### CHAPTER 11. NATIONAL IMPACT ANALYSIS

TABLE OF CONTENTS 11.1 INTRODUCTION ............................................................................................................. 11-1
11.1.1 General Approach .............................................................................................. 11-2
11.1.2 NES and NPV Input Summary .......................................................................... 11-3
11.2 NATIONAL ENERGY SAVINGS ................................................................................... 11-4
11.2.1 NES Definition................................................................................................... 11-4
11.2.2 NES Inputs ......................................................................................................... 11-5 11.2.2.1 Annual Unit Energy Consumption.................................................... 11-5 11.2.2.2 Shipments .......................................................................................... 11-9 11.2.2.3 Equipment Stock ............................................................................... 11-9 11.2.2.4 National Annual Energy Consumption ............................................. 11-9 11.2.2.5 Site-to-Source Conversion Factor ................................................... 11-10
11.3 NET PRESENT VALUE ................................................................................................ 11-11
11.3.1 Net Present Value Definition ........................................................................... 11-11
11.3.2 Net Present Value Inputs ................................................................................. 11-11 11.3.2.1 Total Annual Installed Cost ............................................................ 11-12 11.3.2.2 Total Annual Operating Cost Savings ............................................ 11-13 11.3.2.3 Discount Factor ............................................................................... 11-14 11.3.2.4 Present Value of Costs .................................................................... 11-15 11.3.2.5 Present Value of Savings ................................................................ 11-15
11.4 NES AND NPV RESULTS ............................................................................................. 11-15
11.4.1 National Energy Savings Results ..................................................................... 11-15
11.4.2 Annual Costs and Savings ............................................................................... 11-18
11.4.3 Net Present Value Results ................................................................................ 11-19

11-i11-ii 

### LIST OF TABLES

Table 11.1.1 Summary of NES and NPV Model Inputs ......................................................... 11-3 Table 11.2.1 Risk Premiums by Risk Class (j) in the NEMS Commercial Model ................. 11-6 Table 11.2.2 Shipment-Weighted Market Shares by Efficiency Level for PTACs, Base Case .................................................................................................................... 11-7 Table 11.2.3 Shipment-Weighted Market Shares by Efficiency Level for PTHPs, Base Case .................................................................................................................... 11-7 Table 11.2.4 Annual Unit Energy Consumption by Efficiency Level .................................... 11-8 Table 11.2.5 Shipment-Weighted Average Annual Unit Energy Consumption by Trial Standard Level ................................................................................................... 11-9 Table 11.2.6 Marginal Site-to-Source Conversion Factors (Btu/kWh) ................................ 11-10 Table 11.3.1 Average Total Installed Cost per Unit by Efficiency Level (2007$) ............... 11-12 Table 11.3.2 Shipment-Weighted Average Total Installed Cost per Unit by Trial Standard Level (2007$).................................................................................... 11-13 Table 11.3.3 Average Annual Repair Cost per Unit (2007$) ............................................... 11-14 Table 11.3.4 Average Annual Maintenance Cost per Unit (2007$) ..................................... 11-14 Table 11.4.1 Cumulative National Energy Savings for PTACs and PTHPs ........................ 11-16 Table 11.4.2 Cumulative National Energy Savings for PTACs and PTHPs Based on Seven-Percent Discount Rate ........................................................................... 11-17 Table 11.4.3 Cumulative National Energy Savings for PTACs and PTHPs Based on Three-Percent Discount Rate ........................................................................... 11-17 Table 11.4.4 Cumulative NPV Results Based on a Seven-Percent Discount Rate (Billion 2007$) ................................................................................................. 11-19 Table 11.4.5 Cumulative NPV Results based on a Three-Percent Discount Rate (Billion 2007$) ................................................................................................. 11-20

LIST OF FIGURES

Figure 11.4.1 National Annual Costs and Savings for Standard Size PTAC, 9,000 Btu/h Cooling Capacity, TSL6 .................................................................................. 11-18

### CHAPTER 11. NATIONAL IMPACT ANALYSIS

11.1 INTRODUCTION
The national impacts analysis evaluates the impact of a proposed standard from a national perspective rather than from the customer perspective represented by the life-cycle cost (LCC) (see Chapter 8 of this TSD). This chapter describes the U.S. Department of Energy (DOE)’s methodology for estimating future national energy savings (NES) from amended energy conservation standards for packaged terminal air conditioners (PTACs) and packaged terminal heat pumps (PTHPs) as well as the national economic impact using the net present value (NPV) metric. DOE determined both the NPV and NES for each trial standard level (TSL) that it considered for all the equipment classes of PTAC and PTHP equipment. DOE considered up to seven TSLs for each equipment class. The detailed discussion on the TSLs can be found in Chapter 9 of this TSD.

For each TSL, DOE calculated the NPV, as well as the NES, as the difference between a base case forecast (without amended standards) and the standards case (with amended standards). The NES refers to cumulative energy savings from 2012 through 2042. The NPV refers to cumulative monetary savings. DOE calculated net monetary savings in each year relative to the base case as the difference between total operating cost savings and increases in total installed cost. Cumulative savings are the sum of the annual NPV over the specified period. DOE accounted for operating cost savings until 2062; that is, until all the equipment installed through 2042 is retired.
Results of the national impact analysis (NIA) described here include: 1) national energy consumption and savings, 2) monetary value of energy savings to the nation as a result of standards, 3) increased total installed costs to the Nation as a result of standards, and 4) the net present value of energy savings (i.e., the difference between the present monetary values of energy savings and increased total installed costs).
To make the analysis more accessible and transparent to all stakeholders, DOE used an MS Excel spreadsheet model to calculate the energy savings and the national economic costs and savings from amended standards. The spreadsheet model is accessible on the Internet at (http://www.eere.energy.gov/buildings/appliance_standards/commercial/packaged_ac_hp.html). Details and instructions for using the spreadsheet are discussed in appendix F. A more detailed set of results is available in appendix G.
Unlike the LCC analysis, the NES spreadsheet does not use distributions for inputs or outputs. DOE examined sensitivities by applying different scenarios. DOE used the NES spreadsheet to perform calculations of energy savings and NPV, using the annual energy consumption and total installed cost data from the LCC analysis. DOE forecasted the energy savings, energy cost savings, equipment costs, and NPV of benefits for each of equipment classes from 2012 through 2042. The forecasts provided annual and cumulative values for all four output parameters as described above.

