CHAPTER 9. SHIPMENTS ANALYSIS

TABLE OF CONTENTS

9.1 INTRODUCTION ........................................................................................................... 9-1

9.2 METHODOLOGY .......................................................................................................... 9-1

9.2.2 Method Overview ................................................................................................ 9-2

9.2.3 Stock Equations ................................................................................................... 9-4

9.2.4 Shipments for New Installations .......................................................................... 9-6

9.3 CUSTOMER CHOICE MODEL ..................................................................................... 9-7

9.3.1 Efficiency Bins..................................................................................................... 9-7

9.3.2 Shipments Partition .............................................................................................. 9-8

9.3.3 Calculation of Market Share Probabilities ........................................................... 9-9

9.4 REPAIR/REPLACE DECISION MODEL...................................................................... 9-9

9.5 DATA INPUTS ............................................................................................................. 9-10

9.5.1 Historical Shipments .......................................................................................... 9-10

9.5.1.2 Historical Shipped Tonnage ..................................................................... 9-12

9.5.2 Commercial Floor Space and Market Saturations ............................................. 9-13

9.5.2.1 Market Saturations ................................................................................... 9-13

9.5.2.2 Commercial Floor Space Projections ....................................................... 9-16

9.5.3 Historical Data (1999-2001) for Development of Parameters ........................... 9-17

9.5.3.1 Efficiency Market Share ........................................................................... 9-17

9.5.3.2 Equipment Price ....................................................................................... 9-18

9.5.3.3 Installation Costs ...................................................................................... 9-21

9.5.3.4 Electricity Costs ....................................................................................... 9-23

9.5.3.5 Maintenance Costs ................................................................................... 9-24

9.5.3.6 Repair Costs ............................................................................................. 9-25

9.5.4 Data for Efficiency Level Distribution Projections ........................................... 9-28

9.5.4.2 Equipment Price ....................................................................................... 9-28

9.5.4.3 Installation Costs ...................................................................................... 9-31

9.5.4.4 Electricity Costs ....................................................................................... 9-31

9.5.4.5 Maintenance Costs ................................................................................... 9-34

9.5.4.6 Repair Costs ............................................................................................. 9-34

9.5.5 Equipment Lifetime ........................................................................................... 9-35

9.6 MODEL CALIBRATION ............................................................................................. 9-36

9.6.1 Estimating Customer Choice Model Parameters ............................................... 9-36

9.6.2 Estimating Repair/Replace Model Parameters .................................................. 9-38

9.7 RESULTS ...................................................................................................................... 9-39

 

9-i 
LIST OF TABLES

Table 9.2.1 Equipment capacities for CUAC and CUHP equipment classes ......................... 9-1

Table 9.5.1 CUAC Market Saturations ................................................................................. 9-14

Table 9.5.2 CUHP Market Saturations ................................................................................. 9-14

Table 9.5.3 Efficiency Market Share for CUACs (1999-2001) ............................................ 9-18

Table 9.5.4 Average Equipment Price Per Unit for CUACs (2001$) (2001) ....................... 9-20

Table 9.5.5 Average Equipment Price Per Unit for CUACs (2013$) (1999-2001) .............. 9-20

Table 9.5.6 Unit, Ton, and Square Footage Relationships ................................................... 9-21

Table 9.5.7 Average Equipment Price (Per SF) for CUACs (2013$) (1999-2001) .............. 9-21

Table 9.5.8 Weight to EER Relationship .............................................................................. 9-22

Table 9.5.9 Average Installation Cost Per Unit for CUACs (2013$) (1999-2001) .............. 9-22

Table 9.5.10 Average Installation Cost Per SF for CUACs (2013$) (1999-2001) ................. 9-22

Table 9.5.11 UEC Relationship to EER .................................................................................. 9-23

Table 9.5.12 Average UEC Per Unit for CUACs (kWh/year) (1999-2001) ........................... 9-23

Table 9.5.13 Average UEC Per SF for CUACs (kWh/year) (1999-2001) ............................. 9-24

Table 9.5.14 Compressor Costs by Ton (2013$) .................................................................... 9-26

Table 9.5.15 RS Means Material Cost Adjustments (2013$) ................................................. 9-26

Table 9.5.16 Repair Costs for CUAC Units Based on RS Means (2013$)............................. 9-26

Table 9.5.17 Average Repair Cost Per Unit for CUACs (2013$) (1999-2001)...................... 9-27

Table 9.5.18 Average Repair Cost Per SF for CUACs (2013$) (1999-2001) ........................ 9-27

Table 9.5.19 CUHP Efficiency Levels.................................................................................... 9-28

Table 9.5.20 Average Customer Price for CUACs (2013$) ................................................... 9-29

Table 9.5.21 CUHP Baseline Manufacturing Cost (2013$) ................................................... 9-29

Table 9.5.22 Average Customer Price (Per Unit) for CUHPs (2013$) ................................... 9-30

Table 9.5.23 Average Customer Price (per SF) for CUACs and CUHPs (2013$) ................. 9-30

Table 9.5.24 Average Installation Cost per Unit for CUACs and CUHPs (2013$) ............... 9-31

Table 9.5.25 Average Installation Cost per SF for CUACs and CUHPs (2012$) .................. 9-31

Table 9.5.26 CUAC UECs ...................................................................................................... 9-32

Table 9.5.27 CUHP Cooling UECs ........................................................................................ 9-32

Table 9.5.28 CUHP Heating UECs ......................................................................................... 9-33

Table 9.5.29 Total UECs by SF for CUAC and CUHPs ........................................................ 9-33

Table 9.5.30 Average Maintenance Cost per SF for CUACs and CUHPs (2013$) ............... 9-34

Table 9.5.31 Average Repair Cost Per Unit for CUACs and CUHPs (2013$)....................... 9-35

Table 9.5.32 Average Repair Cost Per SF for CUACs and CUHPs (2013$) ......................... 9-35

Table 9.6.1 Consumer choice model calibration parameters ................................................ 9-37

Table 9.6.2 Repair/Replace decision model constraints and calibration parameters ............ 9-39

LIST OF FIGURES

Figure 9.5.1 Historical Shipments Data (Estimated and Actual) ........................................... 9-12

Figure 9.5.2 Historical stock saturations and model fit (orange triangles) for small and 

large CUACs. ..................................................................................................... 9-15

Figure 9.5.3 Small CUAC Equipment Price to EER Relationship ........................................ 9-19

Figure 9.5.4 Large CUAC Equipment Price to EER Relationship ........................................ 9-19

9-ii
Figure 9.5.5 AEO Historic Price Index .................................................................................. 9-24

Figure 9.5.6 Compressor Costs by Ton (Drillspot, Grainger) ................................................ 9-25

Figure 9.5.7 Repair Cost by CUAC Capacity ........................................................................ 9-34

Figure 9.7.1 Base case shipment for all CUAC and CUHP equipment classes. ................... 9-40

Figure 9.7.2 Model shipments for small CUACs for the base case and standards cases. ..... 9-41

Figure 9.7.3 Model shipments for large CUACs for the base case and standards cases. ...... 9-42

Figure 9.7.4 Model shipments for very large CUACs for the base case and standards 

cases. .................................................................................................................. 9-43

Figure 9.7.5 Total model shipments for all CUAC equipment classes for the base case 

and standards cases. ........................................................................................... 9-44

Figure 9.7.6 Shipments-weighted IEER shipments for small CUACs for the base case 

and standards cases. ........................................................................................... 9-45

Figure 9.7.7 Shipments-weighted IEER shipments for large CUACs for the base case 

and standards cases. ........................................................................................... 9-46

Figure 9.7.8 Shipments-weighted IEER shipments for very large CUACs for the base 

case and standards cases. ................................................................................... 9-47

Figure 9.7.9 Number of units repaired and replaced for small CUACs for the base case 

and standards cases. ........................................................................................... 9-48

Figure 9.7.10 Number of units repaired and replaced for large CUACs for the base case 

and standards cases. ........................................................................................... 9-49

Figure 9.7.11 Number of units repaired and replaced for very large CUACs for the base 

case and standards cases. ................................................................................... 9-50

9-iii
CHAPTER 9. SHIPMENTS ANALYSIS

9.1 INTRODUCTION

 The U.S. Department of Energy (DOE) analyzes shipments of affected equipment as part 

of every rulemaking regarding new or amended energy efficiency standards for appliances or 

commercial and industrial equipment. Estimates of equipment shipments are a necessary input 

for calculating national energy savings (NES) and net present value (NPV) of the investment, 

which are required to justify potential new or amended energy efficiency standards. Shipments 

also are a necessary input to the manufacturer impact analysis. This chapter describes DOE’s 

method and results of projecting annual shipments for small, large, and very large air-cooled 

CUAC and CUHPs. 

 To project shipments of small, large, and very large air-cooled CUAC and CUHP, DOE 

considered specific market segments, the results for which are then aggregated to estimate total 

shipments. DOE accounted for three market segments: (1) shipments to new construction, (2) 

replacement shipments going into existing buildings, and (3) existing buildings acquiring new 

equipment for the first time.

The shipments models are prepared as Microsoft Excel spreadsheets that are accessible 

on the Internet (www.eere.energy.gov/buildings/appliance_standards/). The rest of this chapter 

explains the shipments model in more detail. Section 9.2 describes the methodology that 

underlies development of the model; section 9.3 describes the customer choice model used to 

predict market share probabilities as a function of efficiency; section 9.4 describes the 

repair/replace decision model that is used to calculate the average number of repairs of broken 

equipment in a given year; section 9.5 describes the input data requirements and model 

development; section 9.6 briefy discusses the approach used to calibrate the shipments model 

and section 9.7 discusses the results in terms of base-case and standards-case shipments.

9.2 METHODOLOGY

 This section outlines the methodology used to develop the shipments model that provides 

projections of shipments for CUAC and CUHP equipment classes defined in Table 9.2.1. First, a 

brief summary of the basic framework is provided in the following section. 

Table 9.2.1 Equipment capacities for CUAC and CUHP equipment classes

Description Equipment capacity (KBtu/hr) Tonnage (Tonnes/unit)

Small 65-135 7.5

Large 135-240 15

Very Large 240-760 30

9-1
9.2.2 Method Overview

 The basic shipments model is used to calculate the number of units shipped, the stock of 

functioning (never repaired) equipment, and the the stock of extended-lifetime (repaired once) 

equipment. Shipments forecasts are calculated for three market segments namely (a) new 

buildings, (b) existing buildings acquiring equipment for the first time and (c) existing building 

replacing broken units. 

 For existing buildings replacing broken equipment, the shipments model uses a stock 

accounting framework. Given the equipment entering the stock in each year and a retirement 

function based on the lifetime distribution developed in the LCC analysis, the model predicts 

how many units reach the end of their lifetime in each year. DOE typically refers to new 

shipments intended to replace retired units as replacement shipments. Such shipments are usually 

the largest part of total shipments.

For CUAC and CUHP, end of lifetime is generally associated with compressor failure. 

The customer has the choice of repairing the existing unit by installing a new compressor, 

thereby extending its life considerably, or purchasing a new unit. A new unit is more expensive 

than compressor replacement, but it may be more energy-efficient than the existing unit, which 

means it would have lower operating costs. If standards increase the cost of new equipment, one 

would expect that the repair option would become more attractive. 

To model the repair vs. replacement decision, for the small and large CUAC and CUHP 

equipment classes DOE used a consumer choice model that estimates customer sensitivity to 

total installation cost. A sensitivity parameter was calculated using efficiency market share data 

for years 1999−2001, along with estimates of equipment prices and installation costs by 

efficiency level. DOE applied this sensitivity to the difference between the total installed cost of 

a new unit and the repair cost of the existing unit. For the very large CUAC and CUHP 

equipment classes, at the first failure DOE assumed that all customers repair the unit because the 

total installed cost of a new unit is so high. (If a very large unit encounters a second failure in the 

shipments model, DOE assumed that the customer replaces the unit with a new one.) 

