### 11-i 

## CHAPTER 11. LIFE-CYCLE CO ST SUBGROUP ANALYSIS

TABLE OF CONTENTS

11.1 INTRODUCTION ......................................................................................................... 11-1 11.2 SMALL ELECTRIC MOTOR CUSTOMER SUBGROUPS ....................................... 11-1 11.2.1 Inputs to the Subgroup Analysis for Customers with and without Space Constraints ..................................................................................................................... 11-1 11.2.2 Inputs to the Subgroup Analysis for Small Businesses ................................................. 11-2 11.3 RESULTS FOR SMALL ELECTRIC MOTOR SUBGROUPS ................................... 11-3

LIST OF TABLES

Table 11.2.1 Discount Rate Difference Between Sm all Company and Market Average ....... 11-3 Table 11.3.1 Polyphase Small Electric Motors: LCC and PBP Results for SpaceConstrained Customers ...................................................................................... 11-4 Table 11.3.2 Polyphase Small Electric Motors: LCC and PBP Results for Non-SpaceConstrained Customers ...................................................................................... 11-4 Table 11.3.3 Polyphase Small Electric Motors: LCC and PBP Results for Small Companies .......................................................................................................... 11-5 Table 11.3.4 Capacitor-Start Induct ion-Run Small Electric Motors: LCC and PBP Results for Space-Constrained Customers ......................................................... 11-5 Table 11.3.5 Capacitor-Start Induct ion-Run Small Electric Motors: LCC and PBP Results for Non-Space-Constrained Customers

................................................. 11-6

11-6

11-7

11-7

11-8 Table 11.3.6 Capacitor-Start Induct ion-Run Small Electric Motors: LCC and PBP Results for Small Companies

............................................................................. Table 11.3.7 Capacitor-Start Capacitor-Run Small Electric Motors: LCC and PBP Results for Space-Constrained Customers

......................................................... Table 11.3.8 Capacitor-Start Capacitor-Run Small Electric Motors: LCC and PBP Results for Non-Space-Constrained Customers

................................................. Table 11.3.9 Capacitor-Start Capacitor-Run Small Electric Motors: LCC and PBP Results for Small Companies

.............................................................................

### 11-1 

## CHAPTER 11. LIFE-CYCLE COST SU BGROUP ANALYSIS

11.1 INTRODUCTION
Chapter 8 describes the life -cycle cost (LCC) and payback period (PBP) analysis that examines impacts of energy conservation standard s on purchasers of the affected products. In analyzing the potential impact of new or amen ded standards on residential, industrial, and commercial customers, DOE further evaluates th e impact on identifiable groups of customers (i.e., subgroups) that may be disproportionately affected by a national standard level. The LCC subgroup analysis evaluates impacts by anal yzing the LCC and PBPs for subgroups of customers. For its analysis of small electric motors, DOE identified three customer subgroups: small businesses and customers with and without space constraints restri cting their choice of
motor.

Because DOE did not conduct its LCC and PBP analysis with a sample of small motor users, it did not develop speci fic subgroup samples for the subgroup analysis. Instead, it varied certain inputs to the LCC and PBP calculations in order to approximate the impacts of potential standards on the considered subgr oups. This chapter de scribes the subgroup an alysis in further detail and gives the results of the LCC a nd PBP analyses for the considered subgroups.

11.2 SMALL ELECTRIC MOTO R CUSTOMER SUBGROUPS
DOE considered three subgroups for the L CC and PBP analyses for small electric motors: (1) customers facing spac e constraints in their motor in stallation, (2) customers without space constraints in their motor inst allation, and (3) small businesses.

For customers with space constraints, DOE analyzed the potential impacts of standards by conducting the analysis with motor designs cons trained to a stack leng th increase of 20% or less. For customers without space constraints, DO E analyzed the potential impacts of standards by conducting the analysis with motor designs cons trained to a stack leng th increase of 100% or less. For small businesses, DOE analyzed the potential impacts of standards by conducting the analysis with different discount rates, as small businesses do not have the same access to capital as larger businesses.

11.2.1 Inputs to the Subgroup Analysis for Custom ers with and without Space Constraints
One of the more cost-effective ways to in crease motor efficiency is by increasing the motor stack length. However, many motor users face space constraints, which restrict their ability to replace existing motors with much longer, more effici ent, designs. The Department’s engineering analysis produced motor designs th at meet space constraint s by restricting stack length increases to 20% or less. The Department also analyzed de signs in which the stack length was free to increase up to 100% (effectively an unconstrained stack length increase).