11-1

### 11.1.1 General Approach
Over time, in the standards case, equipment that is more efficient gradually replaces less efficient equipment. This affects the calculation of both the NES and NPV, both of which are a function of the total number of units in use and their efficiencies, and thus are dependent on annual shipments and equipment lifetime, including changes in shipments and retirement rates in response to changes in equipment costs due to standards. Both calculations start by using the estimate of shipments, and the quantity of units in service, that are derived from the shipments model.
With regard to estimating the NES, because more efficient PTACs and PTHPs gradually replace less efficient ones, the energy per unit of capacity used by the PTACs and PTHPs in service gradually decreases in the standards cas e relative to the base case. DOE calculated the NES by subtracting energy use under a standards scenario from energy use in a base-case scenario.
Unit energy savings for each equipment class are the same weighted-average values as calculated in the LCC and PBP spreadsheet. To estimate the total energy savings for each TSL, DOE first calculated the national site energy consumption (i.e., the energy directly consumed by the units of equipment in operation) for PTACs or PTHPs for each year, beginning with the expected effective date of the standards (2012), for the base case forecast and the standards case forecast. Second, DOE determined the annual site energy savings, consisting of the difference in site energy consumption between the base case and the standards case. Third, DOE converted the annual site energy savings into the annual amount of energy saved at the source of electricity generation (the source energy), using a site-to-source conversion factor. Finally, DOE summed the annual source energy savings from 2012 to 2042 to calculate the total NES for that period. DOE performed these calculations for each TSL considered in this rulemaking.
To estimate NPV, DOE calculated the net impact as the difference between total operating cost savings (including electricity, repair, and maintenance cost savings) and increases in total installed costs (which consists of MSP, sales taxes, distribution chain markups, and installation cost). DOE calculated the NPV of each TSL over the life of the equipment, using the following three steps. First, DOE determined the difference between the equipment costs under the TSL case and the base case in order to obtain the net equipment cost increase resulting from the TSL. Second, DOE determined the difference between the base case operating costs and the TSL operating costs, in order to obtain the net operating cost savings from the TSL. Third, DOE determined the difference between the net operating cost savings and the net equipment cost increase in order to obtain the net savings (or expense) for each year. DOE then discounted the annual net savings (or expenses) to the year 2008 for PTACs and PTHPs bought on or after 2012 and summed the discounted values to provide the NPV of a TSL. An NPV greater than zero shows net savings (i.e., the TSL would reduce customer expenditur es relative to the base case in present value terms). An NPV that is less than zero indicates that the TSL would result in a net increase in customer expenditures in present value terms.
Although voluntary energy efficiency programs may increase the share of energyefficient equipment prior to the implementation date of any new or amended energy conservation standards, DOE was not able to obtain information that quantified how such programs affect

11-2

### equipment efficiencies on a national basis. Consequently, DOE did not explicitly incorporate the impact of market-based voluntary energy efficiency programs into the shipment forecasts detailed in Chapter 10 of this TSD.
11.1.2 NES and NPV Input Summary
The important inputs of national energy consumption for each PTAC and PTHP equipment class include: 1) shipments of each equipment class, 2) existing stock of eachequipment class 3) national average energy consumption for each equipment class, and 4) site-tosource conversion factor to translate electricity consumption at the site of use into the amount of energy that must be generated at the power plant (source ) and then transmitted to the site where it is consumed. Chapter 10 provides a detailed description of the shipments model that DOE used to forecast future purchases of PTAC and PTHP equipment. Table 11.1.1 summarizes the inputs to the NES spreadsheet model. For each input a brief description of the data source is given.
Table 11.1.1 Summary of NES and NPV Model Inputs
Inputs Description Shipments Annual shipments from shipments model (see Chapter 10 of the TSD). Effective Date of Standard September 2012 Base Case Efficiencies Distribution of base-case shipments by efficiency level. Standard Case Efficiencies Distribution of shipments by efficiency level for each standards case. Standards case annual shipment-weighted market shares remain constant for base case and each standard level for all efficiencies above the TSL. All other shipments are at the TSL efficiency Annual Energy Use per Unit Annual national weighted-average values are a function of efficiency level (Chapter 7 of the TSD). Total Installed Cost per Unit Annual weighted-average values are a function of efficiency level (Chapter 8 of the TSD). Repair Cost per Unit Annual weighted-average values increase with manufacturer’s cost level (Chapter 8 of the TSD). Maintenance Cost per Unit Annual weighted-average value equals $117 (Chapter 8 of the TSD) Escalation of Electricity Prices 2008 EIA AEO forecasts (to 2030) and extrapolation for beyond 2030 (Chapter 8 of the TSD). Electricity Site-to-Source Conversion Factor Conversion factor varies yearly and is generated by EIA’s NEMS* model. Includes the impact of electric generation, transmission, and distribution losses. Discount Rate 3 and 7 percent real. Present Year Future costs are discounted to year 2008. * Chapter 14 on the utility im pact analysis provides more detail on NEMS.

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### 11.2 NATIONAL ENERGY SAVINGS

11.2.1 NES Definition
DOE calculates annual national energy savings for a given year (t) as the difference between two scenarios: a base case (without new or amended standards) and a standards case (with new or amended standards). Positive values of NES correspond to net annual energy savings, i.e., annual national energy consumption (AEC) with standards is less than AEC in the base case.