The replacement cost at each efficiency level is the total installed cost derived in the LCC 

analysis. For repair cost, DOE developed its own estimates of the material costs for compressors. 

(DOE examined RS Means material costs for compressors and concluded that they were 

inaccurate for all size classes, as several of the estimates exceeded the costs for an entire new 

unit.) For labor and non-compressor material costs, DOE used data in RS Means Facilities 

Maintenance & Repair Cost Data, 2013. Within each equipment class, DOE used repair costs 

that increase in direct proportion with the price of the equipment and with IEER level. 

DOE recognizes that the repair or replace decision is not solely a function of the 

difference between the total installed cost of a new unit and the repair cost of the existing unit. 

The difference in operating costs may also play a role, as may general economic conditions and 

other factors. DOE did not have sufficient information to incorporate these factors explicitly into 

9-2
its model, so it developed an alternative approach that assumes that the factors influencing the 

repair or replace decision will be similar in the future as they were in the past. DOE estimated an 

historical average repair rate by minimizing the difference between actual historical shipments 

and model-predicted shipments in a “no-repairs” scenario. DOE developed a series for historical 

shipments using data provided by AHRI in 2001 for the small and large CUAC and CUHP 

equipment classes for the years 1980 to 2001, combined with Census data on manufacturer 

shipments as the basis for shipments in earlier and later years, and for very large CUAC and 

CUHP. 

The repair/replace model is a binary choice model with two parameters, “alpha” and 

“gamma.” "Alpha" represents customer sensitivity to the efficiency-weighted average cost 

difference between total installed cost of replacement and repair costs. DOE assumed that the 

"alpha" is equal to the parameter used to represent customer sensitivity to total installed cost in 

the customer choice model. Since repair costs are generally lower than total installed costs of 

equipment, "gamma" is a scenario parameter that limits the number of repairs and can be thought 

of as representing "unknown replacements." Since "alpha" is assumed to be known, DOE 

estimated "gamma" by minimizing the difference between the historical average repair rate and 

the repair probability predicted by the repair/replace model. This approach ensures that the 

estimated repair rate in each forecast year in the base case is close to the historical average rate. 

In the standards cases, which have higher installed cost, the repair rate is higher. 

If a unit is repaired, its life is extended by another lifetime, based on the retirement 

function. If a unit encounters its second failure, the model assumes that the customer replaces the 

unit with a new one. 

For existing buildings acquiring new equipment for the first time, DOE first estimated 

saturation values (percentages of total floor space served by different cooling capacities or types 

of equipment) for the stock. CBECS provides overall CUAC and CUHP saturation values. To 

derive percentages of floor space served by different cooling capacities or types of equipment, 

DOE used shipments data from the Census. DOE derived the approximate historical floor space 

saturations for each of the CUAC and CUHP equipment classes by multiplying the CUAC and 

CUHP saturation values from CBECS by the shipment shares from the Census. DOE used a 

logistic regression procedure to fit the CBECS historical stock saturations to get a smooth time 

series of saturation estimates for the analysis period.

Shipments for existing buildings acquiring new equipment for the first time in each future 

year are estimated by multiplying the difference in projected stock saturation values between the 

future year and the previous year with the estimated floor space without CUAC and CUHP 

equipment in the previous year. In other words, the shipments account for the incremental 

increase in stock saturation.

For new commercial buildings acquiring equipment, shipments are estimated by 

multiplying new construction floor space in each future year by saturation values (percentages of 

new floor space served by different cooling capacities or types of equipment). The shipments 

9-3
model relies on AEO 2013 for forecasts of new construction floor space. It assumes that the 

saturation value in new commercial buildings is the same as the stock-average saturation for each 

year.

The methods described above provide total shipments in each equipment class for each 

year. To estimate the market shares of the considered efficiency levels in future shipments, DOE 

developed a customer choice model. The model was calibrated by estimating values for two 

parameters, representing customer sensitivity to total installation cost and annual operating cost. 

To calibrate the model, DOE used data on market shares by EER for small and large CUAC 

equipment classes provided by AHRI for the previous rulemaking. These market shares are for 

1999−2001. DOE used the equipment prices by EER level from the 2004 ANOPR to assign 

equipment prices to each EER bin. The same installation costs and maintenance costs developed 

for the NOPR were the basis for the installation costs in 1999−2001. DOE derived unit energy 

consumption (UEC) values for each of the EER bins using the UEC to EER relationships 

presented in the 2004 ANOPR TSD, and then applied historic electricity prices to calculate 

annual energy costs. 

To estimate values for the parameters, DOE used a non-linear regression approach that 

minimized the sum of the squared difference between historical market shares and the model 

predicted values at each efficiency level. Starting in 2013, application of the parameters, along 

with data on the installed cost and operating cost at each efficiency level considering this 

rulemaking, determines the market shares of each efficiency level.

9.2.3 Stock Equations

 The stock equations for either equipment type are used to describe changes in the 

distribution of stock from year y to year y +1. The total stock U(y) in a given year can be 

separated into functioning stock UF(y, v), carried over from the previous year and stock whose 

life has been extended through repairs UX(y, v, yb). i.e. 

 U(y) = ∑ UF

y

v (y, v) + ∑ ∑ UX�y, v, yb� y

yb>v

y

v (1) 

 

where:

• v is the vintage of the equipment and corresponds to the year in which a unit was shipped. 

By definition, the functioning stock of vintage v < y corresponds to all surviving stock 

from the previous year. 

• The age a of stock of vintage v in year y is a = y − v. 

• y

b is the year in which the unit breaks. The age of a broken unit ab is then defined as 

ab

=y

b

−v. We assume that ab>0, i.e. stock cannot break down in the same year it was 

shipped. 

9-4
The surviving stock in year y corresponds to functioning stock carried over from the previous 

year and is given by the expression, 

 UF(y, v) = ηF(y − v)UF(y − 1, v)

 = ηF(a)UF(y − 1, v) (2)

where: 

• ηF(a) is the “survival function” for functioning stock and represents the fraction of stock 

of age a that doesn’t break. The “non-survival” function for functioning stock UF(y, v) is 

1 − ηF(a); this is the fraction of stock of age a that does break. 

• The probability that an equipment will survive up to an age a is given by a Weibull 

cumulative distribution function, 

 η(a; θ, λ) = 1 − e−�a

λ�

θ

 (3)

where θ and λ are shape and scale parameters respectively, that are estimated using the 

calibration procedure described in section 9.6.2. 

The functioning stock of vintage v = y are just the shipments S(y) in year y, 

UF(y, y) = S(y) (4)

where: 

• S(y) = SN(y) + SE(y) + SRep(y); SN(y) corresponds to shipments that go into new 

floor space, SE(y) pertains to shipments that go into existing floor space that did not have 

the equipment before and SRep(y) are shipments that go to replace broken stock. 

To update extended life stock UX(y, v, yb) we consider several components. The stock of vintage 

v (<y) that breaks in year y is given by �1 − ηF(a)�UF(y − 1, v). 

Broken stock can either get repaired or be replaced. Repairs are proportional to an average repair 

rate ρ′

(y) (defined in Section 9.4) and hence become the extended-lifetime stock of the current 

year 

 UX(y, v, yb) = ρ′

(y)�1 − ηF(a)�UF(y − 1, v) for v < yb = y (5)

and the replacements are given by (1 − ρ′

(y))�1 − ηF(a)�UF(y − 1, v). These replacements 

contribute to the determination of SRep(y). 

The surviving stock of equipment that have undergone life-extending repairs carried over from 

the previous year is given by 

 UX(y, v, yb) = ηX(y − yb) UX(y − 1, v, yb) for v < yb < y (6)

where: 

• ηX(ab) is the survival function for extended-life stock UX(y, v, yb) and its complement 

1 − ηX(ab) represents the non-survival function. 

9-5
The “non-surviving" extended stock (1 − ηX(y − yb)) UX(y − 1, v, yb) corresponds to 

extended-life stock that breaks down again and hence are due for replacement. These also 

contribute to the determination of SRep(y). Based on this accounting, shipments for 

replacements in year y is given by 

 SRep(y) = ∑ (1 − ρ′

(y))�1 − ηF(a)�UF(y − 1, v) + v<y

v 

 ∑ ∑ (1 − ηX(y − yb)) UX�y − 1, v, yb� yb<y

yb

v<y

v (7) 

9.2.4 Shipments for New Installations 

In order to calculate total shipments S(y) in year y, we need to determine shipments to 

new installations that we define as shipments to new floorspace (SN(y) ) plus shipments to 

existing floorspace that did not previously have the equipment (SE(y)). The model equations for 

these shipments are based on time series of floorspace and saturations, which are assumed to be 

known. 

In year y, the total floorspace cooled by equipment of capacity k is x

k

μ(y)FE(y). 

Here, 

• FE(y) is the existing floor space in year y, 

• μ is the CBECS market saturation in year y and represents the percentage of floorspace 

cooled by all capacities of the equipment, and 

• x

k is the fraction of the total floor space cooled by the equipment of capacity k and is 

defined as 

x

k

= 

sfk

∑

k

sfk

. (8)

where 

sfk= 

nk

c

k

r

k

 (9)

is the total number of square feet associated with each equipment class k. In the above 

equation, n

k is the average number of units shipped per year, ck is the capacity in tons and 

r

k

 is the required tons per square foot of capacity for equipment of capacity k. 

With regard to the above definitions, the number of units shipped to new floorspace is equal to 

SN(y)= 

x

k

r

k

c

k

μ(y)FN(y) (10) 

9-6
where FN(y) corresponds to new floor space added in year y. The number of units shipped to 

existing floor space that did not have the equipment before is determined by considering the 

growth in saturation. From year y−1 to year y, the increase in floorspace is 

FE(y)=FE(y−1)+FN(y)−FD(y) (11) 

where FD(y) is floor space demolished in year y. The stock in existing buildings is proportional 

to μ(y)FE(y); equivalently 

μ(y)FE(y) = μ(y)FE(y−1)+μ(y)FN(y)−μ(y)FD(y) 

= {μ(y−1)FE(y−1)+[μ(y)−μ(y−1)]FE(y−1)} 

Error! Bookmark not defined. + μ(y)FN(y)−μ(y)FD(y) 

(12) 

The last term represents units taken out of the stock with demolished buildings and can 

be ignored. The middle term represents shipments to new buildings which are already accounted 

for in equation (10). The first term has two parts, the first representing stock carried over from 

the previous year and the second an increment due to the increase in saturation. This increment is 

what we define as SE(y); hence 

SE(y)= 

x

k

r

k

c

k

[μ(y)−μ(y−1)]FE(y−1) (13) 

9.3 CUSTOMER CHOICE MODEL

 The Consumer Choice model developed by the Department comprises of a logit model 

that is used to generate market share probabilities corresponding to predefined efficiency bins. 

The probabilities are then used to partition the total shipments in a given year into these 

efficiency bins whose boundaries represent minimum allowed efficiencies for that particular 

equipment type and class. This section outlines the steps involved in the calculation of these 

probabilities. 

9.3.1 Efficiency Bins

For years y ≥ ystd, the shipments are partitioned into efficiency bins labelled j = 0...M

(currently M=4). The bin boundaries represent the efficiency levels used in the analysis; these are 

hypothetical minimum allowed efficiencies. The fraction of shipments that fall into each bin is 

determined by a consumer choice model, described below. However before we get into the 

details of the consumer choice model, a short summary on notation is provided below first. 

9-7
• ELj is the efficiency level j for j = 0...M. The base case EL0 corresponds to the current 

market minimum efficiency. 

