### CHAPTER 11 . LIFE

- CYCLE COST SUBGROUP ANALYSIS

TABLE OF CONTENTS

11.1 INTRODUCTION

................................ ................................ .............................................. 11 -1

11.2 SUB

- GROUPS DEFINITION

................................ .......................................................... 11 -1

11.2.1 Commercial Customer Sub

- Group

................................ ....................................... 11 -1

11.2.2 Small Business Commercial Discount Rate

......................................................... 11 -1

11.2.3 Life

- Cycle Cost and Payback Period Results for Small Business Sub

Group

................................ ................................ ...................................................... 11 -2

LIST OF TABLES

Table 11.2.1 Discount Rate Difference between Small Company and Sector Average

................................ ................................ ............................................ 11 -2

Table 11.2.2 P TAC 9,000 Btu/h Units: LCC Results Comparison between Small

Business and Sub

- Group and All Buildings

.................................................. 11 -3

Table 11.2.3 PTAC 15,000 Btu/h Units: LCC Results Comparison Between Small

Business and Sub

- Group and All Buildings

.................................................. 11 -3

Table 11.2.4 PTHP 9,000 Btu/h Units: LCC Results Comparison Between Small

Business and Sub

- Group and All Buildings

.................................................. 11 -4

Table 11.2.5 PTHP 15,0 00 Btu/h Units: LCC Results Comparison Between Small

Business and Sub

- Group and All Buildings

.................................................. 11 -4

Table 11.2.6 PTAC 9,000 Btu/h Units: PBP Results Comparison Between Small

Business Sub

- Group and All Buildings

......................................................... 11 -5
Table 11.2.7 PTAC 15,000 Btu/h Units: PBP Re sults Comparison Between Small

Business Sub

- Group and All Buildings

......................................................... 11 -5
Table 11.2.8 PTHP 9,000 Btu/h Units: PBP Results Comparison Between Small

Business Sub

- Group and All Buildings

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

Table 11.2.9 PTHP 15,000 Btu/h Units: PBP Results Comparison B etween Small

Business Sub

- Group and All Buildings

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

11-i

### CHAPTER 11. LIFE

- CYCLE COST SUBGROUP ANALYSIS

11.1 INTRODUCTION

The life

- cycle cost (LCC) sub

- group analysis evaluates impacts on any identifiable groups of commercial customer s of pac kaged terminal air conditioners (PTAC s ) and packaged terminal heat pumps (PTHP s) who may be disproportionately affected by a national energy

efficiency standard. The U.S. Department of Energy ( DOE ) accomplished this, in part, by analyzing the LCC and payback period (PBPs) for those commerci al customer s that fall into specific sub

- groups.

DOE determined the impact on commercia l customer sub

- groups us ing the LCC spreadsheet model. The standard LCC and PBP analysis (described in Chapter 8) includes various types of commercial buildings that use PTAC equipment. The LCC spreadsheet model

allows for the identification of certain sub

- groups of commercial customer s that can then be analyzed by sampling only that sub

- group. ( Chapter 8 explains in detail the inputs to the spreadsheet model used in determining the LCC and PBP.)

This chapter describes the subgroup identification in furthe r detail and gives the re sults of the LCC and PBP analysi s for the considered subgroup s.

11.2 SUB

- GROUPS DEFINITION

11.2.1 Commercial Customer Sub -G roup

DOE identified small businesses as a sub

- group that possibly could be disproportionately affected by PTAC efficiency standards. DOE was concerned that increases in the purchase price of equipment could have negative impacts on small businesses ( i.e. , those with low annual revenues).

The U.S. Small Business Administration ( SBA ) established size standards to define small

businesses for types of economic activity, or industry, under the North American Industry Classification System ( NAICS) 1



### . The SBA defines a small business by either its annual receipts ( i.e. , revenues) or its number of employees. In the case of traveler accommodations, firms with annual revenues of $7 million or less are categorized as small businesses. Generally, chain hotels

do not meet t his criterion, but a substantial portion of independent hotels do. Based on data reported by Ducker Worldwide , DOE established that independent hotels are the primary small business subgroup, represen ting approximately 10% of the total building sample. 2



### 11.2.2 Small Business Commercial Discount Rate

The capital asset pricing model (CAPM) underestimates the cost of capital for small companies. In CAPM, the risk premium β is used to account for the higher returns a ssociated with greater risk. However, for small companies, particularly very small companies, historic

