Efficiency Level 

Efficiency 

(%) 

Equipment Price 

(2008$) 

Shipping Cost 

(2008$) 

Installation 

Cost 

(2008$) 

Total Installed 

Cost 

(2008$) 

Baseline 71.00 $275.84 $13.02 $252.90 $541.76 

1 74.30 $285.42 $13.72 $252.90 $552.04 

2 78.30 $308.36 $16.59 $252.90 $577.86 

3 80.30 $317.72 $17.95 $252.90 $588.57 

4 81.60 $333.30 $19.94 $252.90 $606.14 

5 82.70 $346.11 $20.04 $252.90 $619.05 

6 83.70 $371.13 $18.33 $252.90 $642.36 

7 85.40 $389.14 $19.28 $252.90 $661.32 

8 87.30 $719.87 $23.11 $252.90 $995.88 

Table 8.2.15 Capacitor-Start Capacitor-Run Motors (0.75 hp): Consumer Equipment 

Prices, Shipping Costs, Installation Costs, and Total Installed Costs for 

Motors that are Space-Constrained 

Energy 

Efficiency Level 

Efficiency 

(%) 

Equipment Price 

(2008$) 

Shipping Cost 

(2008$) 

Installation 

Cost 

(2008$) 

Total Installed 

Cost 

(2008$) 

Baseline 71.00 $275.84 $13.02 $252.90 $541.76 

1 74.30 $285.42 $13.72 $252.90 $552.04 

2 78.30 $322.31 $14.11 $252.90 $589.32 

3 80.30 $331.96 $14.81 $252.90 $599.67 

4 81.60 $338.87 $15.28 $252.90 $607.05 

5 82.70 $352.80 $16.04 $252.90 $621.73 

6 83.70 $507.68 $15.14 $252.90 $775.72 

7 85.40 $522.00 $15.87 $252.90 $790.76 

8 87.30 $3,327.19 $15.83 $252.90 $3,595.92 

8.2.3 Operating Cost Inputs 

 DOE defines the operating cost, OC, by the following equation: 

= + + MCRCECOC

Where: 

8-16 

EERE-2007-BT-STD-0007 COMMENT 33
EC = energy expenditure associated with operating the equipment, 

RC = repair cost associated with component failure, and 

MC = cost for maintaining equipment operation. 

 Table 8.2.16 shows the inputs for determining the operating costs. The inputs listed in 

Table 8.2.16 are also necessary for determining the present value of lifetime operating expenses, 

which include the energy price trends, product lifetime, discount rate, and effective date of the 

standard. 

Table 8.2.16 Inputs for Operating Cost 

Annual Energy Consumption 

Energy Prices 

Repair and Maintenance Costs 

Energy Price Trends 

Product Lifetime 

Discount Rate 

Effective Date of Standard 

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

equipment. Energy prices are the prices paid by end users for energy supply including both 

energy and demand charges. Multiplying the annual energy and demand by the appropriate 

prices yields the annual energy cost. Repair costs are associated with repairing or replacing 

components that have failed, and maintenance costs are associated with maintaining the 

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

the future and, along with the product lifetime and discount rate, to establish the lifetime energy 

supply costs. The product lifetime is the age at which the equipment is retired from service. The 

discount rate is the rate at which DOE discounted future expenditures to establish their present 

value. DOE calculated the operating cost for baseline products based on the following equation: 

BASE ENERGY BASE BASE

BASE BASE BASE BASE

AEC PRICE RC MC

OC EC RC MC

= × ++

= + +

Where: 

OCBASE = baseline operating cost, 

ECBASE = energy expenditure associated with operating the baseline equipment 

which may include reactive power costs, 

RCBASE = repair cost associated with component failure for the baseline 

equipment, 

MCBASE = cost for maintaining baseline equipment operation, 

AECBASE = annual energy consumption for baseline equipment, 

8-17 

EERE-2007-BT-STD-0007 COMMENT 33
PRICEENERGY = energy price. 

 DOE calculated the operating cost for standard-level products based on the following 

equation: 

8-18 

( ) ( ) ( ) BASE STD ENERGY BASE STD BASE STD

STD ENERGY STD STD

STD STD STD STD

AEC AEC PRICE RC RC MC MC

AEC PRICE RC MC

OC RCEC MC

= ×Δ Δ++Δ++

×= ++

++=

__

Where: 

OCSTD = standard-level operating cost, 

ECSTD = energy expenditure associated with operating standard-level equipment, 

RCSTD = repair cost associated with component failure for standard-level 

equipment, 

MCSTD = cost for maintaining standard-level equipment operation, 

AECSTD = annual energy consumption for standard-level equipment, 

PRICEENERGY = energy price, 

ΔAECSTD = decrease in annual energy consumption caused by standard-level 

equipment, 

ΔRCSTD = change in repair cost caused by standard-level equipment, and 

ΔMCSTD = change in maintenance cost caused by standard-level equipment. 

 The remainder of this section provides information about each of the above input 

variables that DOE used to calculate the operating costs for small electric motors. 

8.2.3.1 Annual Energy Consumption 

 Chapter 6, Energy Use Characterization, details how DOE determined the annual energy 

consumption for baseline and standard-level products. Table 8.2.17 provides the average annual 

energy consumption by efficiency level for each small motor equipment class. DOE captured the 

variability in energy consumption by estimating energy consumption for a variety of motor-using 

applications. 

EERE-2007-BT-STD-0007 COMMENT 33
8-19 

Table 8.2.17 Average Annual Electricity Use by Efficiency Level for Small Electric 

Motors 

Polyphase (1 hp) CSIR (0.5 hp) CSCR (0.75 hp) Efficiency 

Level Efficiency 

(%) 

Energy Use 

(kWh/yr) 

Efficiency

(%) 

Energy Use 

(kWh/yr) 

Efficiency

(%) 

Energy Use 

(kWh/yr) 

Baseline 77.2 1763 57.7 1277 71.0 1451 

1 78.7 1734 59.5 1226 74.3 1389 

2 80.0 1698 62.0 1164 78.3 1278 

3 81.6 1645 64.2 1110 80.3 1233 

4 82.5 1629 68.5 1020 81.6 1239 

5 85.2 1549 71.2 971 82.7 1226 

6 86.7 1529 73.0 942 83.7 1219 

7 88.3 1494 77.0 877 85.4 1175 

8 NA NA NA NA 87.3 1144 

8.2.3.2 Energy Prices 

 To estimate the energy prices faced by small motor end users throughout the U.S., DOE 

estimated electricity prices for end users in each sector using EIA Form 861 data.2

 These data 

are published annually and include annual electricity sales in kilowatt-hours (kWh), revenues 

from electricity sales, and number of consumers, for the residential, commercial, and industrial 

sectors, for every utility serving final consumers. 

 DOE sorted the volumes of electricity sold as reported by the year 2007 EIA Form 861 

by price and customer class and calculated the distribution of electricity prices for each customer 

class. DOE used these electricity price distributions to represent the customer cost of electricity 

for the different classes of motor owners. DOE assigned the electricity price distribution for 

industrial customers to the class of agricultural motor owners. The resulting electricity price 

distributions are shown in Figure 8.2.1. 

EERE-2007-BT-STD-0007 COMMENT 33
0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

$0.00 $0.05 $0.10 $0.15 $0.20

Price (2007$)

Cumulative Probability

Industrial Commercial Residential

Figure 8.2.1 Electricity Price (2007$/kWh) Distributions 

 

8.2.3.3 Energy Price Trends 

 DOE used price forecasts by the EIA to estimate the trends in electricity prices. To arrive 

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

forecast of annual average price changes in EIA’s AEO 2009. To estimate the trend after 2030, 

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

used the average rate of change during 2020–2030 for electricity prices. 

