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 Increas es 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 a nd Application Lifetimes

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

............................................................................................. From rulemaking on distribu tion 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 PAYB ACK PERIOD RESULTS FOR REPRESENTATIVE PRODUCT CLASSES

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

............................................................................................... 8.4.2 Capacitor-Start I nduction-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 Payba ck Period Analysis: Capacitor-Start Induction-Run Motors

..........................................................................................8-ii Table 8.2.3 Inputs for Life-Cycle Cost and Payba ck 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 Ma nufacturer Selling Price

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

......... Table 8.2.7 Capacitor-Start Induct ion-Run Motors: Manufac turer Selling Price Increases, 0.5 Horsepower

................................................................................. Table 8.2.8 Capacitor-Start Capacitor-Run Moto rs: 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 Installe d Costs for Motors that are SpaceConstrained

........................................................................................................ Table 8.2.12 Capacitor-Start Induct ion-Run Motors (0.5 hp) : Consumer Equipment Prices, Shipping Costs, Installation Co sts, and Total Installed Costs for Motors that are Not Space-Constrained

............................................................. Table 8.2.13 Capacitor-Start Induct ion-Run Motors (0.5 hp) : Consumer Equipment Prices, Shipping Costs, Installation Co sts, and Total Installed Costs for Motors that are Space-Constrained

.................................................................... Table 8.2.14 Capacitor-Start Capacitor-Run Moto rs (0.75 hp): Consumer Equipment Prices, Shipping Costs, Installation Co sts, and Total Installed Costs for Motors that are Not Space-Constrained

............................................................. Table 8.2.15 Capacitor-Start Capacitor-Run Moto rs (0.75 hp): Consumer Equipment Prices, Shipping Costs, Installation Co sts, 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 Effi ciency Level for Small Electric Motors

................................................................................................................ Table 8.2.18 Adjusted Real Discount Rates for Updated Values of R f 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 Inductio n-Run Motors: Life-Cycle Cost and Payback Period Results

....................................................................................................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 fo r a Shipments-Weighted Distribution of Motor Capacities and Poles fo r 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 fo r a Shipments-weighted Distribution of Motor Capacities and Poles fo r 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 Inductio n-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 Dete rmination 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 Payb ack Periods for Efficiency Level 5

..... Figure 8.4.3 Capacitor-Start Inductio n-Run Motors: Distribution of Life-Cycle Cost Savings for Efficiency Level 7

......................................................................... Figure 8.4.4 Capacitor-Start Inductio n-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

..........................................................................8-iv Figure 8.4.6 Capacitor-Start Capacitor-Run Motors : Distribution of Payback Periods for Efficiency Level 3

....................................................................................... 8-398-1 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 sta ndards 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 (usua lly increased). This chapter describes three metrics DOE used to determine the effect of sta ndards on individual end users:

• Life-cycle cost (LCC) is the total consumer expe nse over the life of an appliance, including purchase expense and operating costs (including ener gy 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 numbe r of years it will take the user to recover the increased purchase expense through d ecreased operating expenses.

• Rebuttable payback period is a special case of the PBP. Where LCC and PBP are estimated over a range of inputs reflecting ac tual conditions, rebuttabl e payback period is based on laboratory conditions, specif ically 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 pr esented in section 8.4. The rebuttable PBP is discussed in section 8.5. Key variables and calc ulations are presented for each metric. DOE performed the calculations discussed here us ing 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 Co st and Payback Period Analysis Recognizing that several i nputs to the determination of consumer LCC and PBP are either variable or uncertain, DOE conducted th e 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 spread sheet 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 characterizi ng several of the inputs to th e analysis with probability distributions, DOE also develope d a sample of end-use applica tions for the equipment. These end-use applications determine the use profile of the motor and the economic characteristics of8-2 the motor owner. Table 8.1.1 shows the market sh ares 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 equi pment class, one of the applications is identified by sampling a distribution of applicat ions for that equipment class. The selected application determines the number of operating h ours per year as well as the motor loading. The operating hours and the motor load ing 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 Comme rcial 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 (E IA) data on electricit y 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 consider ed 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 and8-3 energy pricing are not uncertain for any partic ular application, their variability across all applications contributes to the range of LCCs and PBPs calculate d for any particular standard level.
Results presented at the end of this chap ter are based on 10,000 samples per Monte Carlo simulation run. DOE displays the LCC and PBP resu lts 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 PB P analysis as follows: (1) inputs for establishing the initial ex pense, otherwise known as the total installed cost, and (2) inputs for calculating the operating cost.
The primary inputs for establishi ng the total insta lled cost are:

• Baseline manufacturer selling price : The price at which the manufacturer sells the baseline equipment, which includes the co sts incurred by the manu facturer to produce equipment meeting existing standards.