• z is the efficiency of a given piece of equipment. 

• Bin j includes all efficiencies z in the range ELj−1 ≤ z ≤ ELj

. 

• z

j is the average equipment efficiency for bin j and L is the efficiency level under 

consideration. 

• p

L,j

(y) is the fraction of shipments that fall into efficiency bin j when the minimum 

efficiency is set at level L. 

• S

L,j

(y) is the total number of shipments that fall into efficiency bin j when the minimum 

efficiency is set at level L. 

9.3.2 Shipments Partition

By definition, 

p

L,j

(y) = 0 for j<L, and (14) 

∑

j

p

L,j

(y) = 1 (15) 

The probabilities are assumed to satisfy 

p

L,j1

pL,j2

=h(j1,j2) (16) 

when both probabilities are non-zero. This means that the ratio of shipments falling into bins j1 

and j2 remains the same under all standard levels. Hence, in any given year, under a change in L

the probabilities are simply renormalized. The probabilities also evolve over time due to changes 

in the parameters that go into the consumer choice model. 

We assume that the partition of shipments into efficiency bins is independent of where the 

shipments are going, i.e. the probability of purchase of higher efficiency equipment is the same 

for new installations and replacements. For a given efficiency level L, we then partition total 

shipments S(y) as 

SL,j

(y)=pL,j(y)S(y) (17) 

9-8
9.3.3 Calculation of Market Share Probabilities

As described earlier, the consumer choice model to estimate market share probabilities 

pL,j(y) is essentially a logit model and is defined in terms of a utility function W(y) as 

p

L,j

(y)= 

e

Wj(y)

∑

j≤L

 [e

Wj(y)

] (18) 

where 

Wj(y) = αTICj(y) + βOCj(y). (19) 

Here 

• Wj(y) is the utility function in year y corresponding to bin j 

• TICj(y) is the total installed cost in year y averaged over bin j 

• OCj(y) is the annual operating cost in year y averaged over bin j 

• α is a sensitivity parameter for installed cost (up front costs) 

• β is a sensitivity parameter for operating costs (continuing costs). 

The parameters α and β are determined by a fit to available market share data as described in 

Section 9.6. 

9.4 REPAIR/REPLACE DECISION MODEL

The repair/replace decision model is a binary logit model that accounts for decisions to 

extend the life of a broken unit through repairs rather than replacing it. The model provides an 

estimate of the probability that a broken unit will be repaired (ρ) by accounting for the total 

installed costs and repair costs of the equipment under consideration as well as its lifetime. 

Specifically for a binary choice, ρ is based on a repair utility function R(y) and takes the 

following form 

ρ(y) = 

eR(y)

1+eR(y) (20) 

The repair utility R(y) is given by 

R(y) = γ + κ Δ(y) (21) 

where: 

9-9
• Δ(y) is the efficiency weighted average difference between total installed cost in the 

current year y and the cost associated with repairing an older unit based on its lifetime. 

• κ is a sensitivity parameter to the cost differential 

• γ is a scaling parameter that represents “unobserved replacements” and can be thought to 

minimize repairs. 

Since consumers decisions regarding purchase of such equipment are primarily first cost drive, 

we assume κ = α and treat γ as a scenario variable that limits the total number of repairs by 

accounting for “unknown” replacements. The procedure used to obtain an estimate of γ is 

described in Section 9.6. 

The above expression for ρ does not take into account the age of the unit when it breaks, a

b

. In 

reality, we expect the repair probability to be higher for relatively newer broken units or lower 

values of a

b

 and lower for older units or higher values of ab. To model this effect, we multiply ρ

by the function 

 f(ab) = 1 − (ab− a1)

(a2− a1) , a1 ≤ ab ≤ a2 (22) 

with f(ab

)=1 for ab<a1 and f(ab)=0 for ab>a2. For both CUACs and CUHPs we set a1=3 years, 

while a2 depends on the lifetimes of either equipment type and is set equal to 18 years for 

CUACs and 15 years for CUHPs. The repair probability is then equal to the product 

 ρ′

(y, ab) = f(ab)ρ(y) (23) 

9.5 DATA INPUTS 

9.5.1 Historical Shipments

Historical shipments are critical to the development of the Shipments Model, since DOE 

used the historical data to calibrate the model. For the years 1980 through 2001 for small and 

large CUAC and CUHP, DOE used shipments data provided by the Air-Conditioning and 

Refrigeration Institute (ARI) in 2005.1

 For the remainder of years (1969-1979 and 2002-2010) 

for small and large CUAC and CUHP and all years for very large equipment, DOE relied upon 

the U.S. Census Bureau’s Current Industrial Reports on Refrigeration, Air Conditioning, and 

Warm Air Heating Equipment.

2

For the three CUAC equipment classes of interest to this analysis small, large, and very 

large, the Census Bureau provides shipments data in the following equipment categories (as 

defined by the Census Bureau): (1) single package air conditioners, with or without evaporator 

fans, including refrigeration chassis and remote-condenser types; (2) year-round air conditioners, 

9-10
single package and remote-condenser type (except heat pumps); and (3) split-system airconditioning condensing units. Within each of the above equipment categories, the shipments 

data are disaggregated into cooling capacity ranges. The capacity ranges and equipment 

categories are defined in a way that allowed DOE to aggregate the Census Bureau shipments 

data into the three equipment classes of interest, with three notable exceptions: (1) the Census 

Bureau specified a capacity range of ≥135,000 Btu/h to <250,000 Btu/h, rather than the desired 

range of ≥135,000 Btu/h to <240,000 Btu/h (large units); (2) the Census Bureau does not specify 

a high-end of capacity, so all of the highest capacity disaggregations may include units that 

surpass 760,000 Btu/h (the limit for very large units); and (3) the Census Bureau combined 

water-cooled and air-cooled equipment. 

 With respect to the first issue, DOE used the Census Bureau shipments data in the 

≥135,000 Btu/h to <250,000 Btu/h capacity range to represent shipments for the large (≥135,000 

Btu/h to <240,000 Btu/h) equipment class. With respect to the second issue, DOE assumed that 

all units in the highest capacity disaggregations (≥ 380,000 Btu/h for single package airconditioners, and ≥640,000 Btu/h for year-round and split system air conditioners) fall into the 

very large (≥240,000 Btu/h to <760,000 Btu/h) equipment class. With respect to the third issue, 

DOE used the ARI shipments data for 1980-2001 to extract the appropriate percentage of watercooled equipment from the aggregated water-cooled and air-cooled shipments for all other years 

(i.e., 98.5% of small units considered air-cooled and 98% of large units considered air-cooled; 

DOE also applied the latter to very large units). DOE also further scaled all Census data for the 

small and large equipment classes downward to account for the difference between ARI and 

Census data in the years 1980 through 2001 (resulting in scaling of 90.5% and 84.9%, 

respectively, for small and large equipment classes). 

For the three CUHP equipment classes of interest to this analysis (small, large, and very 

large), the Census Bureau provides shipments data in the following equipment categories (as 

defined by the Census Bureau): (1) air source heat pumps (excluding room air-conditioners), 

single package; and (2) air source heat pumps (excluding room air-conditioners), split system. 

However, for both of these equipment categories, the only capacity range relevant to this 

rulemaking is 65,000 Btu/h and over. In order to disaggregate this category into the three CUHP 

equipment classes, DOE calculated the average percent of CUHP attributed to each equipment 

class (capacity range) for all years available with ARI data. The result was 66% small, 12% 

large, and 21% very large. However, the entire very large class in the years with ARI data was 

estimated based on the difference between census shipments and ARI reported shipments for 

CUHP between 65,000 and 250,000 Btu/h. Based on a comparison of this percentage to the 

percentage of CUAC units in the very large equipment class, DOE determined that this estimate 

was unrealistic. As a result, for all years, DOE calculated shipments to very large CUHP based 

on shipments of large CUHP times the ratio of CUAC very large to CUAC large shipments. 

 In some intermediate years with no data (1971-1973, 1976-1979, 1981-1982), DOE used 

linear interpolation to estimate shipments. The most recent year for which the census reports 

shipments is 2010. Figure 9.5.1 shows the historical shipments data (estimated and actual) for all 

CUAC and CUHP equipment classes. 

9-11
Figure 9.5.1 Historical Shipments Data (Estimated and Actual)

9.5.1.2 Historical Shipped Tonnage 

Historical shipped tonnage represents the annual amount of cooling capacity (in tons) 

shipped and is an alternative way to express shipments data. DOE determined the actual shipped 

tonnage for any given year by multiplying each unit shipped by its associated cooling capacity or 

tonnage, and then summing all the tonnage values. 

DOE converted shipped tonnage to percent of shipped tonnage for use in the Shipments 

Model to establish the CUAC and CUHP market shares attributed to each equipment class. The 

market share calculation and its use in projecting shipments are explained in section 9.5.2.1. 

DOE calculated the percent of shipped tonnage for CUAC by dividing the shipped tonnage for 

each equipment class by the total shipped tonnage for all CUAC equipment. DOE calculated the 

percent of shipped tonnage for CUHP by dividing the shipped tonnage for each equipment class 

by the total shipped tonnage for all CUHP equipment. 

DOE used shipments data from the U.S. Census Bureau’s Current Industrial Reports on 

Refrigeration, Air Conditioning, and Warm Air Heating Equipment to derive shipped tonnages 

 -

 20,000

 40,000

 60,000

 80,000

 100,000

 120,000

 140,000

 160,000

 180,000

 200,000

Shipments (Units)

Year

Small CUAC Large CUAC Very Large CUAC

Small CUHP Large CUHP Very Large CUHP

9-12
for each of the six CUAC and CUHP equipment classes.The Census Bureau classifies the range 

of cooling capacities for the entire set of commercial unitary air conditioners from less than 

22,000 Btu/h to greater than 640,000 Btu/h. Across this span of cooling capacities, the Census 

Bureau disaggregated shipments into as many as 16 smaller capacity ranges. For each capacity 

range, DOE used the mid-point of the range as the representative capacity for the rangea.Then 

DOE determined the shipped tonnage for each capacity range by multiplying the representative 

capacity by the number of shipments in the range. Because the Census Bureau disaggregated 

shipments into several capacity ranges, DOE was able to establish the annual shipped tonnage 

for each of the six CUAC and CUHP equipment classes and the entire set of commercial unitary 

air conditioners and heat pumpsb.

The ARI shipments data were instrumental in separating water-cooled air-conditioning 

and heat pump equipment from air-cooled CUAC and HP equipment. Furthermore, the ARI

shipments data identified which air conditioners and heat pumps with cooling capacities less than 

65,000 Btu/h were commercial equipment and which were residential products. Although DOE 

derived CUAC data for the years back to 1969, it did not obtain the necessary shipments data to 

derive shipped tonnage for the following years: 1971–1973, 1976–1979, and 1981–1982. For 

CUHP equipment, available data only goes back to 1980, and also excludes 1995-1996. The

most recent year for which shipments data are reported is 2010. The percent of shipped tonnage 

for each CUAC and CUHP equipment class does not vary greatly from year to year. As a result, 

DOE used average fixed values for inputs to the Shipments Model, as shown in section 9.5.2.1. 

9.5.2 Commercial Floor Space and Market Saturations

9.5.2.1 Market Saturations

DOE defined market saturation, MKT_SAT(y), for each class of commercial unitary 

equipment as the ratio of existing cooled floor space, by class, to all existing floor space, EFS(y). 

It is one of the constraints DOE used to calibrate the Shipments Model. 