 DOE calculated LCC and PBP using three separate projections from AEO 2009: 

American Recovery and Reinvestment Act, Low Economic Growth, and High Economic 

Growth. These three cases reflect the uncertainty of economic growth in the forecast period. The 

high and low growth cases show the projected effects of alternative growth assumptions on 

energy markets. Figure 8.2.2 shows the industrial electricity price trends based on the three AEO 

2009 projections. For the LCC results presented in section 8.4, DOE used only the energy price 

forecasts from the Department’s reference case, the American Recovery and Reinvestment Act 

scenario published by EIA as a supplement to AEO 2009. 

8-20 

EERE-2007-BT-STD-0007 COMMENT 33
0.60

0.70

0.80

0.90

1.00

1.10

1.20

1.30

2005 2010 2015 2020 2025 2030 2035 2040 2045

Year

Price Trend (2008=1)

Industrial Reference

Ind. High Growth

Ind. Low Growth

Figure 8.2.2 Industrial Electricity Price Trends 

8.2.3.4 Repair and Maintenance Costs 

 DOE understands that small electric motors are usually not repaired. Most small motors 

are mass produced and are not constructed or designed to be repaired because the manufacturing 

process uses spot welding welds and rivets to fasten or secure the frame and assembled 

components, not nuts and bolts. DOE found no evidence that any repair or maintenance costs 

would increase with higher motor energy efficiency. Thus, it did not include any changes in 

repair and maintenance costs for motors more efficient than baseline products. 

8.2.4 Motor Lifetime 

 DOE relied on several sources to inform its model of the lifetime of small electric motors. 

A study by Easton Consultants, prepared for the Department in 2001, surveyed experts in OEM 

industries, analyzed causes of motor failure, and developed estimates for typical motor lifetime 

of 7 years for capacitor-start motors and 9 years for small polyphase motors (two-digit frame 

series). The Department used Weibull distributions based on these values in its preliminary 

analysis. (The Weibull distribution is a standard distribution used to model failure processes.) 

DOE has developed a more sophisticated model for motor lifetime for use in this stage of 

the analysis. This model combines annual hours of motor operation with OEM application 

lifetimes to estimate the distribution of motor lifetimes. This model results in a negative 

correlation between annual hours of operation and motor lifetime; motors operated many hours 

8-21 

EERE-2007-BT-STD-0007 COMMENT 33
per year are likely to be retired sooner than motors which are used for only a few hundred hours 

per year. 

 The Department’s motor lifetime model relies on four distributions: 1) the duty factor or 

annual hours of operation distribution derived for use in the energy use analysis (see chapter 6), 

2) the distribution of motor shipments into five application areas, each with its own distribution 

of annual hours of operation, 3) a Weibull distribution of mechanical motor lifetimes, expressed 

in total hours of operation before failure, and 4) a Weibull distribution of application lifetimes, 

expressed in years. DOE combined expert interviews (conducted by Easton Consultants) 

regarding motor lifetime in hours with its estimates of typical motor lifetime to develop the 

parameters for the Weibull distributions for both polyphase and single-phase motors. DOE’s 

Monte Carlo analysis of the motor life cycle cost selected an application, an appropriate number 

of hours of operation, motor mechanical lifetime, and application lifetime from these 

distributions in order to calculate the sampled motor’s lifetime in years. 

 The Department determined the mechanical lifetime of each motor in years by dividing 

its mechanical lifetime in hours by its annual hours of operation. DOE then compared this 

mechanical lifetime (in years) with the sampled application lifetime (also in years), and assumed 

that the motor would be retired at the younger of these two ages. For example, a pump motor 

with a duty factor of 2500 hours per year may have a mechanical lifetime of 30,000 hours and an 

application lifetime of 10 years. The mechanical lifetime would be 12 years, which is greater 

than 10 years, so DOE would assume the motor would retire in 10 years, when its application 

reached its lifetime, even if the motor itself could run for several more years. If the pump motor 

were to run for 6000 hours per year, with the same mechanical and application lifetimes, DOE 

would assume it would retire after 5 years due to motor failure upon reaching its mechanical 

lifetime of 30,000 hours. 

8.2.4.1 The Weibull Distribution 

 The Weibull distribution is a probability distribution commonly used to measure failure 

rates.a

 Its 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 particular fashion. 

The cumulative Weibull distribution takes the form: 

e x

xP

β

α

θ ⎟

⎠

⎞ ⎜

⎝

⎛ − −

)( = for x > θ and 

P(x) = 1 for x ≤ θ

Where: 

P(x) = probability that the equipment is still in use at age x; 

 

8-22 

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/>. 

EERE-2007-BT-STD-0007 COMMENT 33
8-23 

x = equipment age; 

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, or location, 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 mechanical equipment, β commonly is greater 

than 1, reflecting an increasing failure rate as equipment ages. 

8.2.4.2 Capacitor-Start Mechanical and Application Lifetimes 

DOE’s derived Weibull parameters for capacitor-start motor mechanical lifetimes are: 

α = 17,000 hours; 

β = 2.5; and 

θ = 15,000 hours. 

These parameters produce a distribution in which no motors suffer mechanical failure until they 

have run at least 15,000 hours. The mean mechanical lifetime is 30,080 hours, and the median is 

29,680 hours. 

DOE’s derived Weibull parameters for capacitor-start motor application lifetimes are: 

α = 3.12 years; 

β = 1.9; and 

θ = 5 years. 

These parameters produce a distribution in which no motors are retired due to their application’s 

retirement until they are at least 5 years old. The mean application lifetime is 7.77 years, and the 

median is 7.57 years. 

 In the course of the life-cycle analysis, DOE combines these two distributions with the 

appropriately weighted duty factor distribution to select a lifetime for each motor. The overall 

mean age at capacitor-start motor retirement is 6.95 years, with a median of 7 years. In this 

model, 95% of polyphase small electric motors have lifetimes between 2.8 and 10.8 years. The 

correlation coefficient between annual hours of operation and motor lifetime is -0.712, indicating 

an inverse relationship as expected. 

8.2.5 Polyphase Mechanical and Application Lifetimes 

Interviews with OEM-industry experts indicate that polyphase motors are expected to be 

used for more years before retirement. Mechanically and electrically, they are simpler than 

capacitor-start motors, due to the lack of a capacitor, and failure of the bearings is expected to be 

the dominant cause of motor failure. DOE therefore derived a polyphase mechanical motor 

lifetime distribution with somewhat higher number of hours until failure than for capacitor-start 

motors. DOE’s derived Weibull parameters for polyphase motor mechanical lifetimes are: 

α = 23,000 hours; 

EERE-2007-BT-STD-0007 COMMENT 33
8-24 

β = 2.5; and 

θ = 20,000 hours. 

These parameters produce a distribution in which no motors suffer mechanical failure until they 

have run at least 20,000 hours. The mean mechanical lifetime is 40,400 hours, and the median is 

39,860 hours. 

DOE’s derived Weibull parameters for polyphase motor application lifetimes are: 

α = 3.03 years; 

β = 1.9; and 

θ = 7 years. 

These parameters produce a distribution in which no motors are retired due to their application’s 

retirement until they are at least 7 years old. The mean application lifetime is 9.69 years, and the 

median is 9.50 years. 

 In the course of the life-cycle analysis, DOE combines these two distributions 

with the appropriately weighted duty factor distribution to select a lifetime for each motor. The 

overall mean age at capacitor-start motor retirement is 8.75 years, with a median of 9 years. In 

this model, 95% of polyphase small electric motors have lifetimes between 3.7 and 12.7 years. 

The correlation coefficient between annual hours of operation and motor lifetime is -0.746, 

indicating an inverse relationship as expected. 

8.2.5.1 Discount Rates 

 DOE derived the discount rates for the LCC and PBP analysis from estimates of the 

finance cost of purchasing the considered products. Following financial theory, the finance cost 

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

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

equipment. 