NES t 

### =AEC base 

### - AEC standard 

### Eq. 11.1
Cumulative energy savings are the sum over a defined time period from the implementation of a standard forward (from 2012 to 2042) of the annual national energy savings.

NES cum 

### = t 

### NES t 

### Eq. 11.2
DOE calculated the AEC by multiplying the number or stock of units of PTAC and PTHP equipment (by vintage) by the unit energy consumption (also by vintage) as shown by the following equation:

AEC = v 

### ( STOCK V 

### x UEC V 

### x src_conv t 

### ) Eq. 11.3
For the above expressions, DOE defined the following quantities:
AEC = Annual national energy consumption each year in quads, summed over vintages of PTAC and PTHP equipment stock, STOCK V 

### , NES = Annual national energy savings (in quads),
STOCK V 

### = Stock of PTAC and PTHP equipment (millions of units) of vintage V surviving in the year for which DOE calculated annual energy consumption, Vintages range from 1 year to approximately 20 years, a function of an assumed 10-year average lifetime for PTAC and PTHP equipment,
UEC V 

### = Annual unit energy consumption in kilowatt hours (kWh) of vintage V
, src_conv t 

### = Time-dependent conversion factor to convert from site energy (kWh) to source energy (quads) (Btu/kWh),

V = Year in which the PTAC or PTHP equipment was purchased as a new unit,

t = Year in the forecast (e.g., 2012 to 2042).
The stock of PTAC and PTHP equipment is dependent on annual shipments and the lifetime of the equipment. DOE believes that the shipment projections under the standards cases could be lower than those in the base case projection, because the higher installed costs would cause some customers to forego new equipment purchases. However, DOE does not have sufficient information that would allow a calculation of this effect. For the notice of final rule, DOE estimated the total shipments assuming that the projections are the same in both the base case and standards cases.

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### 11.2.2 NES Inputs
The inputs for the determination of NES are listed below:

Annual unit energy consumption (kWh/year) (section 11.2.2.1)

Shipments (section 11.2.2.2)

Equipment stock (section 11.2.2.3)

National annual energy consumption (section 11.2.2.4)

Site-to-source conversion factor (section 11.2.2.5)
11.2.2.1 Annual Unit Energy Consumption The annual unit energy consumption (UEC) is the site energy consumed by a PTAC or PTHP unit per year. The UEC is directly tied to the efficiency of the unit. Thus, knowing the efficiency of a PTAC or PTHP unit determines the corresponding annual energy consumption. DOE estimated the annual unit energy consumption for each of PTAC and PTHP equipment classes, as discussed in the energy use characterization analysis in Chapter 7. As described below, DOE determined annual forecasted shipment-weighted average equipment efficiencies that, in turn, enabled a determination of shipment-weighted annual energy consumption values. First, DOE converted the 2006 PTAC and PTHP equipment shipments by equipment class into market shares by equipment class, then adapted an economic model that employed a cost-based method used in the Energy Information Administration (EIA)’s National Energy Modeling System (NEMS) to estimate market shares for each equipment class by TSL. 1 

### Then, from those market shares and projections of shipments by equipment class, DOE extrapolated future trends of PTAC and PTHP equipment efficiency both for a base case scenario (i.e., without new standards) and various standards case scenarios (i.e., with new standards). The difference in equipment efficiency between the base case and standards cases was the basis for determining the reduction in per-unit annual energy consumption that could result from new standards. The market share for each equipment class by TSL is defined as EFF_Level_Share(i,y)
, for each equipment class y at TSL i . Because the average lifetime of each equipment class is presumed to be the same, and because DOE had no information regarding future changes in market shares between equipment classes, DOE assumed the market share for a particular equipment class to be constant over time. DOE calculated the EFF_Level_Share(i,y) for each TSL i using the following formula, based on the relative annualized cost of each TSL.



#  

 

 



 

###    

    



k

i v

yi n j j yi v

yi n j j yi m

j j 

### OC
r r IC OC
r r IC byiShare LevelEFF

1 ).( ),( ).( ),(

1 

### )1(1 )1(1 ),(__ 

### Eq. 11.4

11-5

### where EFF_Level_Share(i,y) = the market share of equipment class y at TSL i , IC(i, y) = installed costs of equipment class y at TSL i , i =1 to k

. OC(i,y) = annual operating cost (maintenance, repair, and energy cost) of equipment class y at TSL i,

r j 

### = private, risk-adjusted discount rate for risk class j . Derived by adding a “timepreference premium” to the risk-free real rate of return in the marketplace (4.39% longterm Treasury bond rate, minus the estimated long-term inflation rate of 2.2% = 2.19%) b

j 

### = market share of equipment users with risk class j , j =1 to m ,

v = risk penalty factor (also known as a measure of market heterogeneity)

n = equipment lifetime
The components for IC and OC came from the same inputs as the life-cycle cost analysis (see Chapter 8, life-cycle cost and payback period analysis). The annualization factor (r

j 

### /(1-(1+r j 

### ) -n 

### ) converts installed cost into its annualized equivalent, so that market shares are based on the relative annualized costs of each TSL, with (generally) higher annualized costs of higher TSLs leading to lower relative market shares. This is consistent with the approaches used in the EIA’s NEMS 1 

### and in Canada’s CIMS model 2 a 

### . The calibration constants are the private risk-based discount rates by risk class r j 

### , taken from the NEMS commercial model as shown in Table 11.2.1

, the default value of v = 10, taken from the CIMS model, and the equipment lifetime of 10 years.
Table 11.2.1 Risk Premiums by Risk Class (j) in the NEMS Commercial Model
Percentage of Users in Class Time Preference Premium Implied Real Discount Rate 1% 0.0% 2.14% 2% 13.6% 15.45% 10% 19.9% 21.61% 15% 30.9% 32.38% 20% 55.4% 56.35% 25% 152.9% 151.75% 27% 1000.0% 980.62% 100% Source: EIA’s NEMS Commercial Model



### Table 11.2.2 and Table 11.2.3 provide estimated base case shipment-weighted market shares for each of the equipment classes of PTACs and PTHPs, respectively, proposed in this rulemaking.

a The CIMS Model was originally known as the Canadian Integrated Modeling System, but as the model is now being applied to other countries, the acronym is now used as its proper name.