To calculate market saturation for a particular class of unitary equipment, DOE first 

calculated the market saturation for all CUAC equipment and a market saturation for all CUHP 

equipment. DOE used CBECS data from 1992, 1995, 1999, and 2003 to determine the 

commercial floor space cooled by CUAC, CUACFS(y), and space cooled by CUHP,

CUHPFS(y), as well as the total amount of existing floor space, EFS(y).

3

 

a For capacity ranges defined as less than a given capacity value (e.g., less than 22,000 Btu/h), DOE used 90 percent 

of the capacity as the representative capacity (e.g., 22,000 Btu/h @ 90% = 19,800 Btu/h). For capacity ranges 

defined as greater than a given capacity value (e.g., 640,000 Btu/h and over), DOE used 110 percent of the capacity 

as the representative capacity (e.g., 640,000 Btu/h @ 110% = 704,000 Btu/h).

b The entire set of commercial unitary air conditioner and heat pumps represents both air-cooled and water-cooled 

equipment and all cooling capacity ranges, from less than 22,000 Btu/h to greater than 640,000 Btu/h.

9-13

 
Then, to estimate the MKT_SAT for a particular class of commercial unitary equipment, 

DOE used the market share, or percent, of unitary equipment of a particular class. DOE used the 

above shipments data to estimate the market share, MKTSHARE(y), of each equipment class.

Because the percent of shipments in each class is relatively constant over time and the lifetime of 

each class is the same, the ratio of shipments to a class is indicative of the market share for that 

class. DOE estimated the MKTSHARE for a particular class to be a constant value equal to the

average of the yearly percent of shipments to that class (from available years 1969 through 

2010). From these data, DOE calculated the MKT_SAT(y) for each commercial unitary air 

conditioning class using the following formula. 

MKTSAT(y) = CUACFS(y)

EFS(y) ∗ MKTSHARE

DOE used a corresponding equation to find MKT_SAT(y) for each CUHP class using

CUHPFS(y) in place of CUACFS(y). 

Table 9.5.1 summarizes the CUAC market saturations for 1992, 1995, 1999, and 2003, 

which are the years for which CUACFS data are available in CBECS. Table 9.5.2 summarizes 

the CUHP market saturations for the same years. 

Table 9.5.1 CUAC Market Saturations

Year

CUAC 

Market 

Saturation 

(CBECS)

Small Commercial 

Packaged AC (AirCooled) - ≥65,000 Btu/h 

and < 135,000 Btu/h

Large Commercial 

Packaged AC (AirCooled) - ≥135,000 

Btu/h and < 240,000 

Btu/h

Very Large 

Commercial Packaged 

AC (Air-Cooled) - 

≥240,000 Btu/h and < 

760,000 Btu/h

Market 

Share MKT_SAT

Market 

Share MKT_SAT

Market 

Share MKT_SAT

1992 21% 24% 4.9% 16% 3.4% 16% 3.3%

1995 24% 24% 5.6% 16% 3.9% 16% 3.8%

1999 32% 24% 7.4% 16% 5.2% 16% 5.0%

2003 51% 24% 12.0% 16% 8.2% 16% 8.1%

Table 9.5.2 CUHP Market Saturations

Year

CUHP 

Market 

Saturation 

(CBECS)

Small Commercial 

Packaged HP (AirCooled) - ≥65,000 Btu/h 

and < 135,000 Btu/h

Large Commercial 

Packaged HP (AirCooled) - ≥135,000 

Btu/h and < 240,000 

Btu/h

Very Large 

Commercial Packaged 

HP (Air-Cooled) - 

≥240,000 Btu/h and < 

760,000 Btu/h

Market 

Share MKT_SAT

Market 

Share MKT_SAT

Market 

Share MKT_SAT

1992 5.1% 3.4% 0.15% 1.2% 0.05% 1.0% 0.04%

1995 6.0% 3.4% 0.18% 1.2% 0.06% 1.0% 0.05%

1999 5.6% 3.4% 0.16% 1.2% 0.06% 1.0% 0.05%

2003 7.2% 3.4% 0.24% 1.2% 0.08% 1.0% 0.07%

9-14
Since projections of shipments going into new and existing buildings require a nearcontinuous series of market saturations for each projection year, a time series of floor space 

saturations was developed for each equipment class by fitting the historical saturations described 

in the above tables using a logistic regression model based on the utility functions in the previous 

rulemaking. Figure 9.5.2 shows the fits to the historical saturations for the small and large CUAC 

equipment categories. A similar fit was derived for all categories of CUHP equipment as well. 

 

 (a)

 

 (b) 

Figure 9.5.2 Historical stock saturations and model fit (orange 

triangles) for small and large CUACs. 

9-15
9.5.2.2 Commercial Floor Space Projections

 The amount of commercial floor space is the main driver for CUAC and CUHP 

equipment shipments and is appropriately one of the basic inputs into the Shipments Model. The 

model divides commercial floor space into three components: floor space from new construction 

(FN(y)), existing floor space (FE(y)),, and demolished floor space (FD(y)),. 

For this analysis, commercial floor space refers to non-residential buildings that are used

primarily for purposes other than industrial or manufacturing. 

Floor Space – New Construction (FN(y)) 

 DOE used new construction floor space prior to 1999 from the previous rulemaking 

(ANOPR TSD).

4

 These values are based on U.S. Census Bureau data for available years and 

linear interpolations for the additional years. 

 For this analysis, DOE obtained new construction floor space for the years 1999-2010 

from the Census Bureau publication: Statistical Abstract of the United States: 2012, Table 966.5

DOE took the projected floor space after the year 2010 from the National Energy Modeling 

System (NEMS) projection published in the Annual Energy Outlook 2013(AEO2013).6 AEO2013 

lists the projections for years through 2040. Beyond 2040, DOE extrapolated NFS from the tenyear trend of NEMS-projected data (2030-2040). The NEMS value in 2003 shows approximately 

50 percent more floor space than the historical Census Bureau data in 2003. To match the Census 

Bureau data with the NEMS projections, DOE calculated the rate of change in NFS for each 

NEMS year and applied it to the Census Bureau data, starting in 2010 and stepping forward each 

year.

Floor Space – Existing Stock (FE(y)) 

 DOE used existing floor space in 1999 and prior from the previous rulemaking. In that 

analysis, DOE used CBECS data for available years along with linear interpolations for the 

missing years.

 For this rulemaking, DOE obtained the latest CBECS data, for 2003. DOE then 

developed floor space for the years 2000-2002 by interpolating between the 2003 and 1999 

CBECS values. DOE took the projected floor space after the year 2003 from the NEMS 

projection published in AEO2013. The projections are listed through 2040. Beyond 2040, DOE 

extrapolated EFS from the 10-year trend of NEMS projected data (2030-2040). There is a small 

difference between the NEMS data for 2003 and CBECS data in 2003. To match the CBECS 

data with the NEMS projections, DOE calculated the rate of change in EFS for each NEMS year. 

DOE then applied this rate to the CBECS data, starting in 2003 and stepping forward each year. 

Floor Space – Demolished (FD(y)) 

9-16
 DOE used the demolition rate through 1999 from the previous rulemaking. This value 

was approximated as 0.0108 for all years. 

For years after 1999, DOE established the demolished floor space from NEMS 

projections. In addition to predicting FN(y) and FN(y), NEMS also predicts surviving square 

feet (FS(y)) (i.e., square feet in the building stock that are not demolished). The following 

formula gives the FD(y) for any given NEMS year.

 FD(y) = FE(y) + FS(y-1) (25) 

After DOE determined the FD(y) for NEMS years (through 2040), it calculated the 

FD(y) rate per year, FD(y)/ FE(y). For the years 2003 through 2040, DOE used the calculated 

value for each year, which are all in the range of 0.011 to 0.012. For the years 2000-2002, and 

2041 through 2048, DOE used the average FD(y) rate for 2003 through 2040, or 0.011. 

9.5.3 Historical Data (1999-2001) for Development of Parameters

DOE developed the parameters of the customer choice model using data only for small 

and large CUAC equipment classes. The parameters developed for the small CUAC equipment 

class were also used for the small CUHP equipment class. The parameters developed for the 

large CUAC equipment class were also used for the very large CUAC, large CUHP, and very 

large CUHP equipment classes.

9.5.3.1 Efficiency Market Share

The only efficiency market share data available were provided by AHRI in the previous 

rulemakingfor the years 1999-2001. DOE used these market shares, shown in Table 9.5.3, to 

develop the customer choice model parameters. 

9-17
Table 9.5.3 Efficiency Market Share for CUACs (1999-2001) 

Equipment 

Class Year

EER Bin

9.9 & 

Under 10-10.9 11-11.9 12-12.9 13-13.9 14-14.9

15 & 

Over

Small 

Commercial 

Packaged 

AC (AirCooled) - 

≥65,000 

Btu/h and < 

135,000 

Btu/h

1999 58.5% 34.5% 6.6% 0.3% 0.0% 0.0% 0.0% 

2000 53.1% 36.7% 9.9% 0.4% 0.0% 0.0% 0.0% 

2001 37.3% 49.1% 13.0% 0.6% 0.0% 0.0% 0.0% 

Large 

Commercial 

Packaged 

AC (AirCooled) - 

≥135,000 

Btu/h and < 

240,000 

Btu/h

1999 77.4% 15.7% 6.3% 0.6% 0.0% 0.0% 0.0% 

2000 72.7% 19.2% 8.1% 0.1% 0.0% 0.0% 0.0% 

2001 59.8% 29.4% 10.7% 0.0% 0.0% 0.0% 0.0% 

9.5.3.2 Equipment Price 

 For each of the efficiency bins for which DOE had market share data, DOE had to 

develop associated costs, including equipment price. DOE used the equipment prices provided 

by efficiency level in the ANOPR TSD to develop relationships between equipment price and 

EER (Figure 9.5.3 and Figure 9.5.4). DOE then used those relationships to calculate equipment 

prices for the EERs assigned to each bin of available market share data (Table 9.5.4). 

9-18
Figure 9.5.3 Small CUAC Equipment Price to EER Relationship 

Figure 9.5.4 Large CUAC Equipment Price to EER Relationship 

y = 209.35x2 - 4191.3x + 25840

R2 = 0.9984

$4,800

$4,900

$5,000

$5,100

$5,200

$5,300

$5,400

$5,500

$5,600

$5,700

$5,800

10 10.5 11 11.5 12 12.5

Equipment Price

EER

y = 301.86x2 - 5851.7x + 37540

R2 = 0.995

$9,000

$9,200

$9,400

$9,600

$9,800

$10,000

$10,200

$10,400

$10,600

$10,800

$11,000

8 9 10 11 12 13

Equipment Price

EER

9-19
Table 9.5.4 Average Equipment Price Per Unit for CUACs (2001$) (2001) 

Equipment Class

EER

9.9 & 

Under 10-10.9 11-11.9 12-12.9 13-13.9 14-14.9

15 & 

Over

9.25 10.25 11.25 12.25 13.25 14.25 15.25

Small Commercial 

Packaged AC (AirCooled) - ≥65,000 

Btu/h and < 135,000 

Btu/h

$4,860* $4,874 $5,184 $5,912 $7,059 $8,625 $10,610 

Large Commercial 

Packaged AC (AirCooled) - ≥135,000 

Btu/h and < 240,000 

Btu/h

$9,240 $9,274 $9,913 $11,155 $13,000 $15,450 $18,503 

*Note this value was adjusted from the regression-predicted value of $4,983 because the regression erroneously 

created an upward trend below 10.0 EER.

 DOE then adjusted the equipment prices from 2001$ to 2013$ and to represent years 

1999 and 2000 in addition to 2001. (DOE assumed the ANOPR prices represented the year 

2001.) For 2001, DOE divided the price in 2001$ by the GDP deflator to arrive at the price in 

2013$.7

 For the years 1999 and 2000, DOE also adjusted the equipment price using the deflated 

PPI.8 (See chapter 8 for a discussion of the PPI used for this rulemaking.) Table 9.5.5 shows the 

resulting average equipment prices by year.