Commercial, Industrial, and Agricultural Owners 

 For motors purchased and used in the industrial, agricultural, and commercial sectors, 

DOE calculated the discount rate for a distribution of representative product owners. This 

distribution of representative owners is the weighted sum of discount rate distributions for 

different ownership categories. DOE calculated a distribution of discount rates for owners within 

each ownership category. The discount rate for an individual owner is the weighted average cost 

of capital (WACC) where, given the mix of debt and equity for that individual owner, a weighted 

average of the discount rates for each loan and investment calculated in which the weights are 

equal to the size of the loan or investment. 

 DOE estimated the cost of equity using the capital asset pricing model (CAPM).3

 The 

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

systematic risk faced by that company, where 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 riskEERE-2007-BT-STD-0007 COMMENT 33
free 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, where the variables are 

defined as above: 

Rk ( ERP) fe β×+=

Where: 

 

ke = cost of equity, 

Rf = expected return on risk-free assets, 

β = risk coefficient of the firm, and 

ERP = equity risk premium. 

 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. So for firm i, the cost of debt financing is: 

+= RRk aifdi

Where: 

 

kd = cost of debt financing for firm, i, 

Rf = expected return on risk-free assets, and 

Rai = risk adjustment factor to risk-free rate for firm, i. 

 DOE estimates the WACC using the following equation: 

= ×+× wkwkWACC ddee

Where: 

WACC = weighted average cost of capital, 

we = proportion of equity financing, and 

wd = proportion of debt financing. 

 Damodaran Online is a widely used source of information about company debt and 

equity financing for most types of firms.4

 

8-25 

 Several parameters of the cost of capital equations can vary substantially over time, and 

therefore the estimates can vary with the time period over which data is selected and the 

technical details of the data averaging method. For guidance on the time period for selecting and 

EERE-2007-BT-STD-0007 COMMENT 33
averaging data for key parameters and the averaging method, DOE used Federal Reserve 

methodologies for calculating these parameters. In its use of the CAPM, the Federal Reserve 

uses a forty-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 riskfree security.” 5

 

 During the preliminary analysis, DOE adjusted the discount rate distributions from a 

previous rulemaking on distribution transformer standards with updated values of the equity risk 

premium, inflation, and the risk-free rate using the 10-year Treasury bond as the risk-free 

security. DOE did not receive comments in response to the preliminary analysis regarding this 

approach and has therefore retained the same estimates for the NOPR. By taking an updated 

forty-year (1967–2007) geometric average of Damodaran Online data, DOE found for this 

analysis a real (inflation-adjusted) risk free rate of 3.15 percent and an equity risk premium of 

3.50 percent. The values for the previous analysis (for distribution transformer standards) were 

3.20 percent and 5.50 percent respectively. Table 8.2.18 shows the conversion from the previous 

set of parameters to the new values and the new discount rate distributions assuming no change 

in the corresponding company weighted-average cost of capital betas. DOE used the CAPM 

equation to derive a relationship between beta and the discount rate that was used to convert 

discount rates to the values that correspond to the new values of risk-free rate and ERP. DOE 

obtained the following equation for beta by solving the CAPM equation: 

ERPRk fe β = − /)(

Where: 

 

ke = cost of equity, 

Rf = expected return on risk-free assets, 

β = risk coefficient of the firm, and 

ERP = equity risk premium. 

 

Table 8.2.18 Adjusted Real Discount Rates for Updated Values of Rf and ERP. 

Previous 

Discount Rate* 

(%) 

CAPM Beta 

Value 

Updated 

Discount Rate 

(%) 

Industrial 

Discount Rate 

Distribution 

(%) 

Commercial 

Discount Rate 

Distribution 

(%) 

0.5 -0.491 1.43 0.0 0.0 

1.5 -0.309 2.07 0.0 0.0 

2.5 -0.127 2.70 0.5 3.1 

3.5 0.055 3.34 1.3 1.2 

4.5 0.236 3.98 4.2 2.1 

5.5 0.418 4.61 14.6 9.8 

6.5 0.600 5.25 24.7 22.4 

8-26 

EERE-2007-BT-STD-0007 COMMENT 33
8-27 

7.5 0.782 5.89 24.9 23.9 

8.5 0.964 6.52 6.6 23.2 

9.5 1.145 7.16 6.5 6.6 

10.5 1.327 7.80 8.6 4.0 

11.5 1.509 8.43 6.8 2.3 

12.5 1.691 9.07 0.9 0.5 

13.5 1.873 9.70 0.2 0.1 

14.5 2.055 10.34 0.1 0.7 

15.5 2.236 10.98 0.0 0.0 

16.5 2.418 11.61 0.0 0.0 

From rulemaking on distribution transformer standards 

Table 8.2.19 shows the average WACC values for the three non-residential ownership 

types in the small electric motors analysis. While WACC values for any sector may trend higher 

or lower over substantial periods of time, these values represent a private sector cost of capital 

that is averaged over major business cycles. For all sectors, the averages are slightly lower than 6 

percent real. 

Table 8.2.19 Weighted Average Cost of Capital for Sectors that Purchase Small Electric 

Motors 

Sector Weighted-Average Cost of Capital 

Industrial 5.92% 

Agricultural 5.92% 

Commercial 5.86% 

Residential Owners 

 Households use a variety of methods to finance equipment. In principle, one could 

estimate the interest rates on the actual financing vehicles used to purchase replacement 

equipment. The shares of different financing vehicles in total equipment purchases are unknown, 

however. 

 DOE’s approach involves identifying all possible debt or asset classes that might be used 

to purchase equipment, including household assets that might be affected indirectly.b

 DOE did 

not include debt from primary mortgages and equity of assets considered non-liquid (such as 

retirement accounts), since these would likely not be affected by equipment purchases. DOE 

estimated the average shares of the various debt and equity classes in the average U.S. household 

equity and debt portfolios using Survey of Consumer Finances (SCF) data for 1989, 1992, 1995, 

1998, 2001, and 2004. Table 8.2.20 shows the average shares of each considered class. DOE 

 

b

 An indirect effect would arise if a household sold some assets in order to pay off a loan or credit card debt that 

might have been used to finance the actual appliance purchase. 

EERE-2007-BT-STD-0007 COMMENT 33
8-28 

used the mean share of each class across the six years as a basis for estimating the effective 

financing of equipment. 

Table 8.2.20 Average Shares of Considered Household Debt and Equity Types 

Type 1989 

SCF 

1992 

SCF 

1995 

SCF 

1998 

SCF 

2001 

SCF 

2004 

SCF 

Mean 

(%) 

Home equity loans 4.3 4.5 2.7 2.8 2.8 4.4 3.6 

Credit cards 1.6 2.1 2.6 2.2 1.7 2.0 2.0 

Other installment loans 2.8 1.7 1.4 1.7 1.1 1.3 1.7 

Other residential loans 4.4 6.9 5.2 4.3 3.1 5.8 4.9 

Other line of credit 1.1 0.6 0.4 0.2 0.3 0.5 0.5 

Checking accounts 5.8 4.7 4.9 3.9 3.6 4.2 4.5 

Savings & money market 19.2 18.8 14.0 12.8 14.2 15.1 15.7 

Certificate of deposit (CD) 14.5 11.7 9.4 7.0 5.4 5.9 9.0 

Savings bond 2.2 1.7 2.2 1.1 1.2 0.9 1.5 

Bonds 13.8 12.3 10.5 7.0 7.9 8.4 10.0 

Stocks 22.4 24.0 25.9 36.9 37.5 28.0 29.1 

Mutual funds 8.0 11.1 20.9 20.1 21.3 23.4 17.5 

Total 100 100 100 100 100 100 100 

 DOE estimated interest or return rates associated with each type of equity and debt. The 

data source for the interest rates for loans, credit cards, and lines of credit is the Federal Reserve 

Board’s SCF in 1989, 1992, 1995, 1998, 2001, and 2004. Table 8.2.21 shows the average 

nominal rates in each year, and the inflation rates used to calculate real rates. For home equity 

loans, DOE calculated effective interest rates in a similar manner as for mortgage rates, since 

interest on such loans is tax deductible. Table 8.2.22 shows the average effective real rates in 

each year and the mean rate across the years. Since the interest rates for each debt carried by 

households in these years were established over a range of time, DOE believes they are 

representative of rates that may be in effect in 2015. 