## DOE assumed that 20% of customers face space constraints in order to develop national average LCC results in chapter 8. For its sp ace-constrained customer subgroup analysis, DOE used its LCC spreadsheet tool, but selected only customers who face space constraints. For its non-space-constrained customer subgroup analysis , DOE selected only customers who do not face space constraints. These customers use the same motor designs at low energy efficiency levels (where all designs the Department consid ered have stack length increases of less than 20%), but constrained designs become distinct at efficiency level (EL) 5 for polyphase, EL 6 for CSIR, and EL 2 for CSCR. Generally, these spac e-constrained designs cost more than less constrained designs to achi eve the same efficiency.

11.2.2 Inputs to the Subgroup Analysis for Small Businesses
The Small Business Administration (SBA) defi nes a small business by its annual receipts or its number of employees. Small motors are used throughout the U.S. economy, so DOE did not assign a different distributi on of motor applications or se ctors of the economy to this subgroup.

To calculate discount rates for small compan ies that purchase small electric motors, DOE used the same methodology as for the general p opulation of small electric motor customers as presented in chapter 8. a 

## Although the methodology is appropriat e, the capital asse t pricing model (CAPM) b 

## described in chapter 8 for th e general population underestimates the cost of capital for small companies. In CAPM, the risk premium β is used to account for the higher returns associated with greater risk. However, for small companies, particularly very small companies, historic returns have been signi ficantly higher than the CAPM e quation predicts. This additional return can be accounted for by adding a size premiu m to the cost of equity for small firms: 

# ( ) SERP Rk

fe 

## + × + = β

k

e 

## = Cost of equity, 

## R

f 

## = Expected return on risk-free assets, 

## β = Risk coefficient of the firm, 

## ERP = Equity risk premium, and S 

## = Size Premium.

DOE obtained size premium data from Ibbotson Associates’ 

## Stocks, Bonds, Bills, and Inflation 2007 Yearbook

. 1 

## For the period of 1926–2006, the average size premium for the smallest companies in all i ndustries is 6.27 percent, implyi ng that on average, historic

a 

### DOE assumed that small businesses as a whole are a r easonable approximation for small businesses which use small electric motors.

11-2 b 

### See 8.2.4.3 for more extensive description of CAPM and its parameters.

### 11-3 

## performance of small companies has been 6.27 pe rcent higher than the CAPM estimate of the small company cost of equity. c



## DOE calculated the real weighted average cost of capital (as described in chapter 8) using the cost of equity including a size premium for small companies instead of the CAPM cost of equity. DOE estimates that in industries that purchase small electric motors, small companies have an average discount rate 4.2 percent higher than the industry average. This conclusion is supported by the similar difference (3.8 percent) between small and average company discount rates for the entire market based on data from Damodaran d

, 2 

## (see Table 11.2.1 ).

Table 11.2.1 Discount Rate Difference Between Sm all Company and Market Average Discount Rate Sector Average Std Dev Difference Entire Market 6.3% 2.3% -- Small Company 10.2% 3.3% 3.8%



## In chapter 8, DOE estimated the average disc ount rate for both indus trial and commercial customers to be 5.9 percent. Applying the a dditional small capitalization (small cap) discount rate premium of 4.2 percent presented above to th ese discount rates for businesses that purchase small electric motors, the average discount rate for small industrial and commercial companies is approximately 10.1 percent.

11.3 RESULTS FOR SMALL ELEC TRIC MOTOR SUBGROUPS

Tables 11.3.1 through 11.3.3 summarize the polypha se small electric motor results for customers with and without space-constrained app lications and those that are small businesses. Tables 11.3.4 through 11.3.6 summari ze the capacitor-start induction -run small electric motor results for the same subgroup types, while Tables 11.3.7 - 11.3.9 summarize the capacitor-start capacitor-run small electric motor results. For the seven energy e fficiency levels for polyphase motors, seven energy efficiency levels for CSIR motors, and the eight energy efficiency levels for CSCR motors, the tables provide the average or mean LCC, the LCC savings or costs relative to the base case, and the percen tage of customers that are burde ned with net costs or realize net savings. The mean and median payback periods ar e also provided. As in chapter 8, these LCC results are for the three repres entative product classes only: 1 hp 4-pole polyphase, 1/2 hp 4-pole CSIR, and 3/4 hp, 4-pole CSCR.