Table 9.5.5 Average Equipment Price Per Unit for CUACs (2013$) (1999-2001) 

Equipment 

Class Year

EER Bin

9.9 & 

Under 10-10.9 11-11.9 12-12.9 13-13.9 14-14.9

15 & 

Over

Small 

Commercial

Packaged AC 

(Air-Cooled) - 

≥65,000 Btu/h 

and < 135,000 

Btu/h

1999 $6,718 $6,738 $7,166 $8,173 $9,758 $11,923 $14,666 

2000 $6,432 $6,450 $6,860 $7,824 $9,342 $11,414 $14,040 

2001 $6,284 $6,302 $6,703 $7,644 $9,128 $11,152 $13,718 

Large 

Commercial 

Packaged AC 

(Air-Cooled) - 

≥135,000 

Btu/h and < 

240,000 Btu/h

1999 $12,772 $12,820 $13,703 $15,419 $17,971 $21,357 $25,577 

2000 $12,227 $12,273 $13,118 $14,762 $17,204 $20,446 $24,486 

2001 $11,947 $11,992 $12,817 $14,423 $16,809 $19,976 $23,924 

 In the shipments model, parameters such as equipment price are used based as a function 

of square footage rather than unit. DOE developed a tons of capacity per square foot value as 

9-20
part of its energy use analysis (see chapter 7). This allowed DOE to calculate a cooled square 

footage per unit value for each CUAC equipment class (Table 9.5.6). DOE then divided the 

equipment prices per unit by the cooled square foot per unit values to arrive at equipment prices 

per square foot (Table 9.5.7).

Table 9.5.6 Unit, Ton, and Square Footage Relationships

Small Commercial Packaged AC 

(Air-Cooled) - ≥65,000 Btu/h and < 

135,000 Btu/h

Large Commercial Packaged AC 

(Air-Cooled) - ≥135,000 Btu/h and < 

240,000 Btu/h

Tons/unit 7.5 15

Tons/SF 0.00260 0.00273

Cooled SF/Unit 2885 5495

Table 9.5.7 Average Equipment Price (Per SF) for CUACs (2013$) (1999-2001) 

Equipment 

Class Year

EER Bin

9.9 & 

Under 10-10.9 11-11.9 12-12.9 13-13.9 14-14.9

15 & 

Over

Small 

Commercial 

Packaged AC 

(Air-Cooled) - 

≥65,000 Btu/h 

and < 135,000 

Btu/h

1999 $2.33 $2.34 $2.48 $2.83 $3.38 $4.13 $5.08 

2000 $2.23 $2.24 $2.38 $2.71 $3.24 $3.96 $4.87 

2001 $2.18 $2.18 $2.32 $2.65 $3.16 $3.87 $4.76 

Large 

Commercial 

Packaged AC 

(Air-Cooled) - 

≥135,000 

Btu/h and < 

240,000 Btu/h

1999 $2.32 $2.33 $2.49 $2.81 $3.27 $3.89 $4.66 

2000 $2.23 $2.23 $2.39 $2.69 $3.13 $3.72 $4.46 

2001 $2.17 $2.18 $2.33 $2.62 $3.06 $3.64 $4.35 

9.5.3.3 Installation Costs 

 The same installation costs developed for the this rulemaking were the basis for the 

installation costs estimated for 1999−2001. The base values used, shown in Table 8.2.5 in 

chapter 8, were $2,476 for small CUAC and $3,346 for large CUAC. DOE assigned these values 

to the 11-11.9 EER bin, as approximately representative of the baseline equipment on the market 

today. For the other EER bins, DOE varied the installation cost in direct proportion to the weight 

of the equipment. DOE estimated the weight for equipment in each bin based on a relationship of 

weight to EER presented in the ANOPR TSD (Chapter 8, Figure 8.2.1; shown here in Table 

9.5.8). Table 9.5.9 shows the resulting average installation cost per unit for CUACs. DOE then 

divided the installation costs per unit by the cooled square foot per unit values shown previously 

9-21
to arrive at installation costs per square foot (Table 9.5.10). DOE used the same installation costs 

for all years 1999-2001. 

Table 9.5.8 Weight to EER Relationship 

Equipment Class Slope Intercept

Small Commercial Packaged AC (Air-Cooled) -

≥65,000 Btu/h and < 135,000 Btu/h 42.1 498.1 

Large Commercial Packaged AC (Air-Cooled) -

≥135,000 Btu/h and < 240,000 Btu/h 171.8 194.6 

Table 9.5.9 Average Installation Cost Per Unit for CUACs (2013$) (1999-2001) 

Equipment 

Class

EER

9.9 & 

Under 10-10.9 11-11.9 12-12.9 13-13.9 14-14.9

15 & 

Over

9.25 10.25 11.25 12.25 13.25 14.25 15.25

Small 

Commercial 

Packaged AC 

(Air-Cooled) - 

≥65,000 Btu/h 

and < 135,000 

Btu/h

Weight 888 930 972 1,014 1,056 1,098 1,141 

Install 

Cost $2,261 $2,368 $2,476 $2,583 $2,690 $2,798 $2,905 

Large 

Commercial 

Packaged AC 

(Air-Cooled) - 

≥135,000 

Btu/h and < 

240,000 Btu/h

Weight 1,784 1,956 2,127 2,299 2,471 2,643 2,815 

Install 

Cost $2,805 $3,076 $3,346 $3,616 $3,886 $4,156 $4,427 

Table 9.5.10 Average Installation Cost Per SF for CUACs (2013$) (1999-2001) 

Equipment Class

EER Bin

9.9 & 

Under 10-10.9 11-11.9 12-12.9 13-13.9 14-14.9

15 & 

Over

Small Commercial 

Packaged AC (AirCooled) - ≥65,000 

Btu/h and < 135,000 

Btu/h

$0.78 $0.82 $0.86 $0.90 $0.93 $0.97 $1.01 

Large Commercial 

Packaged AC (AirCooled) - ≥135,000 

Btu/h and < 240,000 

Btu/h

$0.51 $0.56 $0.61 $0.66 $0.71 $0.76 $0.81 

9-22
9.5.3.4 Electricity Costs 

 DOE derived unit energy consumption (UEC) values for each of the EER bins and then 

applied historic electricity prices to calculate annual energy costs.

 The ANOPR TSD provided a relationship between EER and UEC: UEC=A*EER+B

(Table 9.5.11). Using this relationship, DOE calculated a UEC for each of the EER bins provided 

by AHRI, using the representative EER value for each bin (Table 9.5.12). DOE used the cooled 

square foot per unit values shown previously to calculate the UEC per square foot for the 

shipments model (Table 9.5.13). DOE used the same UECs for all years 1999-2001. 

Table 9.5.11 UEC Relationship to EER

Equipment Class A B

Small Commercial Packaged AC (Air-Cooled) -

≥65,000 Btu/h and < 135,000 Btu/h -1,168.8 27,835 

Large Commercial Packaged AC (Air-Cooled) -

≥135,000 Btu/h and < 240,000 Btu/h -2,488.9 57,386 

Table 9.5.12 Average UEC Per Unit for CUACs (kWh/year) (1999-2001) 

Equipment Class

EER Bin (with Representative EER)

9.9 & 

Under 10-10.9 11-11.9 12-12.9 13-13.9 14-14.9

15 & 

Over

9.25 10.25 11.25 12.25 13.25 14.25 15.25

Small Commercial 

Packaged AC (AirCooled) - ≥65,000 

Btu/h and < 135,000 

Btu/h

17,024 15,855 14,686 13,517 12,348 11,180 10,011 

Large Commercial 

Packaged AC (AirCooled) - ≥135,000 

Btu/h and < 240,000 

Btu/h

34,364 31,875 29,386 26,897 24,408 21,919 19,430 

9-23
Table 9.5.13 Average UEC Per SF for CUACs (kWh/year) (1999-2001) 

Equipment Class

EER Bin (with Representative EER)

9.9 & 

Under 10-10.9 11-11.9 12-12.9 13-13.9 14-14.9

15 & 

Over

9.25 10.25 11.25 12.25 13.25 14.25 15.25

Small Commercial 

Packaged AC (AirCooled) - ≥65,000 

Btu/h and < 135,000 

Btu/h

5.90 5.50 5.09 4.69 4.28 3.88 3.47 

Large Commercial 

Packaged AC (AirCooled) - ≥135,000 

Btu/h and < 240,000 

Btu/h

6.25 5.80 5.35 4.90 4.44 3.99 3.54 

DOE developed a historic price index based on AEO data to calculate annual energy 

costs in the past.9 Figure 9.5.5 shows the price index. This trend was applied to the marginal 

electricity prices (MEP) that were developed separately for CUACs and CUHPs as discussed in 

Section 8.2.2.2. 

Figure 9.5.5 AEO Historic Price Index

9.5.3.5 Maintenance Costs

The same maintenance costs developed for this NOPR were the basis for the maintenance 

costs in 1999−2001. These costs are $297 for both Small and Large CUAC. See Chapter 8 for 

more details. DOE divided the maintenance cost by the cooled square foot per unit values shown 

previously to arrive at the total maintenance cost per square foot used in the shipments model, or 

$0.10 for small CUAC and $0.05 for large CUAC. 

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015

Historic Price Index (2013=1)

Year

9-24
9.5.3.6 Repair Costs

DOE assumed that any routine or minor repairs are included in the annualized 

maintenance costs. As a result, repair costs were not explicitly modeled in the LCC and PBP 

analysis. Instead, DOE incorporated a one-time cost for major repair (compressor replacement)

as a primary input to the repair/replace customer choice model in the shipments analysis. 

 RS Means provides repair costs for various types of heat pumps and compressors. The 

costs include both labor and material costs. DOE reviewed these costs and noted that the material 

costs were inaccurate for all size classes, as several of the estimates exceeded the costs for an 

entire new unit. For labor and non-compressor material costs, DOE used data in RS Means 

Facilities Maintenance & Repair Cost Data, 2013.

10 DOE substituted compressor costs 

developed from a review of Grainger and Drillspot websites.11,12 

 DOE reviewed compressor costs for 316 units from 3.2 tons to 21.1 tons on the Grainger 

and Drillspot websites. DOE calculated the average prices for 5, 7.5, 10, and 15 ton units, 

sometimes including compressors in a small ton range surrounding those points. DOE also used 

the full data range to develop a relationship of compressor cost to tons (Figure 9.5.6). DOE used 

this relationship to estimate compressor costs for 25 ton and 60 ton units (Table 9.5.14). 

Figure 9.5.6 Compressor Costs by Ton (Drillspot, Grainger) 

y = 311.11x - 191.54

R2 = 0.9205

0

1000

2000

3000

4000

5000

6000

7000

0.0 5.0 10.0 15.0 20.0 25.0

Compressor Cost (2013$)

Tons

9-25
Table 9.5.14 Compressor Costs by Ton (2013$) 

Tons Avg Price Predicted Price

5 $1061 $1,364

7.5 $2,608 $2,142

10 $2661 $2,920

15 $5,083 $4,4751

25 N/A $7,5861

60 N/A $18,475

 DOE used these compressors costs - average if available, and predicted otherwise - to 

revise the material costs found in RS Means (Table 9.5.15). Table 9.5.16 shows the RS Means 

costs, combined with the revised material costs, used to arrive at the final total repair cost with 

O&P. To calculate the Material Costs with O&P, DOE assumed the revised compressor cost 

already contained O&P as it was based on end-user (website) pricing. Therefore DOE only 

added the typical RS Means O&P multiplier of 1.25 to the non-compressor material costs.