EERE-2007-BT-STD-0007 COMMENT 33
8-29 

Table 8.2.21 Average Nominal Interest Rates for Household Debt Classes (percent) 

Type 1989 

SCF 

1992 

SCF 

1995 

SCF 

1998 

SCF 

2001 

SCF 

2004 

SCF 

Mean 

(%) 

Home equity loans 11.5 9.6 9.6 9.8 8.7 5.7 9.2 

Credit cards* - - 14.2 14.5 14.2 11.7 13.6 

Other installment loans 9.0 7.8 9.3 7.8 8.7 7.4 8.3 

Other residential loans 8.8 7.6 7.7 7.7 7.5 6.0 7.5 

Other line of credit 14.8 12.7 12.4 11.9 14.7 8.8 12.5 

Inflation rate 4.82 3.01 2.83 1.56 2.85 2.66 

* No interest rate data available for credit cards in 1989 or 1992. 

Table 8.2.22 Average Real Effective Interest Rates for Household Debt Classes (percent) 

Type 1989 

SCF 

1992 

SCF 

1995 

SCF 

1998 

SCF 

2001 

SCF 

2004 

SCF 

Mean 

(%) 

Home equity loans 3.8 4.3 4.4 5.8 3.8 1.9 4.0 

Credit cards* - - 11.0 12.7 11.1 9.1 11.0 

Other installment loans 4.9 5.8 7.0 6.6 6.1 5.4 6.0 

Other residential loans 4.0 4.7 4.8 6.0 4.6 3.3 4.6 

Other line of credit 9.6 9.4 9.3 10.2 7.3 6.0 8.7 

* No interest rate data available for credit cards in 1989 or 1992.

 To account for variation among new households, DOE sampled a rate for each household 

from a distribution of rates for each of the above debt classes. DOE developed a probability 

distribution of interest rates for each debt class based on the SCF data. 

 Similar rate data are not available from the SCF for the asset classes, so DOE derived 

data for these classes from national-level historical data. The interest rates associated with 

certificates of deposit (CDs), 6

 savings bonds,7 and bonds (AAA corporate bonds) 8 are from 

Federal Reserve Board time-series data covering 1977–2005. DOE assumed rates on checking 

accounts to be zero. Rates on savings and money market accounts are from Cost of Savings 

Index data covering 1984–2005. 9

 The rates for stocks are the annual returns on the Standard and 

Poor’s (S&P) 500 in the 1977–2005 period. 10 The mutual fund rates are a weighted average of 

the stock rates (two-thirds weight) and the bond rates (one-third weight) in each year of the 

1977–2005 period. DOE adjusted the nominal rates to real rates using the annual inflation rate in 

each year. Average nominal and real interest rates for the classes of assets are shown in Table 

8.2.23. Since the interest and return rates for each asset type cover a range of time, DOE believes 

they are representative of rates that may be in effect in 2015. 

EERE-2007-BT-STD-0007 COMMENT 33
8-30 

Table 8.2.23 Average Nominal and Real Interest Rates for Household Equity Types 

Type Average Nominal Rate (%) Average Real Rate (%) 

Checking accounts - 0.0 

Savings and money market 5.5 2.3 

CDs 6.9 2.4 

Savings bonds 8.0 3.5 

Bonds 8.8 4.2 

Stocks 13.3 8.8 

Mutual funds 11.6 7.0 

 To account for variation among households, DOE sampled a rate for each household 

from a distribution of rates for each of the above asset types. DOE developed a normal 

probability distribution of interest rates for each asset type by using the mean value and standard 

deviation from the distribution. 

Table 8.2.24 summarizes the mean real effective rates of each type of equity or debt. 

DOE determined the average share of each debt and asset using SCF data for 1989, 1992, 1995, 

1998, 2001, and 2004. Each year of SCF data provides the debt and asset shares for U.S. 

households. DOE averaged the debt and asset shares over the six years of survey data to arrive at 

the shares shown below. The average rate across all types of household debt and equity, 

weighted by the shares of each class, is 5.6 percent. 

EERE-2007-BT-STD-0007 COMMENT 33
8-31 

Table 8.2.24 Shares and Interest or Return Rates Used for Household Debt and Equity 

Types 

Type Average Share of Household 

Debt plus Equity (%)* 

Mean Effective Real 

Rate (%)** 

Home equity loans 3.6 4.0 

Credit cards 2.0 11.0 

Other installment loans 1.7 6.0 

Other residential loans 4.9 4.6 

Other line of credit 0.5 8.7 

Checking accounts 4.5 0.0 

Savings and money market accounts 15.7 2.3 

CDs 9.0 2.4 

Savings bonds 1.5 3.5 

Bonds 10.0 4.2 

Stocks 29.1 8.8 

Mutual funds 17.5 7.0 

Total/Weighted-average discount rate 100 5.6 

* Not including primary mortgage or retirement accounts.

** Adjusted for inflation and, for home equity loans, loan interest tax deduction.

8.2.5.2 Effective Date of Standard 

 The effective date of an energy conservation standard is the future date when a new 

standard becomes operative. Section 346(b)(3) of the Energy Policy and Conservation Act 

(EPCA) requires that any standard for small electric motors "shall apply to small electric motors 

manufactured 60 months after the date such rule is published." (42 USC 6317(b)(3)) In view of 

the Report to Congress on Appliance Energy Efficiency Rulemakings, dated February 2008, 

DOE is required to publish an energy conservation standard final rule by February 28, 2010. 

(See http://www1.eere.energy.gov/buildings/appliance_standards/schedule_setting.html.) 

Therefore, the effective date of any new energy conservation standards for small electric motors 

would be in February 2015. DOE calculated the LCC and PBP for all end users as if they each 

would purchase a new piece of equipment in the year the standard takes effect. 

8.2.6 Product Energy Efficiency in the Base Case 

For purposes of conducting the LCC analysis, DOE analyzed efficiency levels relative to 

a base case (i.e., the case without new energy efficiency standards). This requires an estimate of 

the distribution of product efficiencies in the base case (i.e., what consumers would have 

purchased in the year 2015 in the absence of new standards). 

EERE-2007-BT-STD-0007 COMMENT 33
In other rulemakings, DOE often uses the distribution of product efficiencies currently in 

the marketplace to develop its estimate of such distribution in the base case. DOE did find some 

models offered in the manufacturer catalogues that were low first cost and then had matching 

higher-efficiency units. These so-called 'matched pairs' would seem to indicate that there is some 

voluntary purchasing of higher-efficiency motors. However, DOE did not have any data on the 

market shares of such motors. Therefore, DOE assumed that all motors purchased in the base 

case would be at the baseline efficiency levels, as shown in Table 8.2.25. 

Table 8.2.25 Product Energy Efficiency in the Base Case 

Product Class Efficiency (%) 

Polyphase, 1 hp 77.15 

CSIR, 0.5 hp 57.70 

CSCR, 0.75 hp 71.00 

8.3 PAYBACK PERIOD INPUTS 

 The payback period is the amount of time it takes the consumer to recover the assumed 

higher purchase expense of more energy-efficient equipment as a result of lower operating costs. 