11-1

### returns have been significantly higher than the CAPM equation predicts. T his additional return

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



# ( ) S ERP Rk

fe



### +×+= β

W here:

k

e 

### = c ost of equity,

R

f 

### = e xpected return on risk

- free assets, β = r isk coefficient of the firm,

ERP = e quity risk premium , and

S 

### = s ize p remium.

DOE obtained size premium data from Ibbotson Associates’ Stocks, Bonds, Bills, and Inflation 200 9 Yearbook

. 3 

### For the period of 1926

- 2008 , the average size premium for the smallest companies in all industries is 5.81%, imply ing that on average, historic performance of small companies has been 5.81 % higher than the CAPM estimate of the small company cost of equity

. a



### 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 e quity. 4 

### Table 11 .2 .1 presents DOE’s estimates of the discount rates for entire sectors, small companies specifically, and the small company discount rate premium.

To estimate the impact of standards specifically on small businesses, the small company

discount rates for each sector were used in the LCC and PBP analysis instead of the sector average discount rates.

Table 11.2 .1 Discount Rate Difference between Small Company and Sector Average

Hotels Discount Rate

Average St andard

Deviation Small Company

Discount Rate Premium

Entire Sector 6.31% 2.03% 1.52 % Small Companies 7.83% 3.12%

11.2.3 Life- Cycle Cost and Payback Period Results for Small Business Sub -G roup

Table 11.2 .2 to Table 11.2 .5 summarize the LCC results for the small business sub

- group for each of the PTAC and P THP equipment classes, and compare them to the results for the total sample of buildings used in the overall LCC analysis. Table 11.2 .6 to Table 11.2 .9 summarize

a In this calculation , small companies are defined as companies with market capitalization of less t han or equal to $218.53 million, the Ibbotson Associates’ definition of Decile 10 companies.

11-2

### the PBP results. Results are provided by trial standard level (TSL). Note t hat this is likely an overestimate of the impact on small businesses; not all independent hotels qualify as small

businesses.

As is evident from the LCC and PBP results, the effect of higher PTAC and PTHP

standards on small businesses is similar to the e ffect on the full sample of commercial customer s. Thus, small businesses are not substantially disadvantaged by increase d PTAC and PTHP equipment standards, as compared to the general population of commercial customer s.

Table 11.2 .2 PTAC 9,000 Btu/h Units : LCC Results Comparison b etween Small Business

and Sub

- Group and All Buildings

TSL EER Small Businesses All Buildings

Mean

LCC Mean Increase

in LCC from

Baseline Percent of

Units with LCC Savings Mean

LCC Mean Increase

in LCC from

Baseline Percent of

Units with LCC Savings

Baseline 11.1 $2,493

- - $2,586

- -

ASHRAE 11.3 $2,494 $1 22% $2,587 $1 30%

1 11.5 $2,501 $8 8% $2,593 $7 11%

2 12 .0 $2,506 $13 10% $2,597 $11 14%

3 12.4 $2,512 $19 11% $2,602 $16 16%

4 12.9 $2,520 $27 10% $2,609 $23 13%

5 13.1 $2,525 $32 9% $2,614 $27 12%



### Table 11.2 .3 PTAC 15,000 Btu/h Units : LCC Results Comparison Between Small Business

and Sub

- Group and All Buildings

EL EER Small Businesses All Buildings

Mean

LCC Mean Increase

in LCC from

Baseline Percent of

Units with LCC Savings Mean

LCC Mean Increase

in LCC from

Baseline Percent of

Units with LCC Savings

Baseline 9.3 $3,070

- - $3,192

- -

ASHRAE 9.5 $3,070 $0 38% $3,191 $0 49%

1 9.7 $3,078 $8 5% $3,198 $6 7%

2 10 .0 $3,088 $17 4% $3,207 $15 6%

3 10.4 $3,105 $35 2% $3,223 $32 3%

4 10.8 $3,130 $60 1% $3,247 $56 1%

5 11.0 $3,146 $76 1% $3,262 $71 1%

11-3

### Table 11.2 .4 PTHP 9,000 Btu/h Units : LCC Results Comparison Between Small Business

and Sub

- Group and All Buildings

EL EER Small Businesses All Buildings

Mean

LCC Mean

Decrease in

LCC from

Baseline * Percent of

Units with

LCC Savings Mean

LCC Mean Increase/(Decrease ) in

LCC from Baseline * Percent of

Units with

LCC Savings

Baseline /

ASHRAE 11.3 $3,144.1

- - $3,284

- -

1 11.5 $3,138.4 ($6) 43% $3,277 ($7) 45%

2 12.0 $3,137.8 ($6) 37% $3,275 ($2) 42%

3 12.4 $3,138.8 ($5) 41% $3,274 ($1) 50%

4 12.9 $3,141.3 ($3) 39% $3,275 $1 48%

5 13.1 $3,143.2 ($1) 36% $3,276 $1 46%
* Parentheses indicated negative values



### Table 11.2 .5 PTHP 15,000 Btu/h Units : LCC Results Comparison Between Small Business

and Sub

- Group and All Buildings

EL EER Small Businesses All Buildings

Mean

LCC Mean Increase/(Decrease )