LCC results for space-constrained and non-space -constrained customers are different in the following tables even at efficiency levels below the level at which the motor designs differ due to randomness resulting from the Monte Carlo sampling method.

c 

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

$84.5 million, the Ibbotson Associates’ definition of Decile 10 companies.
d 

### The Damodaran database for the entire market used for th is analysis includes 6559 companies, 2605 of which are

small companies.

### 11-4 

## In general, the benefits of moving to a highe r efficiency are less in the case of the small business subgroups than in the overall sample. Sp ace-constrained users achieve fewer benefits at high efficiency levels, where space constraints result in significantly different motor designs, technology, and materials than unconstrained moto rs. Non-space constrained customers receive greater benefits (or lower bur dens) than the overall sample, consistent with their lower incremental cost of efficiency.

Table 11.3.1 Polyphase Small Electric Motors: LCC and PBP Results for SpaceConstrained Customers
Life-Cycle Cost Life -Cycle Cost Savings

Consumers with Payback Period (years) Energy Efficiency

Level Efficiency Average Installed

Price Average Annual Energy Use

(KWh) Average Annual Operating Cost Average Life-Cycle Cost Average Life-Cycle Cost Savings Net Cost Net Benefit Average Median

Baseline 77.2% $511 1743 $131.16 $1,276

1 78.7% $524 1714 $128.99 $1,276 $0 62.0% 38.0% 33.7 10.6

2 80.0% $531 1678 $126.31 $1,267 $9 48.7% 51.4% 23.0 7.3

3 81.6% $542 1626 $122.34 $1,255 $22 44.0% 56.0% 20.2 6.3

4 82.5% $550 1610 $121.15 $1,256 $20 47.5% 52.5% 22.6 7.1

5 85.2% $756 1525 $114.77 $1,425 -$149 92.2% 7.8% 87.6 27.3

6 86.7% $768 1501 $112.95 $1,427 -$151 90.9% 9.1% 82.3 25.8

7 88.3% $3,572 1459 $109.77 $4,212 -$2, 936 100.0% 0.0% 836.5 261.1



## Table 11.3.2 Polyphase Small Electric Motors: LCC and PBP Results for Non-SpaceConstrained Customers
Life-Cycle Cost Life -Cycle Cost Savings

Consumers with Payback Period (years) Energy Efficiency

Level Efficiency Average Installed

Price Average Annual Energy Use

(KWh) Average Annual Operating Cost Average Life-Cycle Cost Average Life-Cycle Cost Savings Net Cost Net Benefit Average Median

Baseline 77.2% $512 1732 $130.83 $1,272

1 78.7% $524 1703 $128.68 $1,272 $0 62.7% 37.3% 34.8 11.0

2 80.0% $531 1668 $125.99 $1,263 $9 49.3% 50.7% 23.7 7.5

3 81.6% $543 1615 $122.01 $1,251 $21 44.6% 55.4% 20.8 6.5

4 82.5% $551 1599 $120.83 $1,253 $20 48.0% 52.0% 23.2 7.3

5 85.2% $616 1522 $114.98 $1,284 -$11 65.1% 35.0% 39.5 12.3

6 86.7% $681 1504 $113.61 $1,341 -$68 79.8% 20.2% 58.8 18.3

7 88.3% $939 1471 $111.12 $1,585 -$312 97.4% 2.6% 129.4 40.5

### 11-5 

## Table 11.3.3 Polyphase Small Electric Motors: LCC and PBP Results for Small Companies
Life-Cycle Cost Life -Cycle Cost Savings

Consumers with Payback Period (years) Energy Efficiency

Level Efficiency Average Installed

Price Average Annual Energy Use

(KWh) Average Annual Operating Cost Average Life-Cycle Cost Average Life-Cycle Cost Savings Net Cost Net Benefit Average Median

Baseline 77.2% $511 1743 $131.16 $1,164

1 78.7% $524 1714 $128.99 $1,166 -$2 68.3% 31.7% 33.7 10.6

2 80.0% $531 1678 $126.31 $1,159 $5 54.3% 45.7% 23.0 7.3

3 81.6% $542 1626 $122.34 $1,150 $14 49.5% 50.5% 20.2 6.3

4 82.5% $550 1610 $121.15 $1,153 $11 53.1% 47.0% 22.6 7.1

5 85.2% $642 1531 $115.22 $1,215 -$51 75.6% 24.4% 47.7 14.2

6 86.7% $697 1512 $113.75 $1,263 -$99 86.7% 13.3% 61.9 19.3

7 88.3% $1,444 1477 $111.12 $1,997

- $833 98.8% 1.2% 260.1 55.6



## Table 11.3.4 Capacitor-Start Induction-Run Sma ll Electric Motors: LCC and PBP Results for Space-Constrained Customers
Life-Cycle Cost Life -Cycle Cost Savings