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

design to a more efficient design) to the decrease in annual operating expenditures. This type of 

calculation is known as a “simple” payback period, because it does not take into account changes 

in operating expense over time or the time value of money; i.e., the calculation is done at an 

effective discount rate of zero percent. 

 The equation for PBP is: 

OC

IC PBP

Δ

Δ =

Where: 

ΔIC = increase in the total installed cost between the more efficient standard level 

and the baseline design, and 

ΔOC = decrease in annual operating expenses. 

 Payback periods are expressed in years. Payback periods greater than the life of the 

product indicate that the increased total installed cost is not recovered in reduced operating 

expenses. 

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

each efficiency level and the annual (first year) operating expenditures for each standard level. 

The inputs to the total installed cost are the equipment price and the installation cost. The inputs 

to the operating costs are the annual energy cost, the annual repair cost, and the annual 

maintenance cost. The PBP uses the same inputs as the LCC analysis as described in section 8.2, 

8-32 

EERE-2007-BT-STD-0007 COMMENT 33
8-33 

except that lifetime, energy price trends and discount rates are not required. Since the PBP is a 

“simple” payback, the required energy price is only for the year in which a new standard is to 

take effect—in this case, the year 2015. The energy price DOE used in the PBP calculation was 

the price projected for that year. 

8.4 LIFE-CYCLE COST AND PAYBACK PERIOD RESULTS FOR 

REPRESENTATIVE PRODUCT CLASSES 

This section presents the LCC and PBP results for small motors. As discussed in section 

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

customers that use motors in each product class. DOE also characterized the uncertainty of many 

of the inputs to the analysis with probability distributions. DOE used a Monte Carlo simulation 

technique to perform the LCC calculations on the customers in the sample. For each set of 

sample customers using motors in each equipment class, DOE calculated the average LCC and 

LCC savings and the median and average PBP for each of the standard levels. 

 In the subsections below, DOE presents figures showing the distribution of LCCs in the 

base case for each equipment class. Also presented below for a specific standard level are figures 

showing the distribution of LCC impacts and the distribution of PBPs. The figures are presented 

as frequency charts that show the distribution of LCCs, LCC impacts, and PBPs with their 

corresponding probability of occurrence. DOE generated the figures for the distributions from a 

Monte Carlo simulation run based on 10,000 samples. The LCC and PBP calculations were 

performed 10,000 times by sampling from the probability distributions that DOE developed to 

characterize many of the inputs. 

Based on the Monte Carlo simulations that DOE performed, for each efficiency level, 

DOE calculated the share of small motor users with a net LCC benefit, with a net LCC cost, and 

with no impact. To illustrate the range of LCC and PBP impacts among the small motor end 

users, the sections below present figures that provide such information for each equipment class. 

8.4.1 Polyphase Motors 

 Figure 8.4.1 is an example of a frequency chart showing the distribution of LCC 

differences for the case of efficiency level 5 for polyphase motors. In the figure, a text box next 

to a vertical line at that value on the x-axis shows the mean change in LCC (a net cost of 

approximately $40 in this example Monte Carlo run). 

EERE-2007-BT-STD-0007 COMMENT 33
Polyphase Life-Cycle Cost Savings for EL5

25% 50% 75% 95%

Mean: -40

0

20

40

60

80

100

-200.0 -150.0 -100.0 -50.0 0.0 50.0 100.0 150.0

Life-cycle Cost Savings (2008$)

Frequency (#)

10000 Trials 488 Outliers

Figure 8.4.1 Polyphase Motors: Distribution of Life-Cycle Cost 

Savings for Efficiency Level 5 

 Figure 8.4.2 is an example of a frequency chart showing the distribution of payback 

periods of efficiency level 5 for polyphase motors. Because many motors operate for very few 

hours per year, this means that there is a significant number of motors that may have extremely 

long payback periods because the operating cost savings is very small compared to the increase 

in first cost. The distribution in the figure illustrates that most motors have a payback of less 

than 20 years, but the mean value of the distribution payback is large (49.5 years) because of the 

small, but significant number of motors with payback periods longer then 100 years. 

Polyphase Payback Period Results for EL5

25% 50% 75%

Mean: 49.5

0

50

100

150

200

250

300

350

0.0 20.0 40.0 60.0 80.0 100.0 120.0 140.0

Payback Period (years)

Frequency

10000 Trials 851 Outliers

Figure 8.4.2 Polyphase Motors: Distribution of Payback Periods 

for Efficiency Level 5 

8-34 

EERE-2007-BT-STD-0007 COMMENT 33
8-35 

Table 8.4.1 summarizes the LCC and PBP results for polyphase motors based on a run of 

10,000 Monte Carlo samples. The highest energy efficiency level with positive average LCC 

savings is level 4, 82.5 percent. Approximately 52 percent of end users are estimated to have a 

net benefit (i.e., LCC decrease) at this level. The increase in average total installed cost at this 

level (relative to the base case) is $38, while operating costs decrease by approximately $10 per 

year. 

Table 8.4.1 Polyphase Motors: Life-Cycle Cost and Payback Period Results 

Life-Cycle Cost Life-Cycle Cost 

Savings 

Customers 

with 

Payback Period 

Energy years

Efficiency 

Level 

Efficiency 

%

Average 

Installed 

Price 

$

Average 

Energy 

Use 

kWh/yr

Average 

Annual 

Operating 

Cost 

$

Average 

LifeCycle 

Cost 

$

Average 

Savings

$

Net 

Cost

%

Net 

Benefit 

%

Average Median

Baseline 77.2 512 1763 132.7 1,274 

1 78.7 524 1734 130.5 1,274 0 62.0 38.0 33.7 10.6 

2 80.0 531 1698 127.8 1,265 9 48.9 51.1 23.1 7.2 

3 81.6 542 1645 123.8 1,253 21 45.1 55.0 20.4 6.3 

4 82.5 550 1629 122.6 1,255 19 48.0 52.0 22.7 7.0 

5 85.2 643 1549 116.6 1,312 -38 70.5 29.5 48.2 13.8 

6 86.7 697 1529 115.1 1,358 -85 82.0 18.0 62.4 18.9 

7 88.3 1,446 1494 112.4 2,089 -818 98.1 1.9 263.1 55.1 

8.4.2 Capacitor-Start Induction-Run Motors 

 Figure 8.4.3 is an example of a frequency chart showing the distribution of LCC impacts 

for the case of efficiency level 7 for CSIR motors. Efficiency level 7 is the maximum 

technologically feasible level for space-constrained CSIR motors. This can be seen by the 

significant population (approximately 20%) of motors that have large negative LCC impacts. 

For those motors that do not have space constraints, a substantial fraction (approximately half) 

experience a net LCC benefit from this level. 

EERE-2007-BT-STD-0007 COMMENT 33
Capacitor-Start Induction Run Life-Cycle Cost Savings for EL7

25%50%75% 95%

Mean: -350.6

0

50

100

150

200

250

300

350

-2000.0 -1500.0 -1000.0 -500.0 0.0

Life-cycle Cost Savings (2008$)

Frequency (#)

10000 Trials 354 Outliers

Figure 8.4.3 Capacitor-Start Induction-Run Motors: 

Distribution of Life-Cycle Cost Savings for 

Efficiency Level 7 

 Figure 8.4.4 is an example of a frequency chart showing the distribution of payback 

periods of efficiency level 7 for CSIR motors. While a majority of motors have a payback time 

less than 12 years, because of a significant fraction of motors with extremely high payback 

periods, the average of the distribution is nearly 100 years. 