in LCC from

Baseline * Percent
of Units

with

LCC Savings Mean

LCC Mean Increase/(Decrease )

in LCC from

Baseline * Percent
of Units

with

LCC Savings

Baseline /

ASHRAE 9.5 $3,853.5

- - $4,033

- -

1 9.7 $3,853.5 ($0) 24% $4,032 ($1) 30%

2 10 .0 $3,852.6 ($1) 25% $4,030 ($4) 31%

3 10.4 $3,859.5 $6 24% $4,034 $1 31%

4 10.8 $3,873.9 $20 16% $4,047 $14 22%

5 11.0 $3,884.0 $31 13% $4,056 $23 18%
* Parentheses indicated negative values

11-4

### Table 11.2 .6 PTAC 9,000 Btu/h Units : PBP Results Comparison Between Small Business

Sub

- Group and All Buildings

EL EER Small Businesses All Buildings

Mean PBP (years) Median PBP (years) Mean PBP (years) Median PBP (years)

ASHRAE 11.3 8.8 8.8 8.8 8.8

1 11.5 9.3 9.4 9.3 9.4

2 12 .0 9.9 9.9 9.9 9.9

3 12.4 10.6 10.6 10.6 10.6

4 12.9 11.1 11.2 11.1 11.2

5 13.1 11.4 11.5 11.4 11.5



### Table 11.2 .7 PTAC 15,000 Btu/h U nits: PBP Results Comparison Between Small Business

Sub

- Group and All Buildings

EL EER Small Businesses All Buildings

Mean PBP (years) Median PBP (years) Mean PBP (years) Median PBP (years)

ASHRAE 9.5 7.3 7.4 7.3 7.4

1 9.7 9.3 9.4 9.3 9.4

2 10 .0 12.0 12.3 12.0 12.3

3 10.4 15.6 15.7 15.6 15.7

4 10.8 18.4 18.7 18.4 18.7

5 11.0 20.1 20.3 20.1 20.3

11-5

### Table 11.2 .8 PTHP 9,000 Btu/h U nits: PBP Results Comparison Between Small Business

Sub

- Group and All Buildings

TSL EER Small Businesses All Buildings

Mean PBP (years) Median PBP (years) Mean PBP (years) Median PBP (years)

1 11.3 4.3 4.4 4.3 4.4

2 11.5 5.9 5.8 5.9 5.8

3 12 .0 6.8 6.9 6.8 6.9

4 12.4 7.4 7.5 7.4 7.5

5 12.9 7.5 7.7 7.5 7.7



### Table 11.2 .9 PTHP 15,000 Btu/h Units : PBP Results Comparison Between Small Business

Sub

- Group and All Buildings

TSL EER Small Businesses All Buildings

Mean PBP (years) Median PBP (years) Mean PBP (years) Median PBP (years)

1 9.7 7.1 7.2 7.1 7.2

2 10 .0 6.9 7.0 6.9 7.0

3 10.4 8.4 8.5 8.4 8.5

4 10.8 9.8 10.0 9.8 10.0

5 11 .0 10.4 10.6 10.4 10.6

11-6

### REFERENCES

1. Title 13, Code of Federal Regulations, Chapter I

- Small Business Administration, Part

121

- Small Business Administration, Subpart A

- Size Eligibility Provisions and Standards

. 2005.

2. Ducker Worldwide, 2000 U.S. Market for Residential and Specialty Air Conditioning: PTAC (Packaged Terminal Air Conditioning), March 2001. Ducker Industrial Standards. Bloomfield Hills, Michigan 48301.

< http://www1.eere.energy.gov/buildings/appliance_standards/commercial/pdfs/ptac_pthp _tsd/chapter_10.pdf >

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

4. Damodaran Online, T he Data Page: Cost of Capital by Industry Sector

. 2012< http://pages.stern.nyu.edu/~adamodar >

11-7