11-6

### Table 11.2.2 Shipment-Weighted Market Shares by Efficiency Level for PTACs, Base Case

Equipment Class Cooling Capacity Shipment-Weighted Market Shares by Efficiency Level *

Baseline (ASHRAE 90.1-1999) Level 1 Level 2 Level 3 Level 4Standard Size PTAC 10,000 Btu/h 22.6 % 21.0% 19.9% 18.8% 17.7% > 10,000 Btu/h 22.8% 21 .1% 19.9% 18.7% 17.5%

Equipment Class Cooling Capacity Baseline (ASHRAE 90.1-1999) Level 1 Level 2 Level 3 Non-Standard Size PTAC All Capacity 27.4% 25.4% 24.3% 22.9%
* Shares may not add to 100% exactly due to rounding.



### Table 11.2.3 Shipment-Weighted Market Shares by Efficiency Level for PTHPs, Base Case

Equipment Class Cooling Capacity Shipment-Weighted Market Shares by Efficiency Level * Baseline (ASHRAE 90.1-1999) Level 1 Level 2 Level 3 Level 4Standard Size PTHP 10,000 Btu/h 22 .5% 20.5% 19.8 % 19.1% 18.1% > 10,000 Btu/h 22.8% 20 .7% 19.9% 18.8% 17.8%

Equipment Class Cooling Capacity Baseline (ASHRAE 90.1-1999) Level 1 Level 2 Level 3 Non-Standard Size PTHP All Capacity 27.4% 25.4% 24.3% 22.9%
* Shares may not add to 100% exactly due to rounding. 

### To project changes in weighted average TSLs as amended standards above baseline efficiency level (i.e., ASHRAE/IESNA Standard 90.1-1999) b 

### are introduced, DOE assumed that market shares above the minimum permitted efficiency level would be reassigned to the new minimum level (i.e., the amended standard). This is called a “roll-up” scenario. For example, if TSL 5 (Efficiency Level 3 in this case) was imposed as the new standard in 2012 on standard size PTAC with a cooling capacity of 9,000 British thermal units per hours (Btu/h) equipment, then the market shares for baseline efficiency level, Level 1 and Level 2 would be assigned to TSL 3, which would result in a total market share of 82.3 percent, i.e., by adding 22.6 percent,

b ASHRAE/IESNA Standard 90.1-1999 stands for the American Society of Heating, Refrigerating, and AirConditioning Engineers, Inc. (ASHRAE) and the Illumi nating Engineering Society of North America (IESNA) Standard 90.1-1999, “Energy Standard for Buildings Except Low-Rise Residential Buildings” (ASHRAE/IESNA Standard 90.1-1999)

.

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### 21.0 percent, 19.9 percent, and 18.8 percent from the first four columns of the first row in Table 11.2.2, beginning in 2012. The market shares for Level 4 (TSL 6) would not be affected because the market already has a choice of that equipment with TSL 5 also available. DOE, thus, assumed that the new standard would not affect the relative attractiveness of equipment with efficiencies higher than the standard.
As stated earlier, annual energy consumption values are tied directly to the efficiency of the equipment. Table 11.2.4 provides annual energy consumption values for specific TSLs for all six representative cooling capacities of PTACs and PTHPs.

Table 11.2.4 Annual Unit Energy Consumption by Efficiency Level

Equipment Class Representative Cooling Capacity Annual unit energy consumption (kWh/year/unit) Baseline (ASHRAE 90.1-1999) Level 1 Level 2 Level 3 Level 4

Standard Size PTAC 9,000 Btu/h 1,045 1,026 1,013 1,001 990 12,000 Btu/h 1,317 1,294 1,279 1,264 1,251 Standard Size PTHP 9,000 Btu/h 2,063 2,013 1,984 1,957 1,945 12,000 Btu/h 2,467 2,406 2,370 2,356 2,343

Equipment Class Representative Cooling Capacity Baseline (ASHRAE 90.1-1999) Level 1 Level 2 Level 3

NonStandard Size PTAC 11,000 Btu/h 1,658 1,584 1,559 1,536

NonStandard Size PTHP 11,000 Btu/h 2,661 2,533 2,508 2,465



### For the annual shipment-weighted efficiency levels specified in the base case and standards case efficiency scenarios, DOE calculated the shipment-weighted UEC values in Table 11.2.5. For each equipment class, the value shown for a given TSL is the efficiency weighted average annual unit energy consumption, after taking into account the non-availability of equipment at the TSL shown below.

11-8

### Table 11.2.5 Shipment-Weighted Average Annual Unit Energy Consumption by Trial Standard Level

Equipment Class Representative Cooling Capacity Shipment-weighted average annual unit energy consumption (kWh/year/unit)

TSL 1 TSL 2 TSL 3 TSL A TSL 4 TSL 5 TSL 6 (Max Tech) Standard Size PTAC 9,000 Btu/h 1,012 1,012 1,007 1,007 1,012 999 990 12,000 Btu/h 1,278 1,278 1,271 1,278 1,278 1,262 1,251 Standard Size PTHP 9,000 Btu/h 1,984 1,972 1,972 1,955 1,955 1,955 1,945 12,000 Btu/h 2,378 2,363 2,363 2,363 2,354 2,354 2,343