Table 9.5.15 RS Means Material Cost Adjustments (2013$) 

Tons*

RS Means Material 

Cost

RS Means 

Compressor Cost

Revised Compressor 

Cost

Revised Material 

Cost

5 $905 $470 $1,061 $1,496

7.5 $1,536 $1,050 $2,608 $3,094

10 $17,761 $17,219 $2,661 $3,202

15 $26,411 $25,700 $5,083 $5,793

25 $34,265 $33,375 $7,586 $8,476

60 $38,562 $38,200 $18,475 $18,837

*DOE used systems described as single zone rooftop units for this analysis. 

Table 9.5.16 Repair Costs for CUAC Units Based on RS Means (2013$) 

Single 

Zone 

Rooftop 

Unit

Labor 

Hour

Bare Costs Total with O&P

Cost per 

Labor 

Hour

Calc. 

Labor 

Cost

Revised 

Mat’l

Cost

Total 

Cost

Cost per 

Person 

Hour

Labor 

Cost

Mat’l

Cost

Total 

Cost

5 ton 18.27 $56.65 $1,035 $1,496 $1,940 $85.30 $1,559 $1,605 $3,163

7.5 ton 21.83 $56.65 $1,237 $3,094 $2,773 $85.30 $1,862 $3,215 $5,078

10 ton 54.79 $56.65 $3,104 $3,202 $20,865 $85.30 $4,674 $3,338 $8,012

15 ton 76.72 $56.65 $4,3467 $5,793 $30,757 $85.30 $6,544 $5,971 $12,515

25 ton 96.57 $52.87 $5,1057 $8,476 $39,370 $79.60 $7,687 $8,698 $16,385

60 ton 298.68 $52.87 $15,791 $18,837 $54,353 $79.60 $23,775 $18,927 $42,702

 DOE took the 7.5 ton and 15 ton costs to be representative of the small and large CUAC 

equipment classes, respectively.c

 Within each equipment class, DOE used repair costs that 

increase in direct proportion with the price of the equipment and with EER level. For historical 

c Cost for the other ton units are shown as a predecessor to developing the cost for very large CUAC equipment (30 

ton) discussed in section 9.3.4.5. 

9-26

 
repair costs, DOE assumed that the repair costs developed in 2013 were representative of the 11-

11.9 EER bin. DOE first adjusted the repair costs for the 11-11.9 bin to represent repair costs 

in1999 using the UAC PPI shown previously. DOE then varied the repair costs for the other bins 

in direct proportion to the equipment prices developed for 1999-2001 (see Table 9.5.5). DOE 

adjusted the repair prices by EER bin from 1999 to 2000 and 2001, also using the PPI. Table 

9.5.17 shows the result. DOE also used the cooled square foot per unit values shown previously 

to calculate the repair cost per square foot for the shipments model (Table 9.5.18).

Table 9.5.17 Average Repair Cost Per Unit for CUACs (2013$) (1999-2001) 

Equipment 

Class Year

EER Bin

9.9 & 

Under 10-10.9 11-11.9 12-12.9 13-13.9 14-14.9

15 & 

Over

Small 

Commercial 

Packaged AC 

(Air-Cooled) - 

≥65,000 Btu/h 

and < 135,000 

Btu/h

1999 $5,059 $5,073 $5,396 $6,154 $7,348 $8,978 $11,043 

2000 $4,843 $4,857 $5,165 $5,891 $7,034 $8,595 $10,572 

2001 $4,732 $4,745 $5,046.84 $5,756 $6,873 $8,397 $10,329 

Large 

Commercial 

Packaged AC 

(Air-Cooled) - 

≥135,000 

Btu/h and < 

240,000 Btu/h

1999 $12,396 $12,442 $13,298 $14,965 $17,441 $20,727 $24,823 

2000 $11,867 $11,911 $12,731 $14,326 $16,697 $19,843 $23,764 

2001 $11,594 $11,638 $12,439 $13,997 $16,313 $19,387 $23,218 

Table 9.5.18 Average Repair Cost Per SF for CUACs (2013$) (1999-2001) 

Equipment 

Class Year

EER Bin

9.9 & 

Under 10-10.9 11-11.9 12-12.9 13-13.9 14-14.9

15 & 

Over

Small 

Commercial 

Packaged AC 

(Air-Cooled) - 

≥65,000 Btu/h 

and < 135,000 

Btu/h

1999 $1.75 $1.76 $1.87 $2.13 $2.55 $3.11 $3.83 

2000 $1.68 $1.68 $1.79 $2.04 $2.44 $2.98 $3.66 

2001 $1.64 $1.65 $1.75 $2.00 $2.38 $2.91 $3.58 

Large 

Commercial 

Packaged AC 

(Air-Cooled) - 

≥135,000 Btu/h 

and < 240,000 

Btu/h

1999 $2.26 $2.26 $2.42 $2.72 $3.17 $3.77 $4.52 

2000 $2.16 $2.17 $2.32 $2.61 $3.04 $3.61 $4.33 

2001 $2.11 $2.12 $2.26 $2.55 $2.97 $3.53 $4.23 

9-27
9.5.4 Data for Efficiency Level Distribution Projections

To develop the efficiency level distribution projections, DOE used costs developed for 

2013 as the basis for its analysis. Many of these costs for CUAC have been discussed previously 

in Chapter 8. 

DOE did not conduct an engineering or LCC analysis for CUHP. For CUHPs, DOE

estimated that a significant portion of the market consists of equipment with electric resistance 

heating. As a result, DOE developed efficiency levels for CUHP based on the difference in 

ASHRAE Standard 90.1-2010 levels for CUAC with electric resistance heating and CUHP with 

electric resistance heating. This difference is 0.2 for small CUHP and 0.5 for large and very large 

CUHP. Table 9.5.19 shows the CUHP efficiency levels analyzed. 

Table 9.5.19 CUHP Efficiency Levels

Efficiency 

Level

IEER

Small Commercial 

Packaged HP (AirCooled) - ≥65,000 Btu/h 

and < 135,000 Btu/h

Large Commercial 

Packaged HP (AirCooled) - ≥135,000 Btu/h 

and < 240,000 Btu/h

Very Large Commercial 

Packaged HP (AirCooled) - ≥240,000 Btu/h 

and < 760,000 Btu/h

0 11.2 10.7 10

1 12.7 11.7 11

2 13.8 12.7 12

3 14.6 13.7 13

4 19.7 17.9 15

9.5.4.2 Equipment Price

The CUAC equipment prices developed for the LCC were shown in Chapter 8. The 

equipment prices used in the shipments model are slightly different, as they are weightedaverage costs based on the regional distribution of buildings in the sample, as outputted by the 

LCC (Table 9.5.20). The equipment costs used in the shipments model are approximately 99% of 

the national average costs.

9-28
Table 9.5.20 Average Customer Price for CUACs (2013$) 

Equipment Class

Efficiency Level

0 1 2 3 4

Small Commercial Packaged AC 

(Air-Cooled) - ≥65,000 Btu/h and 

< 135,000 Btu/h

$5,840 $6,048 $6,885 $7,252 $8,270 

Large Commercial Packaged AC 

(Air-Cooled) - ≥135,000 Btu/h and 

< 240,000 Btu/h

$10,628 $11,400 $12,358 $13,176 $13,760 

Very Large Commercial Packaged 

AC (Air-Cooled) - ≥240,000 Btu/h 

and < 760,000 Btu/h

$22,591 $23,641 $25,098 $26,139 $28,536 

 

 For CUHP, which were not analyzed in the LCC, DOE developed baseline manufacturing 

costs in the engineering analysis (Table 9.5.21). DOE then applied the incremental costs 

developed for CUAC (see Chapter 8) to these baseline CUHP costs to arrive at manufacturing 

costs per equipment class and efficiency level. Finally, DOE applied the same markups 

developed for CUAC (see Table 8.2.1 in Chapter 8) to the CUHP baseline manufacturing costs 

to arrive at equipment prices for CUHPs. Table 9.5.22 shows the CUHP equipment prices used 

in the shipments model. DOE also divided the per unit equipment prices by the cooled square 

foot per unit values shown previously to arrive at average equipment prices per square foot 

(Table 9.5.23). 

Table 9.5.21 CUHP Baseline Manufacturing Cost (2013$) 

Equipment Class Baseline Manufacturing Cost

Small Commercial Packaged HP (Air-Cooled) - ≥65,000 

Btu/h and < 135,000 Btu/h $2,081 

Large Commercial Packaged HP (Air-Cooled) - ≥135,000 

Btu/h and < 240,000 Btu/h $4,002 

Very Large Commercial Packaged HP (Air-Cooled) -

≥240,000 Btu/h and < 760,000 Btu/h $7,889 

9-29
Table 9.5.22 Average Customer Price (Per Unit) for CUHPs (2013$) 

Equipment Class

Efficiency Level

0 1 2 3 4

Small Commercial Packaged 

HP (Air-Cooled) - ≥65,000 

Btu/h and < 135,000 Btu/h

$6,287 $6,494 $7,331 $7,699 $8,716 

Large Commercial Packaged 

HP (Air-Cooled) - ≥135,000 

Btu/h and < 240,000 Btu/h

$11,914 $12,686 $13,643 $14,461 $15,045 

Very Large Commercial 

Packaged HP (Air-Cooled) - 

≥240,000 Btu/h and < 760,000 

Btu/h

$24,817 $25,866 $27,323 $28,364 $30,760 

 

Table 9.5.23 Average Customer Price (per SF) for CUACs and CUHPs (2013$) 

Equipment Class

Efficiency Level

0 1 2 3 4

Small Commercial Packaged AC 

(Air-Cooled) - ≥65,000 Btu/h and 

< 135,000 Btu/h

$2.02 $2.10 $2.39 $2.51 $2.87 

Large Commercial Packaged AC 

(Air-Cooled) - ≥135,000 Btu/h and 

< 240,000 Btu/h

$1.93 $2.07 $2.25 $2.40 $2.50 

Very Large Commercial Packaged 

AC (Air-Cooled) - ≥240,000 Btu/h 

and < 760,000 Btu/h

$2.02 $2.11 $2.24 $2.34 $2.55 

Small Commercial Packaged HP 

(Air-Cooled) - ≥65,000 Btu/h and 

< 135,000 Btu/h

$2.18 $2.25 $2.54 $2.67 $3.02 

Large Commercial Packaged HP 

(Air-Cooled) - ≥135,000 Btu/h and 

< 240,000 Btu/h

$2.17 $2.31 $2.48 $2.63 $2.74 

Very Large Commercial Packaged 

HP (Air-Cooled) - ≥240,000 Btu/h 

and < 760,000 Btu/h

$2.22 $2.31 $2.44 $2.53 $2.75 

 

 As discussed in chapter 8, DOE examined historical PPI data for “unitary airconditoiners, except heat pumps” as a method to project future prices, but DOE determined that 

the extent to which the trends of the past years will continue is very uncertain, and as a result, 

chose to apply a constant price trend. DOE also examined PPI data for heat pumps: “Air source 

heat pumps, except room air” (2007-2009) and “heat pumps” (2009-2013).13 However, because 

of the short length of time available and the inconsistency between the two series, DOE decided 

to use the AC trend for both AC and HP, and as a result, DOE also used constant real prices for 

CUHP.

9-30
9.5.4.3 Installation Costs 

The installation costs developed for the LCC were shown in Chapter 8. The installation 

costs used in the shipments model are slightly different, as they are weighted-average costs based 

on the regional distribution of buildings in the sample, as outputted by the LCC (Table 9.5.24). 

The installation costs are approximately 93% of the national average costs. DOE used the same 

installation costs developed for CUACs for the equivalent CUHP equipment classes. DOE also 

divided the per unit installation costs by the cooled square foot per unit values shown previously 

to arrive at average installation costs per square foot (Table 9.5.25).