Capacitor-Start Induction Run Payback Period Results for EL7

25%50% 75%

Mean: 99.1

0

100

200

300

400

500

600

700

800

0.0 50.0 100.0 150.0 200.0 250.0

Payback Period (years)

Frequency

10000 Trials 724 Outliers

Figure 8.4.4 Capacitor-Start Induction-Run Motors: 

Distribution of Payback Periods for Efficiency 

Level 7 

 Table 8.4.2 summarizes the LCC and PBP results for CSIR motors based on a run of 

10,000 Monte Carlo samples. The highest energy efficiency level with positive average LCC 

8-36 

EERE-2007-BT-STD-0007 COMMENT 33
8-37 

savings is level 6, 73.0 percent. However, approximately 53 percent of end users are estimated to 

have a net cost (i.e., LCC increase) at this level. The increase in average total installed cost at 

this level (relative to the base case) is $97, while annual operating costs decrease by $25. 

Table 8.4.2 Capacitor-Start Induction-Run Motors: Life-Cycle Cost and Payback Period 

Results 

Life-Cycle Cost Life-Cycle Cost 

Savings 

Customers 

with 

Payback Period 

Energy years

Efficiency 

Level 

Efficiency 

%

Average 

Installed 

Price 

$

Average 

Energy 

Use 

kWh/yr

Average 

Annual 

Operating 

Cost 

$

Average 

LifeCycle 

Cost 

$ 

Average 

Savings

$ 

Net 

Cost

%

Net 

Benefit 

%

Average Median

Baseline 57.7 490 1277 96.2 941 

1 59.5 499 1226 92.3 932 9 39.6 60.4 13.9 4.3 

2 62.0 505 1164 87.7 916 25 32.7 67.3 10.4 3.2 

3 64.2 507 1110 83.6 899 41 27.7 72.3 8.3 2.6 

4 68.5 525 1020 76.9 885 55 33.7 66.3 11.0 3.3 

5 71.2 543 971 73.2 886 54 39.7 60.3 13.8 4.3 

6 73.0 587 942 70.9 919 21 52.8 47.2 23.1 6.7 

7 77.0 977 877 66.0 1,284 -346 64.0 36.0 95.5 11.2 

8.4.3 Capacitor-Start Capacitor-Run Motors 

 Figure 8.4.5 is an example of a frequency chart showing the distribution of LCC savings 

for the case of efficiency level 3 for CSCR motors. DOE can generate a frequency chart like the 

one shown in Figure 8.4.5 for every efficiency level. 

EERE-2007-BT-STD-0007 COMMENT 33
Capacitor-Start Capacitor-Run Life-Cycle Cost Savings for EL3

5% 25% 50% 75% 95%

Mean: 28.1

0

20

40

60

80

100

120

-50.0 0.0 50.0 100.0 150.0 200.0

Life-cycle Cost Savings (2008$)

Frequency (#)

10000 Trials 344 Outliers

Figure 8.4.5 Capacitor-Start Capacitor-Run Motors: 

Distribution of Life-Cycle Cost Savings for 

Efficiency Level 3 

 Figure 8.4.6 is an example of a frequency chart showing the distribution of payback 

periods of efficiency level 3 for CSCR motors. DOE can generate a frequency chart like the one 

shown in Figure 8.4.6 for every efficiency level. 

8-38 

EERE-2007-BT-STD-0007 COMMENT 33
Capacitor-Start Capacitor-Run Payback Period Results for EL3

25% 50% 75%

Mean: 17.7

0

50

100

150

200

250

300

350

0.0 10.0 20.0 30.0 40.0 50.0 60.0

Payback Period (years)

Frequency

10000 Trials 676 Outliers

Figure 8.4.6 Capacitor-Start Capacitor-Run Motors: 

Distribution of Payback Periods for Efficiency 

Level 3 

 Table 8.4.3 summarizes the LCC and PBP results for CSCR motors based on a run of 

10,000 Monte Carlo samples. The highest energy efficiency level with positive average LCC 

savings is level 5, 82.7 percent. Approximately 40 percent of end users are estimated to have a 

net benefit at this level. The increase in average total installed cost at this level (relative to the 

base case) is $68, while average annual operating costs decrease by $17. 

8-39 

EERE-2007-BT-STD-0007 COMMENT 33
Table 8.4.3 Capacitor-Start Capacitor-Run Motors: Life-Cycle Cost and Payback Period 

Results 

Life-Cycle Cost Life-Cycle Cost 

Savings 

Customers 

with 

Payback Period 

Energy years

Efficiency 

Level 

Efficiency 

%

Average 

Installed 

Price 

$ 

Average 

Energy 

Use 

kWh/yr

Average 

Annual 

Operating 

Cost 

$ 

Average 

LifeCycle 

Cost 

$ 

Average 

Savings

$ 

Net 

Cost

%

Net 

Benefit 

%

Average Median

Baseline 71.0 542 1451 109.3 1,054 

1 74.3 552 1389 104.7 1,042 12 38.2 61.8 12.7 4.1 

2 78.3 580 1278 96.3 1,031 23 45.8 54.2 17.1 5.3 

3 80.3 591 1233 92.9 1,025 28 46.3 53.7 17.4 5.4 

4 81.6 606 1239 93.3 1,043 10 55.6 44.4 23.2 7.4 

5 82.7 620 1226 92.4 1,052 2 59.9 40.1 26.3 8.4 

6 83.7 668 1219 91.8 1,098 -44 73.0 27.0 41.6 12.3 

7 85.4 686 1175 88.6 1,101 -47 72.6 27.5 40.3 12.1 

8 87.3 1,496 1144 86.2 1,897 -846 99.1 0.9 228.9 50.3 

8.5 LIFE CYCLE COSTS FOR ALL PRODUCT CLASSES 

 The Department’s engineering analysis (chapter 5) along with the markups analysis 

(chapter 6) allowed the Department to develop a distribution of consumer purchase costs for each 

of the three representative product classes analyzed in detail in the engineering analysis. 

However, in order to present national impacts (chapter 10), examine the LCC results for other 

product classes (section 8.6), and to model the current market interplay between CSIR and CSCR 

motors, the Department developed a power-law-based scaling relation to estimate the costs of 

motors in other product classes. This scaling relation applies to the purchase cost of the motor, 

and not to installation costs (which DOE assumed were fixed and equal for all product classes). 

 The Department first used manufacturer catalog data to develop average list prices for 

each product class available for sale. DOE then fit the price of each combination of motor 

category and number of poles to a power law function of motor horsepower. That is, DOE 

developed a best-fit power law function for the prices of 4 pole CSIR motors, 6 pole polyphase 

motors, etc. The power law equations for each motor category take the following form: 

),(

),4$()(),$(

Catp

ref

ref hp

hp hppChpp

γ

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

×= ×

Where: 

8-40 

EERE-2007-BT-STD-0007 COMMENT 33
8-41 

$(p, hp) = the purchase cost of an hp horsepower motor with p poles, 

hpref = the horsepower of the motor analyzed by DOE in the engineering analysis for the 

equipment category (1 hp for polyphase, 3⁄4 hp for CSCR, and 1⁄2 hp for CSIR), 

C(p) = the ratio of the purchase cost of an hpref horsepower motor with p poles to one 

with 4 poles, and 

γ(p, Cat) = the best-fit power law exponent to average list price data collected from 

manufacturer catalogs, for motors in category Cat with p poles. 

The best-fit values for C and γ are given in Table 9.4.7. DOE did not calculate power law fit 

parameters (γ) for 2 pole CSCR or 6 pole CSCR motors because it determined that there were not 

enough published prices to derive an accurate scaling relation. Instead, DOE assigned the power 

law of the 4 pole CSCR motors to all CSCR classes, and used only C to match the average prices 

of 3⁄4 hp CSCR motors with each number of poles. These scaling relations allow the Department 

to estimate the list prices of motors, such as small CSCR motors with 2 or 6 poles, not currently 

available from any manufacturer. 