• Manufacturer selli ng 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 a ssociated with converting the manufacturer cost to a consumer equipm ent price. The markups and sale tax are described in detail in Chapter 7, Mark ups for Equipment Price Determination.

• Installation cost : The cost to the consumer of inst alling the equipment. The installation cost represents all costs required to inst all the equipment othe r than the marked-up consumer equipment price. The installati on 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 calcul ating the operating cost are:

• Equipment energy consumption and reactive power : The equipment energy consumption is the site energy use associated with opera ting the equipment. Reactive power is power that is reflected back to the electrical sy stem by a change in th e phase of alternating current power. Chapter 6, Energy Use Characte rization, 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 e quipment efficiency and how equipment efficiency relates to actual equipment energy use.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 co sts 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 fu ture 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 a nd 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).Figure 8.1.1 Flow Diagram of Inputs for the De termination of Life-Cycle Cost and Payback Period

8.2 LIFE-CYCLE COST INPUTS Life-cycle cost is the total customer e xpense over the life of a piece of equipment, including purchase expense a nd operating costs (including ener gy expenditures). DOE discounts future operating costs to the time of purchase, an d 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,

8-58-6 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 capac itor-run (CSCR) resp ectively. Each table summarizes the total installed co st inputs and the ope rating cost inputs in cluding the lifetime, discount rate, and energy price tr ends. DOE characterized all of th e total cost inputs with singlepoint values, but characterized several of the opera ting cost inputs with probability distributions that capture the input’s uncertainty and/or variability. For th ose inputs characterized with probability distributions, the values provided in th e following tables are the average or typical values. Also listed in the following tables is th e 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.8-7 Table 8.2.1 Inputs for Life-Cycle Cost and Paybac k 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 estimates20% 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

Re p air 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. A nnual use decreases with increased product efficiency.8-8 Table 8.2.2 Inputs for Life-Cycle Cost and Paybac k 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 estimates20% 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. A nnual use decreases with increased product efficiency.Table 8.2.3 Inputs for Life-Cycle Cost and Paybac k 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. A nnual use decreases with increased product efficiency.

8.2.2 Total Installed Cost Inputs

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

INST EQPIC + =

8-9 Where:EQP = equipment price (i.e., customer cost for the equipment only), expressed in dollars, and INST = installation cost or the customer pric e to install equipment (i.e., the cost for labor and materials), also in dollars.
The equipment price is based on how the cu stomer (end user) purchases the equipment. As discussed in Chapter 7, Markups for Equipm ent Price Determination, DOE defined markups and sales taxes for converting manufacturing sell ing 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 pr oducing equipment at a standard level. Markups and sales
tax convert the manufacturer selling pri ce to a consumer equipment price. The installation cost is the cost to the consumer of installing the equipmen t and represents all costs required to install the equipment other than the marked-up consumer e quipment 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:

BASE BASE OVERALL MFG BASE BASE BASE INST MU MSP INST EQP IC

+ ×= + =

_ Where:

IC BASE = baseline total installed cost, EQP BASE = consumer equipment price for baseline models, INST BASE = baseline installation and shipping cost, MSP MFG = manufacturer selling pr ice for baseline models, and MU OVERALL_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:

8-108-11 

## ) )

here:

IC STD = 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$) 

## ( ) ( ( ) ( 

# ( )
STD INCR OVERALL MFG BASE STD STD BASE BASE STD BASE STD BASE STD STD STD

INST MU MSP IC INST EQP INST EQP INST INST EQP EQP INST EQP IC

Δ+ ×Δ+= Δ+Δ+ + = Δ+ +Δ+ = +=

_
W

EQP STD = consumer equipment price for stan INST STD = standard-level installation cost, EQP BASE = consumer equipment price for ba Δ EQP STD = change in equipment price for standard-level models, INST BASE = baseline installation and shipping cost, Δ

INST STD = change in installation and shi pping cost IC BASE = baseline total installed cost, Δ

MSP MFG change in manufacturer sellin MU OVERALL_INCR = incremental overall markup (p roduct of manufacturer markup, incremental retailer or distri butor markup, and sales tax).