Equipment Class Representative Cooling Capacity TSL 1 TSL 2 TSL 3 TSL 4 TSL 5

NonStandard Size PTAC 11,000 Btu/h 1,567 1,567 1,554 1,567 1,536

NonStandard Size PTHP 11,000 Btu/h 2,511 2,498 2,498 2,465 2,465



### 11.2.2.2 Shipments
DOE forecasted shipments for the base case and all standards cases (see Chapter 10, shipment analysis).
11.2.2.3 Equipment Stock
In a given year, PTAC and PTHP equipment stock is the total units of PTAC and PTHP equipment shipped from earlier years which survive in that year. The NES spreadsheet model keeps track of the total number of PTAC and PTHP units shipped each year. DOE assumed that the existing PTAC and PTHP units are retired by following a Weibull distribution with an average lifetime of 10 years. The Weibull distribution shows that approximately 8 percent of the existing PTAC and PTHP units are retired from 2012 to 2019 (i.e. by year 7), then tail off gradually to less than one percent per year by year 20. Retired units are replaced until 2042. For units shipped in 2042, any units still remaining at the end of 2062 are replaced.
11.2.2.4 National Annual Energy Consumption
The national AEC is the product of the annual UEC and the stocks of PTAC and PTHP units of each vintage. This approach accounts for differences in unit energy consumption from year to year. Equation 11.3 above was used for determining the national annual energy consumption of PTAC and PTHP equipment.

11-9

### In determining AEC, DOE initially calculated the annual energy consumption at the site (i.e., electricity in kWh consumed by the PTAC and PTHP unit). DOE then calculated primaryenergy consumption converted from site energy consumption by applying a marginal site-tosource conversion factor to account for losses associated with the generation, transmission, and distribution of electricity.

11.2.2.5 Site-to-Source Conversion Factor
The site-to-source conversion factor is the multiplier used for converting site energy consumption, expressed in kWh, into primary or source energy consumption, expressed in quads. The site-to-source conversion factor accounts for losses in electricity generation, transmission, and distribution. DOE used annual site-to-source marginal conversion factors based on a detailed analysis contained in appendix H. These factors take into account the fact that energy savings that would occur as a result of adopting more efficient equipment standard for PTACs and PTHPs would be most likely to reduce demand for energy from power plants used for peaking power and load following, and which have heat rates lower than the U.S. average values. As shown in Table 11.2.6, the conversion factors vary over time, due to projected changes in electricity generation sources (i.e., the power plant types projected to provide electricity to the country). Detailed discussion on calculations of marginal site-to-source conversion factors can be found in appendix H.

Table 11.2.6 Marginal Site-to-Source Conversion Factors (Btu/kWh)

Year PTACs Year PTHPs 2012 9,191 2012 8,111 2013 9,191 2013 8,111 2014 9,073 2014 8,368 2015 9,756 2015 9,080 2016 10,012 2016 9,186 2017 10,491 2017 9,359 2018 10,293 2018 9,587 2019 10,103 2019 9,909 2020 10,961 2020 10,478 2021 11,647 2021 10,573 2022 12,602 2022 10,756 2023 12,007 2023 10,312 2024 11,940 2024 10,394 2025 11,797 2025 10,674 2026 12,477 2026 11,306 2027 13,212 2027 11,602 2028 13,654 2028 11,739 2029 13,978 2029 11,885 2030-2042 13,978 2030-2042 11,885

11-10

### 11.3 NET PRESENT VALUE

11.3.1 Net Present Value Definition
The NPV is the value in the present of a time series of costs and savings. The NPV is given by the equation:

NPV = PVS – PVC Eq. 11.5 where PVS = present value of operating cost savings (including energy, repair, and maintenance costs), PVC = present value of increased total installed costs (including equipment and installation).

The PVS and PVC are determined according to the following expressions:

PVS 

### = 

# 

t 

### OCS t 

### x 

### DF t 

### Eq. 11.6

PVC 

### = 

# 

t 

### TIC t 

### x 

### DF t 

### Eq. 11.7 where: OCS = total annual operating cost savings, TIC = total annual inst alled cost increases, DF = discount factor,
t = year ( PVS is summed over 2012–2062, and PVC is summed over 2012–2062).

DOE determined the contribution to PVC for each year, from the effective date of the amended standard (year 2012) to the year 2062, discounted for the final rule analysis, to the year 2008. All dollar values are reported in constant 2007 dollars. The contribution to PVS was calculated for each year, from the effective date of the same amended standard (year 2012) to the year when units purchased in 2042 retire (assumed to be 2062). DOE calculated costs and savings as the difference between a standards case (i.e., with an amended standard) and a base case (i.e., without new standards). DOE calculated a discount factor from the discount rate and the number of years between the “present” (i.e., year to which the sum is being discounted) and the year in which the costs and savings occur. The net present value is the sum over time of the discounted net savings, which is equivalent to the approach shown in Eq. 11.5 to Eq. 11.7.
11.3.2 Net Present Value Inputs
The inputs to the NPV calculation are listed below:

Total Annual Installed Cost (section 11.3.2.1)

Total Annual Operating Cost Savings (section 11.3.2.2)

Discount Factor (section 11.3.2.3)

Present Value of Costs (section 11.3.2.4)

Present Value of Savings (section 11.3.2.5)

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### 11.3.2.1 Total Annual Installed Cost
The increase in the total annual installed cost is equal to the annual change in the per-unit total installed cost (diff erence between base case and standa rds case) multiplied by the shipments forecasted in the standard case. The total installed cost includes both the equipment cost and the installation price. DOE based average equipment costs on average manufacturer selling prices multiplied by average overall markup values (see Chapter 8, life-cycle cost and payback period analyses). DOE based average installation prices on nationally representative values for each equipment class (see Chapter 8). Table 11.3.1 shows the resulting average total installed costs per unit for each of the equipment classes of PTAC and PTHP equipment by efficiency levels.
Table 11.3.1 Average Total Installed Cost per Unit by Efficiency Level (2007$)

Equipment Class Representative Cooling Capacity Average Total Installed Co st per Unit (2007$) Baseline (ASHRAE 90.1-1999) Level 1 Level 2 Level 3 Level 4