Consumers with Payback Period (years) Energy Efficiency

Level Efficiency Average Installed

Price Average Annual Energy Use

(KWh) Average Annual Operating Cost Average Life-Cycle Cost Average Life-Cycle Cost Savings Net Cost Net Benefit Average Median

Baseline 57.7% $490 1291 $97.65 $949

1 59.5% $499 1239 $93.71 $940 $10 39.2% 60.9% 13.7 4.2

2 62.0% $505 1177 $89.00 $923 $26 31.9% 68.1% 10.3 3.2

3 64.2% $507 1122 $84.85 $906 $43 25.9% 74.1% 8.2 2.5

4 68.5% $535 1021 $77.24 $898 $51 38.1% 61.9% 13.3 4.1

5 71.2% $543 982 $74.26 $892 $57 39.1% 60.9% 13.6 4.2

6 73.0% $659 942 $71.28 $994 -$45 72.4% 27.7% 38.6 12.0

7 77.0% $2,527 869 $65.73 $2,835 -$1, 886 100.0% 0.0% 385.7 119.3

### 11-6 

## Table 11.3.5 Capacitor-Start Induction-Run Sma ll Electric Motors: LCC and PBP Results for Non-Space-Constrained Customers
Life-Cycle Cost Life -Cycle Cost Savings

Consumers with Payback Period (years) Energy Efficiency

Level Efficiency Average Installed

Price Average Annual Energy Use

(KWh) Average Annual Operating Cost Average Life-Cycle Cost Average Life-Cycle Cost Savings Net Cost Net Benefit Average Median

Baseline 57.7% $491 1294 $96.85 $942

1 59.5% $499 1242 $92.95 $933 $9 39.4% 60.6% 13.6 4.3

2 62.0% $505 1179 $88.28 $917 $25 31.8% 68.2% 10.2 3.2

3 64.2% $508 1124 $84.16 $900 $42 26.1% 73.9% 8.2 2.6

4 68.5% $523 1036 $77.55 $884 $58 30.8% 69.3% 10.1 3.2

5 71.2% $544 984 $73.66 $887 $55 39.3% 60.7% 13.6 4.3

6 73.0% $571 956 $71.59 $904 $38 48.1% 51.9% 18.7 5.9

7 77.0% $607 892 $66.80 $918 $24 54.3% 45.7% 22.9 7.3



## Table 11.3.6 Capacitor-Start Induction-Run Sma ll Electric Motors: LCC and PBP Results for Small Companies
Life-Cycle Cost Life -Cycle Cost Savings

Consumers with Payback Period (years) Energy Efficiency

Level Efficiency Average Installed

Price Average Annual Energy Use

(KWh) Average Annual Operating Cost Average Life-Cycle Cost Average Life-Cycle Cost Savings Net Cost Net Benefit Average Median

Baseline 57.7% $490 1291 $97.65 $892

1 59.5% $499 1239 $93.71 $885 $7 43.0% 57.0% 13.7 4.2

2 62.0% $505 1177 $89.00 $872 $21 35.7% 64.3% 10.3 3.2

3 64.2% $507 1122 $84.85 $857 $36 29.5% 70.5% 8.2 2.5

4 68.5% $525 1031 $78.00 $846 $46 36.1% 63.9% 10.8 3.3

5 71.2% $543 982 $74.26 $849 $43 42.9% 57.1% 13.6 4.2

6 73.0% $587 952 $72.00 $883 $9 56.7% 43.4% 22.6 6.7

7 77.0% $976 886 $67.03 $1,251 -$359 66.7% 33.3% 91.9 11.0

### 11-7 

## Table 11.3.7 Capacitor-Start Capacitor-Run Sma ll Electric Motors: LCC and PBP Results for Space-Constrained Customers
Life-Cycle Cost Life -Cycle Cost Savings

Consumers with Payback Period (years) Energy Efficiency Level Efficiency Average Installed