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

The engi neering analysis pr ovides a baseline manufacturer includes all manufacturer markups (see TSD chapte r 5). Table 8.2.5 presents the baseline M and the associated energy efficiency for each eq uipment class for the baseline models analyzed in the engineering analysis.

T Product Clas s Baseline Efficien cy (%) Ba
P olyphase (1 hp) 77.15 $97.74

CSIR (0.5 hp) 57.70 $91.04
C SCR (0.75 hp) 71.00 $110.82

8.2.2.2 Manufacturer Selling Price Increases for Higher-Efficiency Products

els for sma DOE dete rmined the MSP increases associated with increases in energy efficiency lev ll electric motors in the engineering an alysis (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.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 Moto rs: 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 $1,204.308-13 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 incremen tal 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 mo tor size for medium motors in the RS Means data, DOE found no evidence that installation costs would be impacted with in creased 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 to8-14 calculate the total installed cost for various ener gy efficiency levels. Tables 8.2.10 through 8.2.15 present the end user equipment pr ice, installation costs, shipping and total installed costs for each small motor equipment class for both the space-c onstrained and the not space-constrained cases.

Table 8.2.10 Polyphase Motors (1 hp): Consumer Equipment Prices, Shipping Costs, Installation Costs, and Total Installe d 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 $3,576.058-15 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 $2,529.32Table 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:

8-16EC = 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 determini ng the operating costs. The inputs listed in Table 8.2.16 are also necessary for determining the present value of lif etime operating expenses, which include the energy price trends, product life time, 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 user s 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 a nd discount rate, to esta blish 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 futu re expenditures to establish their present value. DOE calculated th e operating cost for baseline products based on the following equation:

BASE BASE ENERGY BASE BASE BASE BASE BASE MC RC PRICE AEC MC RC EC OC

++ × = + + =

Where:

OC BASE = baseline operating cost, EC BASE = energy expenditure associated w ith operating the baseline equipment which may include reactive power costs, RC BASE = repair cost associated with component failure for the baseline equipment, MC BASE = cost for maintaining baseline equipment operation, AEC BASE = annual energy consumption for baseline equipment,

8-17PRICE ENERGY = energy price.
DOE calculated the operating cost for sta ndard-level products based on the following equation:

8-18 

## ) 

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

MC MC RC RC PRICE AEC AEC MC RC PRICE AEC MC RCEC OC

Δ++Δ++ ×Δ = ++ ×= ++=

__ Where:

OC STD = standard-level operating cost, EC STD = energy expenditure associated with operating standard-level equipment, RC STD = repair cost associated with component failure for standard-level equipment, MC STD = cost for maintaining sta ndard-level equipment operation, AEC STD = annual energy consumption fo r standard-level equipment, PRICE ENERGY = energy price, Δ

AEC STD = decrease in annual energy c onsumption caused by standard-level equipment, Δ RC STD = change in repair cost cause d by standard-level equipment, and Δ

MC STD = 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 pr oducts. 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 en ergy consumption for a variety of motor-using applications.8-19 Table 8.2.17 Average Annual Electricity Use by E fficiency 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 sm all 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 k ilowatt-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 ca lculated the distribution of elec tricity prices for each customer class. DOE used these electricity price distributions to represent th e customer cost of electricity for the different classes of motor owners. DOE assigned the electricity price distribution for industrial customers to the cla ss of agricultural motor owners. The resulting electricity price distributions are shown in Figure 8.2.1.0.0 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 mu ltiplied the average prices descri bed 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 Ac t, 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 industria l electricity price tren ds 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.