Table 8.5.1 Parameters for Motor Purchase Cost Model 

Polyphase CSIR CSCR 

Six Poles 

C(6, Cat) 1.2957 1.5780 1.3033

γ 0.2492 0.6746 0.3646

Four Poles 

C(4, Cat) 1.0000 1.0000 1.0000

γ 0.3387 0.5007 0.3646

Two Poles 

C(2, Cat) 0.9167 0.8396 0.7923

γ 0.3442 0.4494 0.3646

 Tables 9.4.8, 9.4.9, and 9.4.10 show the consumer purchase cost scaling relation derived 

from this model, where the value of 1.0 in each motor category is assigned to the motor 

examined in detail in the engineering analysis. Product classes in which there are no shipments 

under any of the Department’s scenarios are marked with a dash in the tables. 

Table 8.5.2 Polyphase Motor Consumer Cost Scaling Factors 

Motor Power Six Poles Four Poles Two Poles 

1/4 hp 0.917 0.625 0.569

1/3 hp 0.985 0.689 0.628

1/2 hp 1.090 0.791 0.722

3/4 hp 1.206 0.907 0.830

1 hp 1.296 1.000 0.917

1 1/2 hp 1.433 1.147 1.054

2 hp -- 1.265 1.164

3 hp -- 1.451 1.338

EERE-2007-BT-STD-0007 COMMENT 33
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Table 8.5.3 CSIR Motor Consumer Cost Scaling Factors 

Motor Power Six Poles Four Poles Two Poles 

1/4 hp 0.989 0.707 0.615

1/3 hp 1.200 0.816 0.699

1/2 hp 1.578 1.000 0.840

3/4 hp 2.074 1.225 1.007

1 hp 2.519 1.415 1.146

1 1/2 hp -- 1.733 1.376

2 hp -- 2.002 1.565

3 hp -- -- 1.878

Table 8.5.4 CSCR Motor Consumer Cost Scaling Factors 

Motor Power Six Poles Four Poles Two Poles 

1/4 hp 0.873 0.670 0.531

1/3 hp 0.969 0.744 0.589

1/2 hp 1.124 0.863 0.683

3/4 hp 1.303 1.000 0.792

1 hp 1.447 1.111 0.880

1 1/2 hp -- 1.288 1.020

2 hp -- 1.430 1.133

3 hp -- -- 1.313

 The cost scaling relations described in Tables 8.5.2, 8.5.3, and 8.5.4, when combined 

with the loss scaling relations derived in Chapter 5, Engineering Analysis, allow the Department 

to analyze the life-cycle cost impacts due to potential standards on customers using motors in 

each product class. Appendix 8D provides these LCC results for every product class. These 

calculations also allow the Department to develop national shipment-weighted average LCC 

results for polyphase, CSIR, and CSCR motors. These results are published in Appendix 8C, 

along with the other sensitivities described in the following section. 

8.6 LIFE-CYCLE COST SENSITIVITY CALCULATIONS 

DOE developed a number of sensitivity analyses in order to analyze the particular 

impacts of many inputs to its life-cycle cost analysis. These sensitivity analyses include lower 

and higher markups, lower and higher hours of motor operation, lower and higher motor loading, 

two models for including the cost of greenhouse gas emissions, variation in the starting year for 

the analysis, and three options for including the costs of reactive power. These sensitivities may 

also be combined with analysis of the LCC for each product class, or for a national shipmentweighted distribution, using the price scaling described in section 8.5 and the loss scaling 

described in chapter 5. Doe also developed the ability to report the distribution of customers with 

net costs and net benefits, including division into three categories for costs above a threshold 

fraction of life-cycle cost, benefits greater than a threshold fraction of life-cycle cost, and 

customers whose impact, whether positive or negative, falls below the user-selected threshold. 

EERE-2007-BT-STD-0007 COMMENT 33
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Table 8.6.1 shows a possible combination of these sensitivity analyses for the case of 

polyphase motors. The data in the table corresponds to the case of motor customers purchasing 

motors in 2030 (rather than the base case of 2015), and uses the national shipment-weighted 

distribution. In addition, this scenario has 100% of customers facing reactive power costs. The 

threshold for division of impacts is 2%. 

Table 8.6.1 Polyphase Small Electric Motors: Life-Cycle Cost and Payback Period 

Sensitivity Results for a Shipments-weighted Distribution of Motor 

Capacities and Poles for Purchase Year 2030 and with 100% Power 

Factor Costs Included 

Life-Cycle Cost Life-Cycle Cost Savings 

Customers with 

Payback Period 

years Energy 

Efficiency

Level 

Efficiency 

%

Average 

Installed 

Price 

$

Average 

Energy 

Use 

kWh/yr

Average 

LifeCycle 

Cost 

$

Average 

Savings

$

>2% 

Net 

Cost 

%

<2% 

Net 

Impact 

%

>2% 

Net 

Benefit 

%

Average Median

Baseline 77.2 510 1875 1,483 

1 78.7 522 1844 1,479 3 2.6 97.3 0.1 28.2 8.7 

2 80.0 529 1806 1,466 17 12.6 68.5 18.9 19.3 6.0 

3 81.6 540 1750 1,445 38 17.5 36.6 45.8 16.9 5.2 

4 82.5 548 1733 1,445 38 24.2 31.6 44.3 18.9 5.8 

5 85.2 640 1649 1,493 -10 54.4 16.5 29.2 40.0 11.5 

6 86.7 694 1628 1,537 -54 67.0 13.9 19.1 51.8 15.7 

7 88.3 1,436 1591 2,261 -778 93.5 4.1 2.4 219.2 44.8 

Table 8.6.2and Table 8.6.3 show the same sensitivity scenario for the case of CSIR and 

CSCR motors, respectively. 

EERE-2007-BT-STD-0007 COMMENT 33
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Table 8.6.2 Capacitor-Start Induction-Run Small Electric Motors: Life-Cycle Cost 

and Payback Period Sensitivity Results for a Shipments-Weighted 

Distribution of Motor Capacities and Poles for Purchase Year 2030 and 

with 100% Power Factor Costs Included 

Life-Cycle Cost Life-Cycle Cost Savings 

Customers with 

Payback Period 

years Energy 

Efficiency

Level 

Efficiency 

%

Average 

Installed 

Price 

$

Average 

Energy 

Use 

kWh/yr

Average 

LifeCycle 

Cost 

$

Average 

Savings

$

>2% 

Net 

Cost 

%

<2% 

Net 

Impact

%

>2% 

Net 

Benefit 

%

Average Median

Baseline 57.7 494 1274 1,044 

1 59.5 503 1222 1,031 13 0.2 78.2 21.6 11.8 3.6 

2 62.0 509 1159 1,010 34 4.3 41.8 53.9 8.9 2.7 

3 64.2 512 1104 987 57 4.1 29.6 66.3 7.1 2.1 

4 68.5 530 1013 964 80 14.1 19.0 66.9 9.3 2.8 

5 71.2 548 963 965 79 25.5 14.3 60.3 11.8 3.6 

6 73.0 593 933 995 49 39.7 11.3 49.0 19.7 5.7 

7 77.0 988 867 1,360 -315 53.0 7.8 39.2 82.8 9.3 

EERE-2007-BT-STD-0007 COMMENT 33
8-45 

Table 8.6.3 Capacitor-Start Capacitor-Run Small Electric Motors: Life-Cycle Cost 

and Payback Period Sensitivity Results for a Shipments-weighted 

Distribution of Motor Capacities and Poles for Purchase Year 2030 and 

with 100% Power Factor Costs Included 

Life-Cycle Cost Life-Cycle Cost Savings 

Customers with 

Payback Period 

years Energy 

Efficiency

Level 

Efficiency 

%

Average 

Installed 

Price 

$

Average 

Energy 

Use 

kWh/yr

Average 

LifeCycle 

Cost 

$

Average 

Savings

$

>2% 

Net 

Cost 

%

<2% 

Net 

Impact

%

>2% 

Net 

Benefit 

%

Average Median

Baseline 71.0 576 2259 1,540 

1 74.3 588 2173 1,505 36 0.2 50.4 49.4 9.5 3.0 

2 78.3 619 2018 1,466 75 14.8 23.7 61.5 13.0 3.9 

3 80.3 631 1956 1,451 89 18.7 19.7 61.7 13.2 4.0 

4 81.6 649 1964 1,457 83 21.9 19.1 59.0 17.4 5.4 

5 82.7 663 1947 1,465 76 27.7 18.3 54.0 19.9 6.1 

6 83.7 717 1937 1,507 33 42.2 16.3 41.5 31.9 9.0 

7 85.4 738 1877 1,507 34 46.1 13.7 40.2 30.8 8.8 

8 87.3 1,641 1833 2,391 -851 91.5 4.0 4.5 179.7 36.6 

As described in more details in chapters 9 and 10, DOE analyzed the market dynamics 