Price Average Annual Energy Use

(KWh) Average Annual Operating Cost AverageLifeCycle Cost Average Life-Cycle Cost Savings Net Cost Net Benefit Average Median

CSIR Baseline 63.4% $543 1732 $131.00 $1,160

CSCR Baseline 71.0% $541 1467 $110.95 $1,062

1 74.3% $552 1404 $106.22 $1,048 $13 33.4% 66.6% 12.8 4.0

2 78.3% $589 1307 $98.85 $1,052 $10 54.0% 46.0% 23.2 7.3

3 80.3% $599 1270 $96.06 $1,048 $14 53.4% 46.6% 22.9 7.2

4 81.6% $606 1260 $95.28 $1,050 $12 54.8% 45.2% 24.4 7.7

5 82.7% $621 1251 $94.64 $1,062 $0 61.3% 38.7% 28.7 9.1

6 83.7% $775 1243 $94.02 $1,211 -$149 94.3% 5.7% 81.1 25.6

7 85.4% $790 1205 $91.15 $1,213 -$151 92.6% 7.4% 73.8 23.3

8 87.3% $3,592 1139 $86.14 $3,993 -$2, 931 100.0% 0.0% 727.9 229.4



## Table 11.3.8 Capacitor-Start Capacitor-Run Sma ll Electric Motors: LCC and PBP Results for Non-Space-Constrained Customers
Life-Cycle Cost Life -Cycle Cost Savings

Consumers with Payback Period (years) Energy Efficiency Level Efficiency Average Installed

Price Average Annual Energy Use

(KWh) Average Annual Operating Cost AverageLifeCycle Cost Average Life-Cycle Cost Savings Net Cost Net Benefit Average Median

CSIR Baseline 63.4% $544 1736 $129.94 $1,150

CSCR Baseline 71.0% $542 1470 $110.06 $1,053

1 74.3% $552 1408 $105.37 $1,041 $13 33.6% 66.4% 12.7 4.1

2 78.3% $578 1291 $96.63 $1,025 $29 41.5% 58.5% 15.8 5.1

3 80.3% $589 1244 $93.08 $1,019 $34 43.0% 57.0% 16.3 5.2

4 81.6% $606 1253 $93.81 $1,038 $15 52.9% 47.1% 23.0 7.5

5 82.7% $619 1240 $92.79 $1,046 $7 57.4% 42.6% 26.0 8.5

6 83.7% $643 1232 $92.23 $1,066 -$13 66.3% 33.7% 32.7 10.7

7 85.4% $662 1187 $88.86 $1,070 -$17 66.7% 33.3% 32.8 10.6

8 87.3% $996 1163 $87.07 $1,396 -$343 98.6% 1.5% 115.1 37.2

### 11-8 

## Table 11.3.9 Capacitor-Start Capacitor-Run Sma ll Electric Motors: LCC and PBP Results for Small Companies
Life-Cycle Cost Life -Cycle Cost Savings

Consumers with Payback Period (years) Energy Efficiency Level Efficiency Average Installed

Price Average Annual Energy Use

(KWh) Average Annual Operating Cost AverageLifeCycle Cost Average Life-Cycle Cost Savings Net Cost Net Benefit Average Median

CSIR Baseline 63.4% $543 1732 $131.00 $1,083

CSCR Baseline 71.0% $541 1467 $110.95 $997

1 74.3% $552 1404 $106.22 $987 $10 37.7% 62.3% 12.8 4.0

2 78.3% $580 1291 $97.68 $979 $18 48.0% 52.0% 17.3 5.3

3 80.3% $590 1246 $94.25 $976 $22 49.0% 51.0% 17.6 5.4

4 81.6% $606 1252 $94.70 $991 $6 58.0% 42.0% 23.3 7.4

5 82.7% $619 1239 $93.74 $1,001 -$3 63.1% 36.9% 26.5 8.4

6 83.7% $667 1232 $93.17 $1,046 -$49 76.2% 23.8% 41.9 12.3

7 85.4% $686 1188 $89.87 $1,051 -$54 76.3% 23.7% 40.6 12.0

8 87.3% $1,494 1156 $87.45 $1,850

- $852 99.1% 0.9% 231.4 50.0

### 11-9 

## REFERENCES

1 

## Ibbotsons Associates. Stocks, Bonds, B ills, and Inflation 2007 Yearbook, 2007. Chicago, IL.

2 

## Damodaran Online. 

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

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