8-200.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30

2005 2010 2015 2020 2025 2030 2035 2040 2045
YearPrice 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 ar e 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 weld s and rivets to fasten or secure the frame and assembled components, not nuts and bolts. DOE found no evid ence 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, a nd developed estimates for typical motor lifetime of 7 years for capacitor-start motors and 9 y ears for small polyphase motors (two-digit frame series). The Department used Weibull distribu tions based on these values in its preliminary analysis. (The Weibull distributi on is a standard distribution used to model failure processes.)
DOE has developed a more sophisticated model for motor lifetime for us e in this stage of the analysis. This model combines annual hour s 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

8-21per year are likely to be retired sooner than mo tors 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 distributio n 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 distri bution 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 estimat es of typical motor lifetime to develop the parameters for the Weibull distributions fo r 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 lifet ime, and application lifetime from these distributions in order to calculate th e 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 ha ve 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 coul d run for several more years. If the pump motor were to run for 6000 hours per year, with the sa me mechanical and appl ication 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 comm only used to measure failure rates. a Its form is similar to an exponential distribu tion, 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/ >.8-23 x = equipment age;

α = scale parameter, which would be the d ecay length in an exponential distribution; β

= shape parameter, which determines the wa y in which the failure rate changes through time; and θ

= delay parameter, or location, which a llows for a delay before any failures occur.

When β = 1, the failure rate is constant over tim e, 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 mechani cal lifetime is 30,080 hour s, and the median is 29,680 hours.
DOE’s derived Weibull parameters for capacito r-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. Th e 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 fact or 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 ope ration and motor lifetime is -0.712, indicating an inverse relationship as expected.

8.2.5 Polyphase Mechanical and Application Lifetimes Interviews with OEM-industry ex perts indicate that polyphase motors are expected to be used for more years before retirement. Mechanic ally and electrically, they are simpler than capacitor-start motors, due to the la ck of a capacitor, and failure of the bearings is expected to be the dominant cause of motor failure. DOE ther efore derived a polyphase mechanical motor lifetime distribution with somewhat higher numbe r of hours until failure than for capacitor-start motors. DOE’s derived Weibull parameters fo r polyphase motor mechanical lifetimes are:

α = 23,000 hours;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 mechani cal lifetime is 40,400 hour s, 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. Th e mean application lifetime is 9.69 years, and the median is 9.50 years.
In the course of the life-cycle analys is, DOE combines these two distributions with the appropriately weighted duty factor dist ribution to select a lifet ime 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 re lationship as expected.

8.2.5.1 Discount Rates

DOE derived the discount rates for the L CC and PBP analysis from estimates of the finance cost of purchasing the c onsidered products. Fo llowing financial theory, the finance cost of raising funds to purchase equipment can be inte rpreted as: (1) the financ ial cost of any debt incurred to purchase equipment, or (2) the oppor tunity cost of any equity used to purchase equipment.
Commercial, Industrial, and Agricultural Owners For motors purchased and used in the industr ial, agricultural, and commercial sectors, DOE calculated the discount rate for a distribu tion of representative product owners. This distribution of representative ow ners is the weighted sum of discount rate distributions for different ownership categories. DOE calculated a distribution of di scount rates for owners within each ownership category. The discount rate for an individual owner is the weighted average cost of capital (WACC) where, given th e mix of debt and equity for th at 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 usi ng the capital asset pricing model (CAPM). 3 The CAPM assumes that the cost of equity ( k e ) 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: th e risk coefficient of the firm ( β ), the expected return on riskfree assets ( R

f ), and the equity risk premium ( ERP ). The risk coefficient of the firm indicates the risk associated with that firm relative to the pr ice 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 st ock market return and the risk-free rate. The cost of equity financing is estimated using the following e quation, where the variables are defined as above: 

## ( ) ERP Rk

fe

×+= β Where:

k e = cost of equity, R

f = expected return on risk-free assets, β = risk coefficient of the firm, and ERP = equity risk premium.
The cost of debt financing ( k d

) is the interest rate paid on money borrowed by a company. The cost of debt is estimated by adding a risk adjustment factor ( R a ) 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:

aifdi RRk += Where:

k d = cost of debt financing for firm, i , R

f = expected return on risk-free assets, and R ai = risk adjustment factor to risk-free rate for firm, i

. DOE estimates the WACC using the following equation:

ddee wkwkWACC ×+× =

Where:

WACC = weighted average cost of capital,

w e = proportion of equity financing, and

w d = proportion of debt financing.