Standard Size PTAC 9,000 Btu/h $1,165 $1,178 $1,188 $1,197 $1,208 12,000 Btu/h $1,404 $1,420 $1,432 $1,444 $1,458 Standard Size PTHP 9,000 Btu/h $1,275 $1,296 $1,306 $1,315 $1,325 12,000 Btu/h $1,511 $1,537 $1,549 $1,561 $1,575

Equipment Class Representative Cooling Capacity Baseline (ASHRAE 90.1-1999) Level 1 Level 2 Level 3

Non-Standard Size PTAC 11,000 Btu/h $1,515 $1,538 $1,550 $1,564

Non-Standard Size PTHP 11,000 Btu/h $1,632 $1,657 $1,669 $1,683



### DOE developed base case and standards case energy efficiency scenarios as discussed in section 11.2.2.1. For both the base case and standards case energy efficiency scenarios, DOE calculated annual shipment-weighted average efficiencies. Associated with each annual shipment-weighted average efficiency value, DOE assigned a total installed cost, based on shipment-weighted total installed cost for all TSLs. DOE based the relationship between efficiency and total installed cost for each PTAC and PTHP equipment class on the data in Table 11.3.2. As shown in Table 11.3.2, DOE estimated the shipments-weighted installed cost. DOE determined forecasted average shipments-weighted total installed costs based on the annual shipments by TSL.

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### Table 11.3.2 Shipment-Weighted Average Total Installed Cost per Unit by Trial Standard Level (2007$)

Equipment Class Representative Cooling Capacity Shipment-Weighted Average Total Installed Cost per Unit (2007$)

TSL 1 TSL 2 TSL 3 TSL A TSL 4 TSL 5 TSL 6 (Max Tech) Standard Size PTAC 9,000 Btu/h $1,189 $1,189 $1,193 $1,193 $1,189 $1,199 $1,208 12,000 Btu/h $1,434 $1,434 $1,439 $1,434 $1,434 $1,447 $1,458 Standard Size PTHP 9,000 Btu/h $1,307 $1,311 $1,311 $1,317 $1,317 $1,317 $1,325 12,000 Btu/h $1,551 $1,556 $1,556 $1,556 $1,564 $1,564 $1,575

Equipment Class Representative Cooling Capacity TSL 1 TSL 2 TSL 3 TSL 4 TSL 5

NonStandard Size PTAC 11,000 Btu/h $1,547 $1,547 $1,553 $1,547 $1,564

NonStandard Size PTHP 11,000 Btu/h $1,666 $1,672 $1,672 $1,683 $1,683



### 11.3.2.2 Total Annual Operating Cost Savings
The annual operating cost savings to the Nation are equal to the change in the annual operating costs (difference between base case and standards case) per unit multiplied by the shipments forecasted in the standards case. The annual operating cost includes electricity, repair, and maintenance costs.
Annual Electricity Cost Savings. As described in Chapter 8, DOE calculated annual electricity costs based on average State-level commercial electricity prices. To calculate annual energy cost savings for a particular equipment class in a given year, DOE first calculated the annual energy costs in each forecast year at each TSL from Table 11.2.5 multiplied by 1) theunits of surviving equipment stock in the equipment class in each year, and then 2) by the salesweighted national average electricity prices for the four business types in Chapter 8. To determine energy cost savings, the national energy costs at each TSL were then subtracted from the national energy costs at the baseline level.
Annual Repair Costs. DOE based average annual repair costs on the value of the PTAC and PTHP equipment (see Chapter 8). Table 11.3.3 shows the average per-unit repair costs for each of the equipment classes of PTACs and PTHPs. The NES spreadsheet provides the capability to allow repair costs to differ by the price of the PTAC and PTHP equipment, and therefore by TSL. For the purposes of this final rule analysis, DOE assumed the repair costs to increase in each equipment class as the manufacturer selling price increases, as shown in Table 11.3.3.

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### Table 11.3.3 Average Annual Repair Cost per Unit (2007$)

Equipment Class Representative Cooling Capacity Average Annual Repair Cost per Unit (2007$) Baseline (ASHRAE 90.1-1999) TSL 1 TSL 2 TSL 3 TSL A TSL4 TSL 5 TSL 6 (Max Tech) Standard Size PTAC 9,000 Btu/h $15.17 $15.47 $15.47 $15.68 $15.68 $15.47 $15.91 $16.14 12,000 Btu/h $15.17 $15.48 $15.48 $15.71 $15.48 $15.48 $15.96 $16.22 Standard Size PTHP 9,000 Btu/h $15.17 $15.60 $15.79 $15.79 $16.00 $16.00 $16.00 $16.21 12,000 Btu/h $15.17 $15.63 $15.84 $15.84 $15.84 $16.07 $16.07 $16.30

Equipment Class Representative Cooling Capacity Baseline (ASHRAE 90.1-1999) TSL 1 TSL 2 TSL 3 TSL4 TSL 5

NonStandard Size PTAC 11,000 Btu/h $15.17 $15.57 $15.78 $15.78 $16.03 $16.03

NonStandard Size PTHP 11,000 Btu/h $15.17 $15.57 $15.76 $15.76 $15.98 $15.98



### Annual Maintenance Costs. DOE was unable to locate any data on annual preventive maintenance cost (see Chapter 8), but annual maintenance is believed to be a relatively simple and inexpensive process for PTAC and PTHP equipment. An annual value of $117 per unit was assigned to all equipment. Table 11.3.4 shows the resulting annual maintenance costs per unit, which does not vary with TSL.
Table 11.3.4 Average Annual Maintenance Cost per Unit (2007$)
Equipment Classes Cost per Unit ($2007) Standard Size PTAC $117 Standard Size PTHP $117 Non-Standard Size PTAC $117 Non-Standard Size PTHP $117



### 11.3.2.3 Discount Factor
DOE determined present value of monetary values in future years using the discount factor. The discount factor DF is described by the equation:

tpt 

### r  

### )1( DF  1 Eq. 11.8



### where:

r = discount rate,
t = year the monetary value is accrued,
t P 

### = year in which the present value is being determined.
DOE estimated national impacts with both a three percent and a seven percent real (adjusted for inflation) discount rate as the average real rate of return on private investment in the

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### U.S. economy. These discount rates are used in accordance with the Office of Management and Budget (OMB)’s guidance to Federal agencies on the development of regulatory analysis (OMB Circular A-4, September 17, 2003), and section E., “Identifying and Measuring Benefits and Costs,” therein. DOE defined the present year as 2008 for the final rule analysis.