Table 9.5.24 Average Installation Cost per Unit for CUACs and CUHPs (2013$) 

Equipment Class

Efficiency Level

0 1 2 3 4

Small Commercial Packaged AC and 

HP (Air-Cooled) - ≥65,000 Btu/h and < 

135,000 Btu/h

$2,316 $2,487 $3,038 $3,070 $3,897 

Large Commercial Packaged AC and 

HP (Air-Cooled) - ≥135,000 Btu/h and 

< 240,000 Btu/h

$3,129 $3,535 $4,501 $4,577 $5,215 

Very Large Commercial Packaged AC 

and HP (Air-Cooled) - ≥240,000 Btu/h 

and < 760,000 Btu/h

$5,194 $5,744 $6,640 $6,689 $7,664 

Table 9.5.25 Average Installation Cost per SF for CUACs and CUHPs (2012$) 

Equipment Class

Efficiency Level

0 1 2 3 4

Small Commercial Packaged AC and 

HP (Air-Cooled) - ≥65,000 Btu/h and < 

135,000 Btu/h

$0.80 $0.86 $1.05 $1.06 $1.35 

Large Commercial Packaged AC and 

HP (Air-Cooled) - ≥135,000 Btu/h and 

< 240,000 Btu/h

$0.57 $0.64 $0.82 $0.83 $0.95 

Very Large Commercial Packaged AC 

and HP (Air-Cooled) - ≥240,000 Btu/h 

and < 760,000 Btu/h

$0.46 $0.51 $0.59 $0.60 $0.68 

9.5.4.4 Electricity Costs

Electricity costs are based on the unit energy consumption for cooling in CUACs and 

both cooling and heating for CUHPs. DOE developed the cooling UECs for CUACs in the 

energy use analysis (Table 9.5.26). To develop cooling UECs for CUHPs, DOE adjusted the 

CUAC UECs based on the relationship of the CUAC and CUHP IEER values for each efficiency 

level. In other words, to obtain the cooling UEC for 7.5 ton units at efficiency level 0, DOE 

multiplied 13,119 (kWh/year) by 11.4/11.2 (IEER/IEER). Table 9.5.27 shows the resulting 

CUHP cooling UECs.

9-31
Table 9.5.26 CUAC UECs

Efficiency Level

Small Commercial 

Packaged AC (AirCooled) - ≥65,000 Btu/h 

and < 135,000 Btu/h

Large Commercial 

Packaged AC (AirCooled) - ≥135,000 

Btu/h and < 240,000 

Btu/h

Very Large 

Commercial Packaged 

AC (Air-Cooled) - 

≥240,000 Btu/h and < 

760,000 Btu/h

IEER

Cooling 

UEC IEER

Cooling 

UEC IEER

Cooling 

UEC

0 11.4 13,119 11.2 22,917 10.1 53,453

1 12.9 11,476 12.2 20,998 11.6 47,272

2 14.0 10,666 13.2 18,655 12.5 44,976

3 14.8 6,760 14.2 16,594 13.5 31,921

4 19.9 3,531 18.4 12,425 15.5 26,412

 

Table 9.5.27 CUHP Cooling UECs

Efficiency Level

Small Commercial 

Packaged HP (AirCooled) - ≥65,000 Btu/h 

and < 135,000 Btu/h

Large Commercial 

Packaged HP (AirCooled) - ≥135,000 

Btu/h and < 240,000 

Btu/h

Very Large Commercial 

Packaged HP (AirCooled) - ≥240,000 

Btu/h and < 760,000 

Btu/h

IEER

Cooling 

UEC IEER

Cooling 

UEC IEER

Cooling 

UEC

0 11.2 13,353 10.7 23,988 10 56,237

1 12.7 11,657 11.7 21,896 11 49,401

2 13.8 10,821 12.7 19,390 12 46,850

3 14.6 6,852 13.7 17,199 13 33,149

4 19.7 3,567 17.9 12,772 15 27,292

 To develop heating UECs for CUHPs, DOE first developed a relationship between IEER 

and COP based on units in the AHRI database.14 DOE then developed an annual energy use per 

square foot based on the CBECS 2003 dataset. This value was 1.37 (kWh/sf), and assumed to be 

representative of a unit with 2.9 COP. Using the tons/sf values developed for CUACs in the 

energy use analysis, DOE calculated an annual energy use per ton (kWh/ton) for each equipment 

class, based on a COP of 2.9. DOE then took the annual energy use per ton for the given 

equipment class, multiplied it by the representative tons for that class, and adjusted it by the ratio 

of 2.9 COP to the COP for that efficiency level. Further details are available in Chapter 10, NIA. 

Table 9.5.28 shows the resulting CUHP heating UECs. 

9-32
Table 9.5.28 CUHP Heating UECs

Efficiency 

Level

Small Commercial 

Packaged HP (AirCooled) - ≥65,000 Btu/h 

and < 135,000 Btu/h

Large Commercial 

Packaged HP (AirCooled) - ≥135,000 Btu/h 

and < 240,000 Btu/h

Very Large Commercial 

Packaged HP (AirCooled) - ≥240,000 Btu/h 

and < 760,000 Btu/h

COP

Heating 

UEC COP

Heating 

UEC COP

Heating 

UEC

0 3.3 3,440 3.3 6,549 3.2 13,898

1 3.4 3,379 3.3 6,549 3.2 13,898

2 3.4 3,336 3.3 6,550 3.2 13,898

3 3.5 3,305 3.3 6,550 3.2 13,898

4 3.7 3,121 3.3 6,551 3.2 13,898

 DOE summed the heating and cooling UECs for CUHP and, for both CUAC and CUHPs, 

divided the UECs by the cooled square foot per unit values shown previously to arrive at the 

total UEC per square foot used in the shipments model (Table 9.5.29). 

Table 9.5.29 Total UECs by SF for CUAC and CUHPs

Equipment Class

Efficiency Level

0 1 2 3 4

Small Commercial Packaged AC 

(Air-Cooled) - ≥65,000 Btu/h and < 

135,000 Btu/h

4.5 4.0 3.7 2.3 1.2 

Large Commercial Packaged AC 

(Air-Cooled) - ≥135,000 Btu/h and < 

240,000 Btu/h

4.2 3.8 3.4 3.0 2.3 

Very Large Commercial Packaged 

AC (Air-Cooled) - ≥240,000 Btu/h 

and < 760,000 Btu/h

4.8 4.2 4.0 2.9 2.4 

Small Commercial Packaged HP 

(Air-Cooled) - ≥65,000 Btu/h and < 

135,000 Btu/h

5.8 5.2 4.9 3.5 2.3 

Large Commercial Packaged HP 

(Air-Cooled) - ≥135,000 Btu/h and < 

240,000 Btu/h 

5.6 5.2 4.7 4.3 3.5 

Very Large Commercial Packaged 

HP (Air-Cooled) - ≥240,000 Btu/h 

and < 760,000 Btu/h

6.3 5.7 5.4 4.2 3.7 

DOE multiplied the UECs by marginal electricity prices (MEP) to calculate energy costs. 

Marginal electricity price values of 0.1100 $/kWh and 0.1014 $/kWh were used for CUACs and 

CUHPs respectively. The AEO 2013 Reference Case forecast of electricity prices was used to 

project energy costs into the future. (See Chapter 8 for more details.) 

9-33
9.5.4.5 Maintenance Costs

 The maintenance costs developed for the LCC were used directly in the shipments model. 

These costs are $297 for both small and large CUAC, and $408 for very large CUAC. 

Maintenance costs do not vary by efficiency level. DOE used the same maintenance costs for the 

equivalent CUHP equipment classes. DOE divided the maintenance cost by the cooled square 

foot per unit values shown previously to arrive at the total maintenance cost per square foot used 

in the shipments model (Table 9.5.30). 

Table 9.5.30 Average Maintenance Cost per SF for CUACs and CUHPs (2013$) 

Equipment Class Maintenance Cost per SF

Small Commercial Packaged AC and HP (Air-Cooled) -

≥65,000 Btu/h and < 135,000 Btu/h $0.10 

Large Commercial Packaged AC and HP (Air-Cooled) -

≥135,000 Btu/h and < 240,000 Btu/h $0.05 

Very Large Commercial Packaged AC and HP(Air-Cooled) -

≥240,000 Btu/h and < 760,000 Btu/h $0.04 

9.5.4.6 Repair Costs

DOE developed repair costs for baseline units in 2013 as discussed in section 9.5.3.6. The 

baseline values for small and large CUAC units were $5,078 and $12,515, respectively (Table 

9.5.16). Because RS Means did not provide data for 30 ton units, DOE developed a linear 

relationship between Repair Cost with O&P and CUAC capacity (Figure 9.5.7). This resulted in 

a value for 30 ton units of $21,390. 

Figure 9.5.7 Repair Cost by CUAC Capacity

y = 704.06x + 267.98

R2 = 0.9942

 $-

 $5,000

 $10,000

 $15,000

 $20,000

 $25,000

 $30,000

 $35,000

 $40,000

 $45,000

0 10 20 30 40 50 60 70

Repair Costs with O&P (2013$)

CUAC Capacity

9-34
 In 2013, these costs were taken as representative of EL0. For all other ELs, DOE varied 

the repair cost in direct proportion to the equipment price, as shown in Table 8.2.4 in Chapter 8. 

DOE used the same repair costs for both CUAC and CUHP in their equivalent equipment classes 

(Table 9.5.31). DOE also divided the repair cost by the cooled square foot per unit values shown 

previously to arrive at the total repair cost per square foot used in the shipments model (Table 

9.5.32).

Table 9.5.31 Average Repair Cost Per Unit for CUACs and CUHPs (2013$) 

Equipment Class

Efficiency Level

0 1 2 3 4

Small Commercial Packaged 

AC and HP (Air-Cooled) - 

≥65,000 Btu/h and < 

135,000 Btu/h

$5,078 $5,258 $5,985 $6,304 $7,188 

Large Commercial Packaged 

AC and HP (Air-Cooled) - 

≥135,000 Btu/h and < 

240,000 Btu/h

$12,515 $13,423 $14,550 $15,513 $16,200 

Very Large Commercial 

Packaged AC and HP(AirCooled) - ≥240,000 Btu/h 

and < 760,000 Btu/h

$21,390 $22,382 $23,761 $24,746 $27,013 

Table 9.5.32 Average Repair Cost Per SF for CUACs and CUHPs (2013$) 

Equipment Class

Efficiency Level

0 1 2 3 4

Small Commercial Packaged 

AC and HP (Air-Cooled) - 

≥65,000 Btu/h and < 

135,000 Btu/h

$1.76 $1.82 $2.07 $2.19 $2.49 

Large Commercial Packaged 

AC and HP (Air-Cooled) - 

≥135,000 Btu/h and < 

240,000 Btu/h

$2.28 $2.44 $2.65 $2.82 $2.95 

Very Large Commercial 

Packaged AC and HP(AirCooled) - ≥240,000 Btu/h 

and < 760,000 Btu/h

$1.91 $2.00 $2.12 $2.21 $2.41 

9.5.5 Equipment Lifetime

The development of the equipment lifetime for CUAC was discussed in Chapter 8. DOE 

used an updated CUAC lifetime with a median of 18.7 years and a mean of 18.4 years. DOE also 

reviewed the equipment lifetime for CUHP for this rulemaking. In the ASHRAE database, the 

9-35
category "heat pump, air-to-air", which has 1296 units with only one retired, shows a median 

lifetime of 14 years.15 Therefore, DOE did not make any major adjustements to the CUHP 

lifetime. DOE used a CUHP lifetime with a median of 15.4 years and a mean of 15.2 years. 

Calibration of the shipments model assisted in arriving at these numbers (see section 9.6). 