Damodaran Online is a widely used sour ce of information about company debt and equity financing for most types of firms. 4

8-25 Several parameters of the cost of capital e quations can vary substantially over time, and therefore the estimates can vary with the time period over whic h data is selected and the technical details of the data av eraging method. For guidance on th e time period for selecting andaveraging 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 cal culating discount rate averages , utilizes the gross domestic product price deflator for estimati ng inflation, and considers the best method for determining the risk free rate as one where “the time horizon of the investor is matc hed with the term of the riskfree security.” 5

During the preliminary analysis, DOE adjust ed the discount rate distributions from a previous rulemaking on dist ribution transformer standards with updated values of the equity risk premium, inflation, and the ri sk-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 reta ined 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 va lues 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 ra te that was used to convert discount rates to the values that correspond to th e new values of risk-free rate and ERP. DOE obtained the following equation for be ta by solving the CAPM equation:

ERPRk

fe /)(

− = β Where:

k e = cost of equity, R

f = 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 R f 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

8-268-27 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 distribu tion transformer standards

Table 8.2.19 shows the average WACC values for the three non-residential ownership types in the small electric motors analysis. Wh ile WACC values for any sector may trend higher or lower over substantial periods of time, these va lues represent a private sector cost of capital that is averaged over major busine ss cycles. For all sector s, the averages are slightly lower than 6 percent real.

Table 8.2.19 Weighted Average Cost of Capital fo r 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 equipmen t. In principle, one could estimate the interest rates on the actual fina ncing vehicles used to purchase replacement equipment. The shares of different financing ve hicles in total equipment purchases are unknown, however.
DOE’s approach involves identifying all possibl e debt or asset classes that might be used to purchase equipment, including household as sets 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 thes e would likely not be affected by equipment purchases. DOE estimated the average shar es of the various debt and equity classes in the average U.S. household equity and debt portfolios using Survey of C onsumer 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.8-28 used the mean share of each cl ass across the six years as a ba sis 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 associ ated 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 eff ective real rates in each year and the mean rate across the years. Si nce the interest rates fo r each debt carried by households in these years were established ov er a range of time, DOE believes they are representative of rates that may be in effect in 2015.8-29 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 househol ds, DOE sampled a rate for each household from a distribution of rates for each of the a bove 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 classe s, so DOE derived data for these classes from national-level histor ical 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 c overing 1977–2005. DOE assumed rates on checking accounts to be zero. Rates on savings and mone y 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 ra tes (one-third weight) in each year of the 1977–2005 period. DOE adjusted the nominal rates to re al rates using the annua l inflation rate in each year. Average nominal and r eal interest rates for the clas ses 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 2015.8-30 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 th e 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 ra tes 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 pr ovides the debt and asset shares for U.S. households. DOE averaged the debt a nd asset shares over the six years of survey data to arrive at the shares shown below. The average rate acr oss all types of house hold debt and equity, weighted by the shares of each class, is 5.6 percent.8-31 Table 8.2.24 Shares and Interest or Return Rates Us ed 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 conservati on standard is the future date when a new standard becomes operative. S ection 346(b)(3) of the Energy Policy and Conservation Act (EPCA) requires that any standard for small electr ic 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 App liance Energy Efficiency Rule makings, dated February 2008, DOE is required to publish an energy conservatio n standard final rule by February 28, 2010. (See http://www1.eere.energy.gov/buildings/a ppliance_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 th e base case (i.e., what consumers would have purchased in the year 2015 in th e absence of new standards).In other rulemakings, DOE often uses the distribution of product efficiencies currently in the marketplace to develop its estimate of such di stribution in the base case. DOE did find some models offered in the manufacturer catalogues th at were low first cost and then had matching higher-efficiency units. These so-called 'matched pa irs' would seem to indicate that there is some voluntary purchasing of hi gher-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 e fficiency 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 operati ng 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:

O C IC PBP Δ Δ

=
Where:

Δ IC = increase in the total installed cost between the more effi cient standard level and the baseline design, and Δ OC = decrease in annual operating expenses.
Payback periods are expressed in years. Pa yback periods greater than the life of the product indicate that the increase d total installed cost is not recovered in reduced operating expenses.
The data inputs to PBP are the total installe d 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 in stalled cost are the equipment price and the installati on cost. The inputs to the operating costs are the annual energy co st, 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,