between CSIR and CSCR motors. In this context, it is illustrative to examine the LCC impacts of 

standards for customers who may switch for CSIR to CSCR motors of the same speed and 

horsepower, or vice versa. Table 8.6.4 shows the LCC results for the case of a 4-pole, 0.5 

horsepower motor customer moving from a baseline CSIR motor to a CSCR motor of each 

efficiency level. 

EERE-2007-BT-STD-0007 COMMENT 33
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Table 8.6.4 Capacitor-Start Small Electric Motors: Life-Cycle Cost and Payback 

Period Sensitivity Results for a Space-Constrained 0.5 hp, 4-pole CSCR 

Motor Customer with a CSIR Motor Baseline 

Life-Cycle Cost Life-Cycle Cost Savings 

Customers 

with 

Payback Period 

Energy years

Efficiency 

Level 

Efficiency 

%

Average 

Installed 

Price 

$ 

Average 

Energy 

Use 

kWh/yr

Average 

Annual 

Operating 

Cost 

$ 

Average 

LifeCycle 

Cost 

$ 

Average 

Savings

$ 

Net 

Cost

%

Net 

Benefit 

%

Average Median

CSIR 

Baseline 57.7 490 1277 96.2 941 

CSCR 

Baseline 65.5 502 1061 80.0 876 64 16.0 84.0 4.3 1.3 

1 69.2 511 1008 76.0 866 74 21.5 78.5 6.0 1.9 

2 73.7 543 926 69.7 869 71 35.7 64.3 11.7 3.7 

3 76.0 552 894 67.4 867 74 37.6 62.4 12.6 3.9 

4 77.5 558 885 66.7 871 70 39.5 60.5 13.5 4.3 

5 78.8 571 878 66.2 881 60 43.8 56.2 15.7 5.0 

6 79.7 703 871 65.7 1,011 -70 75.5 24.5 40.8 12.9 

7 82.0 716 839 63.2 1,012 -72 75.0 25.0 40.1 12.7 

8 84.2 3,133 783 59.0 3,410 -2,469 100.0 0.0 417.5 131.4 

 DOE used the results shown in Table 8.6.4, combined with the market share shifts 

forecast to occur under the Department’s segmented market scenario (see section 9.4 for details 

on CSIR/CSCR market share shifts), to calculate the shipment-weighted average LCC results for 

0.5 hp, 4-pole CSIR customers under each trial standard level. Table 8.6.5 shows these results. 

EERE-2007-BT-STD-0007 COMMENT 33
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Table 8.6.5 Capacitor-Start Induction-Run Motors: Shipment-Weighted Life-Cycle 

Cost and Payback Period Results for a 4-Pole One-Half Horsepower 

Motor with Switching to CSCR 

Life-Cycle Cost Life-Cycle Cost Savings 

Customers 

with 

Trial 

Standard 

Level 

Average 

Installed 

Price 

$

Average Energy

Use kWh/yr

Average Annual 

Operating Cost Average LifeCycle Cost 

Average 

Savings Net 

Cost

%

Net 

Benefit

%

Baseline 490 1277 96.2 941 

1 525 1020 76.9 885 56 33.5 66.5 

2 525 1020 76.9 885 56 33.5 66.5 

3 543 971 73.2 886 55 39.8 60.3 

4 586 941 70.9 918 23 52.3 47.7 

5 586 941 70.9 918 23 52.3 47.7 

6 975 877 66.0 1,284 -343 63.1 37.0 

7 580 884 66.6 892 49 50.6 49.4 

8 613 873 65.7 921 20 58.0 42.0 

 DOE has collected the results of each sensitivity analysis, applied individually, in 

Appendix 8C. The Department’s life-cycle analysis and payback period spreadsheet tool is 

available for download via the Internet, and allows the user to examine the results for the 

sensitivity scenario of their choice. 

8.7 REBUTTABLE PAYBACK PERIOD 

 A more energy efficient motor will usually cost more to buy than a motor of standard 

energy efficiency. However, the more efficient motor will usually cost less to operate due to 

reductions in operating costs (i.e., lower energy bills). The PBP is the time (usually expressed in 

years) it takes to recover the additional installed cost of the more efficient motor through energy 

cost savings. EPCA provides a rebuttable presumption that, in essence, an energy conservation 

standard is economically justified if the increased purchase cost for a product that meets the 

standard is less than three times the value of the first-year energy savings resulting from the 

standard. However, DOE routinely conducts a full economic analysis that considers the full 

range of impacts, including those to the customer, manufacturer, Nation, and environment, as 

required under 42 U.S.C. 6295(o)(2)(B)(i) and 42 U.S.C. 6316(e)(1). The results of this analysis 

serve as the basis for DOE to evaluate definitively the economic justification for a potential 

standard level (thereby supporting or rebutting the results of any preliminary determination of 

economic justification). 

EERE-2007-BT-STD-0007 COMMENT 33
8-48 

 The results of DOE’s rebuttable payback period calculations are shown in Tables 8.5.1 

and 8.5.2 below. 

Table 8.7.1 Rebuttable Presumption Payback for Polyphase Motors 

TSL 

Payback Period 

years 

1 3.6 

2 3.1 

3 3.2 

4 3.5 

5 7.9 

6 9.9 

7 40.4 

Table 8.7.2 Rebuttable Presumption Payback for Capacitor-Start Motors 

Induction-Run (1/2 hp, 4 poles) Capacitor-Run (3/4 hp 4 poles) 

TSL CSIR Efficiency 

Level 

Payback Period 

years

CSCR 

Efficiency Level 

Payback Period 

years

1 4 1.9 2 2.8 

2 4 1.9 3 2.9 

3 5 2.4 3 2.9 

4 6 3.9 4 3.5 

5 6 3.9 3 2.9 

6 7 19.6 8 36.2 

7 7 19.6 3 2.9 

8 7 19.6 7 6.0 

EERE-2007-BT-STD-0007 COMMENT 33
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 RS Means. Electrical Cost Data, 28th Annual Edition, 2005. Kingston, MA. p. 97. 

2

 U.S. Department of Energy-Energy Information Administration. Form EIA-861 for 2004, 

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 Ibbotsons Associates. SBBI Valuation Edition 2001 Yearbook, 2001. Chicago, IL. pp. 38, 44. 

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 Damodaran Online. The Data Page: Cost of Capital by Industry Sector, 2006. 

<http://pages.stern.nyu.edu/~adamodar/> 

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

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

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

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

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 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, 2006. 

Washington, DC. <http://www.federalreserve.gov/releases/H15/data.htm> 

9

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

2006. <http://mortgage-x.com/general/indexes/default.asp> (Last accessed, October 10, 

2006). 

10 Damodaran Online. The Data Page: Historical Returns on Stocks, Bonds, and Bills – United 

States, 2006. <http://pages.stern.nyu.edu/~adamodar/> 

EERE-2007-BT-STD-0007 COMMENT 33