9.6 MODEL CALIBRATION

 The shipments model is used to project future shipments of commercial unitary airconditioners and heat pumps for the base case with no standards implemented and all standards 

cases wherein equipment must conform to a certain minimum efficiency level L. Two of the 

main components of the shipments model include the consumer choice model, that predicts 

market shares as a function of efficiency (Section 9.3), and the Repair/Replace decision model 

(Section 9.4) which provides an average repair probability for broken units. Both models consist 

of sets of unknown parameters (α, β) and (κ, γ) that reflect sensitivities to various costs that need 

to be prescribed. The calibration step of the shipments model involves estimating values for 

these parameters and is described in this section.

9.6.1 Estimating Customer Choice Model Parameters

 The consumer choice model consists of two parameters: α and β and that reflect 

sensitivities to total installed cost (up-front costs) and operating costs respectively. For each type 

of equipment and capacity class, these parameters were estimated using three years (1999-2001) 

of historical input data for CUACs described in section 9.5.3. The procedure to estimate the two 

parameters of the consumer choice model is described below. 

1. First, the utility function of the consumer choice model W(y) given by 

Wj

(m) (y) = α(m)

TICj

(m)

(y) + β(m)OCj

(m)

(y), (26) 

was defined for a particular equipment type for each of the three years (1999-2001) using 

arbitrary values of α(

 ͫ ) and β( ͫ ). Here,

• TICj

(m)

(y) = EPj

(m)

(y) + ICj

(m)

(y) is the total installation cost in 2012$ per sq. ft for 

equipment of capacity m (= small & large) in year y averaged over EER bin j (j=

0, ... , N and N = 7). 

 EPj

(m)

(y)and ICj

(m)

(y) are the equipment price and installation cost for the 

aforementioned capacities of equipment whose values are listed as a function of 

EER in Tables 9.5.8 and 9.5.11 respectively. 

• OCj

(m)

(y)= MCj

(m)

(y) + MEP × UECj

(m)

(y) × AEO_ElecPrice(y) is the total operating 

and maintenance cost in 2012$ per sq. ft for equipment of capacity m averaged over EER 

bin j. Here,

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 MCj

(m)

(y)is the total maintenance cost in 2012$ for equipment of capacity m in 

year y. These costs are described in section 9.3.3.5. 

 UECj

(m)

(y) is the unit energy consumption in KWh per sq.ft per year for 

equipment of capacity m in year y, whose values are listed in Table 9.5.14. 

 MEP corresponds to the marginal price of electricity which is equal to 0.1100 

$/KWh for CUACs and 0.1014 $/KWh for CUHPs.

 AEO ElecPrice(y) is the historic price trend (see Figure 9.5.4) developed from 

AEO data. Three price trends were developed for the analysis period based on 

low, high and a reference case economic growth scenarios. For the shipments 

model, the price trend corresponding to the reference case was used to calculate 

the cost of electricity in a given year as part of total operating and maintenance 

costs. 

2. The Department then estimated values of α(m) and β(m) for small and large CUAC 

equipment classes by using a non-linear least squares optimization routine (Excel's 

Solver) that minimized the sum of the squared difference between historical efficiency 

level shares qj

(m) (Table 9.5.3) and market share probabilities pj(m)

 predicted by the 

consumer choice model (see Section 9.3.3) i.e. 

 

 Min �∑ �qj

(m)

(y) − pj

(m)

(y))2� 2001

y=1999 � → �α(m)

, β(m)� (27) 

 

Since DOE did not have the necessary input data to calibrate the model parameters for very large 

equipment, DOE set these values to those used for the large equipment type. DOE also assumed 

that the α's and β’s for the CUHPs were that same as those calculated for the CUACs. Table 

9.6.1 shows the consumer choice model parameters for different classes of CUACs and CUHPs. 

 

Table 9.6.1 Consumer choice model calibration parameters

CUAC (KBtu/hr) CUHP (KBtu/hr)

Parameters 65-135 135-240 240-760 65-135 135-240 240-760

α -12.144 -9.082 -9.082 -12.144 -9.082 -9.082

β -14.922 -2.055 -2.055 -14.922 -2.055 -2.055 

It is important to note that during the calibration β was highly sensitive to slight changes in the 

cost trends across the EER bins in any given year. This resulted in positive values for the large 

equipment class. However, we speculate that since the total operating costs are invariably lower 

than the total installed costs, the model would tend to produce probabilities which are primarily 

first cost driven irrespective of operating costs. This perhaps explains the large α that we obtain 

for all equipment types. In other words, the predicted probabilities would not be greatly affected 

by resorting to a single parameter model that reflects sensitivity to first cost alone. 

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9.6.2 Estimating Repair/Replace Model Parameters

The repair/replace decision model is a simple binary choice logit model that provides an estimate 

of the average repair probability associated with broken units in a given year. Like the consumer 

choice model, it consists of two parameters γ and κ. κ represents customer sensitivity to the 

average efficiency weighted cost differential between total installed cost and the cost of repairing 

an older unit in a give year. Since repair costs are generally smaller than total installed costs, γ is 

a scenario parameter that is thought to represent “unknown" replacements by limiting the number 

of repairs in a given year. For simplicity, we assume that κ is equal to the cost sensitivity 

parameter α used in the consumer choice model. This assumption is reasonable because we 

expect a repair/replace decision to be first cost driven. Therefore, the only parameter that needs 

to be ascertained is γ. The steps involved in estimating γ are outlined below: 

1. For a given equipment type and capacity m, an average historical repair rate �r̅ (m)�is 

first calculated by using an iterative optimization procedure that utilizes a combination of 

average equipment lifetime �η̅ (m)

� and an adjustment factor�A0

(m)

� for market saturation

to minimize the difference between historical shipments and model predicted shipments

with zero repairs. It is assumed that the average historical repair rate represents the 

fraction of model predicted shipments that are larger than historical shipments with 

repairs set equal to zero. Note that r̅ (m) represents a repair fraction averaged across all 

efficiencies for a particular equipment class in a given year.

 A0

(m) represents an adjustment factor that is applied to the fitted stock saturation 

trends (see Section 9.5.2.1; Figure 9.5.2) in combination with mean lifetime η̅ (m) to 

minimize the sum of the difference between historical shipments and model predicted 

shipments with repairs set equal to zero. In other words, A0

(m) and η̅ (m) represent two 

parameters that maximize the likelihood of obtaining r̅ (m) by minimizing the 

difference between cumulative historical and model predicted shipments with zero

repairs. These parameters are calculated as part of the optimization procedure used to 

determine r̅ (m) . 

 The mean lifetime of a particular type of equipment of capacity η̅ (m) is given by

 η̅ (m) = λГ�1 + 1

θ

� (28) 

where θ and λ are the shape and scale parameters of the equipment lifetime function 

defined earlier (see equation (3)).

 For CUACs, the calibration approach yielded values θ = 10.0 and λ = 19.35 that 

resulted in mean and median lifetimes of 18.4 and 18.7 years respectively. For 

CUHPs, these values were θ = 10.0 and λ= 16.0 that produced mean and median 

lifetimes of 15.22 and 15.44 years respectively. 

2. Next, the utility function R(m)

(y)is calculated based on the efficiency weighted average 

cost difference Δ(m)Δ between total installed costs TIC(m)(y) and repair costs 

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R(m)

(y)for the given year y. The repair costs associated with small and large CUACs for 

years 1999-2001 are described in Table 9.5.19. 

3. The scenario parameter γ(m) is then obtained by minimizing the sum of the squared 

difference between r̅ (m) and the model predicted value ρ′(m) using historical cost data 

from years 1999-2001 that are used tocalculate R(y) for each year y. 

4. Mathematically, this procedure can be expressed as

 Min�∑ �r̅ (m)

(y) − ρ′(m)(y))2� 2001

y=1999 � → �γ(m)

� (29) 

Table 9.6.2 presents a summary of the constraints used in the calibration of the Repair/Replace 

decision model as well as the calibrated parameters.

Table 9.6.2 Repair/Replace decision model constraints and calibration parameters

CUAC (KBtu/hr) CUHP (KBtu/hr)

Parameters 65-135 135-240 240-760 65-135 135-240 240-760

A0 0.645 0.760 0.760 1.95 2.15 4.28

r̅ 0.176 0.204 0.278 0.096 0.156 0.259

γ -14.431 -3.450 -5.065 -14.551 -5.940 -5.665

 

9.7 RESULTS

 Figures 9.7.1 shows the base case shipments for all CUAC and CUHP equipment classes 

considered. Figures 9.7.2-9.7.3 compare model shipments between the base case and all 

standards cases for small and large CUACs. The variability in the model shipments stem

primarily from shipments for replacements that depend upon the number of units getting repaired 

and hence the repair rate predicted by the repair/replace model in each of the projection years. 

Since we do not apply any equipment price learning, the repair probabilities predicted by the 

repair/replace model remain constant for all projection years in the analysis period. For the base 

case, the repair probability is close to the historical average repair rate described in Section 9.6.2. 

For the standards cases, even though the repair costs increase in proportion to the installation 

costs, they are still generally smaller than the installation costs and this difference is most 

significant at the highest standard level EL4. Consequently, this results in a larger number of 

units getting repaired and hence a significant drop in shipments for the standards cases (see 

Figures 9.7.2-3). 

 Figures 9.7.9-10 illustrate the number of units getting repaired for the base case and all 

the standards cases for small and large CUACs based on the repair rate predicted by the 

repair/replace decision model. The number of repairs are close for standards cases EL2 and EL3 

because the cost differential between efficiency weighted average total installed cost and repair 

costs are relatively close for these two levels. 

9-39
 For very large equipment (240-760 KBtu/hr), the repair rate is equal to the historical 

average repair rate till year 2013 after which DOE assumed that all units get repaired at first 

failure resulting in a huge drop in shipments as seen in Figure 9.7.4. Since broken units get 

another lifetime after repairs, these units are replaced at second failure and cause a spike in the 

number of shipments in future years. 

Figure 9.7.1 Base case shipment for all CUAC and CUHP 

equipment classes.

9-40
Figure 9.7.2 Model shipments for small CUACs for the base case 

and standards cases.

9-41
Figure 9.7.3 Model shipments for large CUACs for the base case 

and standards cases.

9-42
Figure 9.7.4 Model shipments for very large CUACs for the base 

case and standards cases.

9-43
Figure 9.7.5 Total model shipments for all CUAC equipment 

classes for the base case and standards cases.

9-44
Figure 9.7.6 Shipments-weighted IEER shipments for small 

CUACs for the base case and standards cases.

9-45
Figure 9.7.7 Shipments-weighted IEER shipments for large 

CUACs for the base case and standards cases.

9-46
Figure 9.7.8 Shipments-weighted IEER shipments for very large 

CUACs for the base case and standards cases.

9-47
Figure 9.7.9 Number of units repaired and replaced for small 

CUACs for the base case and standards cases.

9-48
Figure 9.7.10 Number of units repaired and replaced for large 

CUACs for the base case and standards cases. 

9-49
Figure 9.7.11 Number of units repaired and replaced for very 

large CUACs for the base case and standards cases.

9-50
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Pump Unit Shipments for 1980-2001, January, 2005. Arlington, VA. Prepared for Lawrence 

Berkeley National Laboratory, Berkeley, CA.

2

 U.S.Census Bureau. Current Industrial Reports for Refrigeration, Air Conditioning, and 

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http://www.census.gov/manufacturing/cir/historical_data/ma333m/index.html

3

 U.S. Department of Energy-Energy Information Administration, Commercial Buildings 

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http://www.eia.gov/consumption/commercial/index.cfm

4

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12 Drillspot, http://www.drillspot.com/. Accessed: 6/11/2013. 

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