8-328-33 except that lifetime, energy price trends and disc ount rates are not requir ed. 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 result s for small motors. As discussed in section 8.1.1, DOE’s approach for conducting the L CC analysis relied on de veloping 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 th e customers in the sample. For each set of sample customers using motors in each equipm ent 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 figur es showing the distribut ion of LCCs in the base case for each equipment class. Also presente d below for a specific sta ndard level are figures showing the distribution of LCC impacts and the distribution of PBPs. Th e figures are presented as frequency charts that show the distribution of LCCs, LCC impacts, and PBPs with their corresponding probability of occu rrence. DOE generated the figures for the distributions from a Monte Carlo simulation run ba sed on 10,000 samples. The LCC and PBP calculations were performed 10,000 times by sampling from the proba bility distributions th at 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 pr ovide such information for each equipment class.

8.4.1 Polyphase Motors Figure 8.4.1 is an example of a freque ncy chart showing the distribution of LCC differences for the case of efficiency level 5 fo r 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).Polyphase Life-Cycle Cost Savings for EL5
95% 25% 50% 75%

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 (#)

488 Outliers 10000 Trials

Figure 8.4.1 Polyphase Motors: Distribut ion of Life-Cycle Cost Savings for Efficiency Level 5
Figure 8.4.2 is an example of a frequenc y chart showing the di stribution of payback periods of efficiency level 5 for polyphase mo tors. Because many motors operate for very few hours per year, this means that th ere is a significant number of motors that may have extremely long payback periods because the op erating 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 distribu tion payback is large (49. 5 years) because of the small, but significant number of motors w ith 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

851 Outliers 10000 Trials

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

8-348-35 Table 8.4.1 summarizes the LCC and PBP results fo r 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 cas e) 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 years Energy Efficiency

Level Efficiency % Average Installed

Price

$ Average Energy

Use kWh/yr Average Annual Operating Cost

$ AverageLifeCycle 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 distri bution of LCC impacts for the case of efficiency leve l 7 for CSIR motors. Efficiency level 7 is the maximum technologically feasible level fo r 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.Capacitor-Start Induction Run Life-Cycle Cost Savings for EL7
95% 25%50%75%

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 (#)

354 Outliers 10000 Trials

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 frequenc y chart showing the di stribution 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 fr action of motors with extremely high payback periods, the average of the dist ribution 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

724 Outliers 10000 Trials

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

8-368-37 savings is level 6, 73.0 percent. However, approx imately 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 ba se case) is $97, while annual ope rating costs decrease by $25.

Table 8.4.2 Capacitor-Start Induction-Run Motors: Li fe-Cycle Cost and Payback Period Results
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 Annual Operating Cost

$ AverageLifeCycle 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 distri bution of LCC savings for the case of efficiency level 3 for CSCR moto rs. DOE can generate a frequency chart like the one shown in Figure 8.4.5 for every efficiency level.Capacitor-Start Capacitor-Run Life-Cycle Cost Savings for EL3
5% 95% 25% 50% 75%

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 (#)

344 Outliers 10000 Trials

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 frequenc y chart showing the di stribution 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.

8-38Capacitor-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

676 Outliers 10000 Trials

Figure 8.4.6 Capacitor-Start Capacitor-Run Motors: Distribution of Payback Pe riods 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 an nual operating costs decrease by $17.

8-39Table 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 years Energy Efficiency

Level Efficiency % Average Installed

Price

$ Average Energy

Use kWh/yr Average Annual Operating Cost

$ AverageLifeCycle 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 (c hapter 5) along with the markups analysis (chapter 6) allowed the Departme nt to develop a dist ribution of consumer purchase costs for each of the three representa tive product classes analyzed in de tail in the engineering analysis. However, in order to present national impacts (c hapter 10), examine the LCC results for other product classes (section 8.6), and to model the current market in terplay between CSIR and CSCR motors, the Department develope d a power-law-based scaling rela tion 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 a nd equal for all product classes).
The Department first used manufacturer cata log data to develop av erage 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:

8-408-41 $(p, hp) = the purchase cost of an hp horsepower motor with p poles, hp ref = 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 hp ref 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 beca use it determined that there were not enough published prices to derive an accurate sca ling 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 c onsumer purchase cost sc aling 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 ar e 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 1.3388-42 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 Chapte r 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 de velop national shipment-weighted average LCC results for polyphase, CSIR, and CSCR motors. These results are published in Appendix 8C, along with the other sensitivities de scribed in the following section.

