11-i

CHAPTER 11. LIFE-CYCLE COST 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 Small 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 Induction-Run Small Electric Motors: LCC and PBP 

Results for Space-Constrained Customers......................................................... 11-5 

Table 11.3.5 Capacitor-Start Induction-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 Induction-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............................................................................. 

EERE-2007-BT-STD-0007 COMMENT 33
11-1 

CHAPTER 11. LIFE-CYCLE COST SUBGROUP ANALYSIS 

11.1 INTRODUCTION 

 Chapter 8 describes the life-cycle cost (LCC) and payback period (PBP) analysis that 

examines impacts of energy conservation standards on purchasers of the affected products. In 

analyzing the potential impact of new or amended standards on residential, industrial, and 

commercial customers, DOE further evaluates the 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 analyzing 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 restricting 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 specific 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 subgroups. This chapter describes the subgroup analysis in further 

detail and gives the results of the LCC and PBP analyses for the considered subgroups. 

11.2 SMALL ELECTRIC MOTOR CUSTOMER SUBGROUPS 

 DOE considered three subgroups for the LCC and PBP analyses for small electric 

motors: (1) customers facing space constraints in their motor installation, (2) customers without 

space constraints in their motor installation, and (3) small businesses. 

 For customers with space constraints, DOE analyzed the potential impacts of standards 

by conducting the analysis with motor designs constrained to a stack length increase of 20% or 

less. For customers without space constraints, DOE analyzed the potential impacts of standards 

by conducting the analysis with motor designs constrained to a stack length 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 Customers with and without Space Constraints 

One of the more cost-effective ways to increase 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 efficient, designs. The Department’s 

engineering analysis produced motor designs that meet space constraints by restricting stack 

length increases to 20% or less. The Department also analyzed designs in which the stack length 

was free to increase up to 100% (effectively an unconstrained stack length increase). 

EERE-2007-BT-STD-0007 COMMENT 33
DOE assumed that 20% of customers face space constraints in order to develop national 

average LCC results in chapter 8. For its space-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 considered 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 space-constrained designs cost more than less 

constrained designs to achieve the same efficiency. 

11.2.2 Inputs to the Subgroup Analysis for Small Businesses 

 The Small Business Administration (SBA) defines 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 distribution of motor applications or sectors of the economy to this 

subgroup. 

To calculate discount rates for small companies that purchase small electric motors, DOE 

used the same methodology as for the general population of small electric motor customers as 

presented in chapter 8.a

 Although the methodology is appropriate, the capital asset pricing model 

(CAPM)b

 described in chapter 8 for the 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 significantly higher than the CAPM equation predicts. This additional 

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

= Rk fe + (β × ) + SERP

ke = Cost of equity, 

Rf = Expected return on risk-free assets, 

β = Risk coefficient of the firm, 

ERP = Equity risk premium, and 

S = Size Premium. 

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 industries is 6.27 percent, implying that on average, historic 

 

a

 DOE assumed that small businesses as a whole are a reasonable 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. 

EERE-2007-BT-STD-0007 COMMENT 33
11-3 

performance of small companies has been 6.27 percent 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 Damodarand, 2

 (see Table 11.2.1). 

Table 11.2.1 Discount Rate Difference Between Small 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 discount rate for both industrial and commercial 

customers to be 5.9 percent. Applying the additional small capitalization (small cap) discount 

rate premium of 4.2 percent presented above to these 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 ELECTRIC MOTOR SUBGROUPS 

Tables 11.3.1 through 11.3.3 summarize the polyphase small electric motor results for 

customers with and without space-constrained applications and those that are small businesses. 

Tables 11.3.4 through 11.3.6 summarize 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 efficiency 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 percentage of customers that are burdened with net costs or realize net 

savings. The mean and median payback periods are also provided. As in chapter 8, these LCC 

results are for the three representative 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 companies 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 this analysis includes 6559 companies, 2605 of which are 

small companies. 

EERE-2007-BT-STD-0007 COMMENT 33
11-4 

In general, the benefits of moving to a higher efficiency are less in the case of the small 

business subgroups than in the overall sample. Space-constrained users achieve fewer benefits at 

high efficiency levels, where space constraints result in significantly different motor designs, 

technology, and materials than unconstrained motors. Non-space constrained customers receive 

greater benefits (or lower burdens) 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 

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

EERE-2007-BT-STD-0007 COMMENT 33
11-6 

Table 11.3.5 Capacitor-Start Induction-Run Small 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 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 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 

EERE-2007-BT-STD-0007 COMMENT 33
11-7 

Table 11.3.7 Capacitor-Start Capacitor-Run Small Electric Motors: LCC and PBP 

Results for Space-Constrained Customers 

Life-Cycle Cost Life-Cycle Cost Savings 

Consumers 

with 

Payback Period 

Energy (years) 

Efficiency Level Efficiency Average 

Installed 

Price 

Average 

Annual 

Energy Use 

(KWh) 

Average 

Annual 

Operating 

Cost 

Average 

LifeCycle 

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 Small Electric Motors: LCC and PBP 

Results for Non-Space-Constrained Customers 

Life-Cycle Cost Life-Cycle Cost Savings 

Consumers 

with 

Payback Period 

Energy (years) 

Efficiency Level Efficiency Average 

Installed 

Price 

Average 

Annual 

Energy Use 

(KWh) 

Average 

Annual 

Operating 

Cost 

Average 

LifeCycle 

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 

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

Table 11.3.9 Capacitor-Start Capacitor-Run Small Electric Motors: LCC and PBP 

Results for Small Companies 

Life-Cycle Cost Life-Cycle Cost Savings 

Consumers 

with 

Payback Period 

Energy (years) 

Efficiency Level Efficiency Average 

Installed 

Price 

Average 

Annual 

Energy Use 

(KWh) 

Average 

Annual 

Operating 

Cost 

Average 

LifeCycle 

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 

 

EERE-2007-BT-STD-0007 COMMENT 33
11-9 

 

REFERENCES 

1

 Ibbotsons Associates. Stocks, Bonds, Bills, 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/> 

EERE-2007-BT-STD-0007 COMMENT 33