11.3.2.4 Present Value of Costs


### The present value of increased installed costs is the annual installed cost increase in each year (i.e., the difference between the standards case and base case), discounted to the present, and summed for the time period over which DOE is considering the installation of PTAC and PTHP equipment (i.e., from the effective date of standards, 2012, to the year 2042, the last year in which installations occur).

The increase in total installed cost re fers to both equipment cost and installation cost associated with the higher energy efficiency of PTAC and PTHP units purchased in the standards case compared to the base case. DOE calculated the difference in installed cost as the difference in between total installed costs with and without the standard case scenarios. Total installed cost in each case was calculated as the unit installed costs of equipment at each TSL, times the number of units of each TSL shipped in each year with and without the standard.
11.3.2.5 Present Value of Savings


### The present value of operating cost savings is the annual operating cost savings (i.e., the difference between the base case and standards case) discounted to the year 2008, the year of the publication of the final rule for this rulemaking, and summed over the period from the effective date, 2012, to the time when the last unit installed in 2042 is retired from service (assumed to be 2062). Savings are decreases in operating costs (including electricity, repair, and maintenance costs) associated with the higher energy efficiency of PTAC and PTHP units purchased in the standards case compared to the base case. Total annual operating cost savings is the savings per unit multiplied by the number of units of each vintage surviving in a particular year. Equipment consumes energy over its entire lifetime, and for units purchased in 2042, the PVS includes the cost of energy consumed until the un it is retired from service.

11.4 NES AND NPV RESULTS


### The NES spreadsheet model provides estimates of the NES and NPV due to various trial standard levels. The inputs to the NES spreadsheet have been discussed earlier in sections 11.2.2 (NES Inputs) and 11.3.2 (NPV Inputs).
11.4.1 National Energy Savings Results


### The following section provides NES results for each energy consumption level considered for the four equipment classes of packaged terminal air conditioner and heat pumps. Results are cumulative to 2042 and are shown as primary energy savings in quads. Inputs to the NES spreadsheet model are based on weighted-average values, yielding results which are discrete point values, rather than a distribution of values as in the life-cycle cost (LCC) analysis.

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### Table 11.4.1 shows the NES results for the trial standard levels analyzed for each equipment class of PTACs and PTHPs. DOE based all the results on electricity price forecasts from the 2008 EIA Annual Energy Outlook (AEO2008) Reference Case. In addition, Table 11.4.2 and Table 11.4.3 also show the magnitude of the energy savings if the savings are discounted at rates of 7 percent and 3 percent, respectively.
DOE reports both undiscounted and discounted values of energy savings. There is evidence that each TSL that is more stringent than the corresponding level in ASHRAE/IESNA Standard 90.1-1999. For the standard size PTAC and PTHP equipment, it results in additional energy savings, ranging from 0.015 quads to 0.068 quads for TSLs 1 through 6. In addition, the additional energy savings for the non-standard equipment range from 0.004 quads to 0.009 quads for TSLs 1 through TSLs 5, as shown in Table 11.4.1.

Table 11.4.1 Cumulative National Energy Savings for PTACs and PTHPs

Equipment Class Cumulative Energy Savings (2012-2042) (quads)
TSL 1 TSL 2 TSL 3 TSL A TSL 4 TSL 5 TSL 6 Standard Size PTAC 0.005 0.005 0.012 0.008 0.005 0.021 0.033

Standard Size PTHP 0.009 0.019 0.019 0.024 0.028 0.028 0.035

Total 0.015 0.024 0.031 0.032 0.033 0.049 0.068

Equipment Class TSL 1 TSL 2 TSL 3 TSL 4 TSL 5 Non-Standard Size PTAC 0.002 0.002 0.003 0.002 0.004

Non-Standard Size PTHP 0.002 0.003 0.003 0.004 0.004

Total 0.004 0.004 0.005 0.006 0.009



### * Detailed changes may not su m to total due to rounding.

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### Table 11.4.2 Cumulative National Energy Savings for PTACs and PTHPs Based on Seven-Percent Discount Rate

Equipment Class Cumulative Energy Savings (2012-2042) (quads)
TSL 1 TSL 2 TSL 3 TSL A TSL 4 TSL 5 TSL 6 Standard Size PTAC 0.001 0.001 0.003 0.002 0.001 0.005 0.007

Standard Size PTHP 0.002 0.004 0.004 0.005 0.006 0.006 0.008

Total 0.003 0.006 0.007 0.007 0.008 0.011 0.015

Equipment Class TSL 1 TSL 2 TSL 3 TSL 4 TSL 5 Non-Standard Size PTAC 0.000 0.000 0.001 0.000 0.001

Non-Standard Size PTHP 0.000 0.001 0.001 0.001 0.001

Total 0.001 0.001 0.001 0.001 0.002



### * Detailed changes may not su m to total due to rounding.



### Table 11.4.3 Cumulative National Energy Savings for PTACs and PTHPs Based on Three-Percent Discount Rate

Equipment Class Cumulative Energy Savings (2012-2042) (quads)
TSL 1 TSL 2 TSL 3 TSL A TSL 4 TSL 5 TSL 6 Standard Size PTAC 0.003 0.003 0.006 0.004 0.003 0.011 0.017