8.6 LIFE-CYCLE COST SENSITIVITY CALCULATIONS DOE developed a number of sensitivity analys es in order to analyze the particular impacts of many inputs to its life- cycle cost analysis. These sens itivity analyses include lower and higher markups, lower and higher hours of motor operation, lo wer 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 fo r each product class, or for a national shipmentweighted distribution, using th e price scaling described in se ction 8.5 and the loss scaling described in chapter 5. Doe also developed the ab ility to report the distribution of customers with net costs and net benefits, incl uding division into three categor ies for costs above a threshold fraction of life-cycle cost, bene fits greater than a threshold fraction of life-cycle cost, and customers whose impact, whether positive or negative, falls below the user-selected threshold.8-43 Table 8.6.1 shows a possible combination of these sensitivity analyses for the case of polyphase motors. The data in the table correspo nds to the case of motor customers purchasing motors in 2030 (rather than th e base case of 2015), and uses the national shipment-weighted distribution. In addition, this scenario has 100% of customers fa cing reactive power costs. The threshold for division of impacts is 2%.

Table 8.6.1 Polyphase Small Electric Motors: Li fe-Cycle Cost and Payback Period Sensitivity Results for a Shipments -weighted Distribution of Motor Capacities and Poles for Purchas e Year 2030 and with 100% Power Factor Costs Included
Life-Cycle Cost Life-Cycle Cost Savings

Customers with Payback Period years Energy Efficienc y

Level Efficiency % Average Installed

Price

$ Avera g e Energy

Use kWh/yr Avera g eLifeCycle 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 8.6.2 and Table 8.6.3 show the same sensitivity scen ario for the case of CSIR and CSCR motors, respectively.8-44 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 Fact or Costs Included
Life-Cycle Cost Life-Cycle Cost Savings

Customers with Payback Period years Energy Efficienc y

Level Efficiency % Avera g e Installed

Price

$ Avera g e Energy

Use kWh/yr AverageLifeCycle 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 9.38-45 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 Fact or Costs Included
Life-Cycle Cost Life-Cycle Cost Savings

Customers with Payback Period years Energy Efficienc y

Level Efficiency % Average Installed

Price

$ Avera g e Energy

Use kWh/yr AverageLifeCycle Cost

$ Avera g e 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 exam ine the LCC impacts of standards for customers who may switch for CS IR 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 base line CSIR motor to a CSCR motor of each efficiency level.8-46 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 years Energy Efficiency

Level Efficiency % Average Installed

Price

$ Average Energy

Use kWh/yr Average Annual Operating Cost

$ AverageLifeCycle 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-w eighted average LCC results for 0.5 hp, 4-pole CSIR customers under each trial standard level. Table 8.6.5 shows these results.8-47 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

$ Avera g e Ener gy 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 sens itivity analysis, applied individually, in Appendix 8C. The Department’s life-cycle analys is and payback period spreadsheet tool is available for download via the In ternet, 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 co st 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 presum ption that, in essence, an energy conservation standard is economically justified if the increas ed purchase cost for a product that meets the standard is less than three times the value of the first-year energy savi ngs resulting from the standard. However, DOE routinely conducts a fu ll economic analysis that considers the full range of impacts, including t hose 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).8-48 The results of DOE’s rebuttable payback pe riod calculations are s hown 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 6.08-49 REFERENCES

1 RS Means. Electrical Cost Data, 28 th Annual Edition , 2005. Kingston, MA. p. 97.

2 U.S. Department of Energy- Energy Information Administration. Form EIA-861 for 2004, 2004. Washington, DC. < http://www.eia.doe.gov/cneaf/e lectricity/page/eia861.html >

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

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

8 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
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10 Damodaran Online. The Data Page: Historical Returns on Stocks, Bonds, and Bills – United States , 2006. < http://pages.stern.nyu.edu/~adamodar/ >