Standard Size PTHP 0.005 0.010 0.010 0.012 0.014 0.014 0.018

Total 0.007 0.012 0.016 0.016 0.017 0.025 0.035

Equipment Class TSL 1 TSL 2 TSL 3 TSL 4 TSL 5 Non-Standard Size PTAC 0.001 0.001 0.001 0.001 0.002

Non-Standard Size PTHP 0.001 0.001 0.001 0.002 0.002

Total 0.002 0.002 0.003 0.003 0.004



### * Detailed changes may not sum to total due to rounding.

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### 11.4.2 Annual Costs and Savings


### As a prelude to providing the NPVs for each trial standard level in each equipment class, this section presents the annual equipment cost (or total installed cost) increases and annual operating cost savings at the national level.
Figure 11.4.1 shows the changes over time of the non-discounted annual equipment price increases and the non-discounted operating cost savings at TSL 6 for standard size PTAC with a cooling capacity of 9,000 Btu/h. The total net annual impact is the discounted value of the difference between annual equipment purchases and annual operating costs at a seven percent discount rate. Appendix G shows comparable figures for other TSLs and other equipment classes. The annual equipment price change is the increase in equipment price for equipment purchased each year over the period 2012–2042. The annual operating cost savings is the savings in operating costs for equipment purchased, and which have not been retired, for each year over the time period 2012-2062. DOE determined the annual costs and savings presented in each figure based on the AEO2008 Reference Case. The NPV is the difference between the cumulative annual discounted savings and the cumulative annual discounted costs.

Net Savings

(0.0065) 0.0000 0.0065

2012 2016 2020 2024 2028 2032 2036 2040 2044 2048 2052 2056 2060
YearBillion 2007$

Undiscounted Total Annual Operating Savings Undiscounted Annual Equipment Purchase Savings Discounted Total Net Annual Impact



### Figure 11.4.1 National Annual Costs and Savings for Standard Size PTAC, 9,000 Btu/h Cooling Capacity, TSL6

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### Figure 11.4.1 initially shows smaller annual operating cost savings compared to the increased equipment price costs (shown on the figure as operating savings). For all trial standard levels, operating cost savings increase with time through 2042, as more and more equipment meeting the efficiency standard comprises the packaged terminal air conditioner and heat pump stock. The savings then decrease as the equipment retires and is not replaced.

11.4.3 Net Present Value Results


### The following section provides NPV results for the trial standard levels considered for the equipment classes of PTACs and PTHPs. Results are cumulative and are shown as the discounted value of these savings in dollar terms. The present value of increased total installed costs is the total installed cost increase (i.e., the difference between the trial standard case and base case), discounted to 2008, and summed over the time period in which DOE evaluates the impact of standards (i.e., from the effective date of standards, 2012, to the year 2062).

Table 11.4.4 shows the NPV results for the TSLs considered for PTAC and PTHPs based upon a seven percent discount rate. DOE based all results on electricity price forecasts from the AEO2007 Reference Case. Detailed results showing the breakdown of the NPV into national equipment costs and national operating costs are provided in appendix G.

Table 11.4.4 Cumulative NPV Results Based on a Seven-Percent Discount Rate (Billion 2007$)

Equipment Class Cumulative NPV – 7% Discount Rate (billion 2007$)*
TSL 1 TSL 2 TSL 3 TSL A TSL 4 TSL 5 TSL 6 Standard Size PTAC ($0.003) ($0.003) ($0.009) ($0.005) ($0.003) ($0.020) ($0.038)

Standard Size PTHP $0.004 $0.012 $0.012 $0.015 $0.010 $0.010 ($0.003)

Total $0.001 $0.008 $0.002 $0.010 $0.006 ($0.011) ($0.041)

Equipment Class TSL 1 TSL 2 TSL 3 TSL 4 TSL 5 Non-Standard Size PTAC $0.002 $0.002 $0.003 $0.002 $0.004

Non-Standard Size PTHP $0.003 $0.004 $0.004 $0.006 $0.006

Total $0.005 $0.006 $0 .007 $0.008 $0.010
* Values in parentheses indicate negative NPV. Detailed changes may not sum to total due to rounding.

### Table 11.4.5 provides the NPV results based on the three percent discount rate and electricity price forecasts from the AEO2007 Reference Case. As with the NPV results based upon a seven percent discount rate, detailed results showing the breakdown of the NPV into national equipment costs and national operating costs based upon a three percent discount rate are provided in appendix G.

Table 11.4.5 Cumulative NPV Results based on a Three-Percent Discount Rate (Billion 2007$)

Equipment Class Cumulative NPV – 3% Discount Rate (billion 2007$)*
TSL 1 TSL 2 TSL 3 TSL A TSL 4 TSL 5 TSL 6 Standard Size PTAC ($0.001) ($0.001) ($0.006) ($0.003) ($0.001) ($0.020) ($0.043)

Standard Size PTHP $0.018 $0.044 $0.044 $0.057 $0.050 $0.050 $0.034

Total $0.017 $0.043 $0.038 $0.054 $0.049 $0.031 ($0.010)

Equipment Class TSL 1 TSL 2 TSL 3 TSL 4 TSL 5 Non-Standard Size PTAC $0.006 $0.006 $0.008 $0.006 $0.011

Non-Standard Size PTHP $0.008 $0.010 $0.010 $0.017 $0.017

Total $0.014 $0.016 $0 .019 $0.023 $0.029
* Values in parentheses indicate negative NPV. Detailed changes may not sum to total due to rounding.

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### REFERENCES



### 1. 1. U.S. Department of Energy/Energy Information Administration (DOE/EIA), Annual Energy Outlook 2008 , June 2008. Washington, D.C. DOE/EIA-0383(2008).

2. Energy Information Administration (EIA). National Energy Modeling System Commercial Model (2004 Version).

3. ERG/MKJ. Energy Research Group & M.K. Jaccard & Associates. 2000. Integration of GHG Emissions Reduction Options using CIMS. <<http://www.emrg.sfu.ca/reports/Rollup.pdf>> (05 June 2001).

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