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Residential Central Air-Conditioner, Small Duct, High Velocity (SDHV) Systems Standards Rulemaking 

# Life-Cycle Cost Analysis

Draft Report for Review 

## Prepared for: Building Technology Program Office of Energy Efficiency and Renewable Energy U.S. Department of Energy Prepared by: Lawrence Berkeley National Laboratory Energy Analysis Department 1 Cyclotron Road MS 90-4000 Berkeley, CA 94720 November 26, 2002

### 1.1 INTRODUCTION ........................................:..............3

1.2 INPUTS TO LCC ANALYSIS ............................................. 3 1.2.1 Baseline and Standard-Level Consumer Equipment Prices ................. 4 1.2.2 Duct Total Installed Cost ............................................ 5 1.2.3 Electricity Price Trend .............................................. 6 1.2.4 Repair Costs ...................................................... 7 1.2.5 Summary of Weighted
-Average Inputs to the LCC Analysis for SDHV ....... 9 1.3 LCC RESULTS ........................................................ 10 1.3.1 Baseline LCC .................................................... 11 1.3.2 Change in LCC ..................................................12 1:3.3 LCC Results Based on ±2 Percent Threshold ........................... 16 1.4 REFERENCES ........................................................ 19

TABLES Table 1.2 . 1 Weighted
-Average Baseline and Standard
-Level SDHV Consumer Equipment Prices

(2001 $) .......................................................... 5 Table 1.2.2 SDHV Weighted-Average Annualized Repair Costs (2001$) ............... 9 Table 1.2.3 Summary of Conventional CAC Product Weighted
-Average Inputs ......... 10 Table 1.3.1 Baseline LCC: Mean, Median, Minimum, and Maximum Values (2001 $) .... 12 Table 1.3.2 Summary of LCC Results .......................................... 16 Table 1.3.3 Summary of LCC Results based upon ±2 Percent Threshold criterion ....... 18
FIGURES Figure 1.2.1 Electricity Price Trends ............................................. 7 Figure 1.3.1 Baseline LCC Distribution .......................................... 11 Figure 1.3.2 Frequency Chart of Differences for 10.51 SEER ........................ 14 Figure 1.3.3 Cumulative Chart of LCC Differences for 10.51 SEER ................... 15

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### SMALL DUCT, HIGH VELOCITY LIFE-CYCLE COST ANALYSIS

1.1 INTRODUCTION
The life-cycle cost (LCC) analysis for small duct, high velocity (SDHV) products was conducted with the same spreadsheet model that was used for the LCC analysis of conventional central air conditioner (CAC) product classes. Minor modifications were made to the spreadsheet model to -incorporate inputs specific to SDHV products . The LCC model was developed using Microsoft Excel spreadsheets combined with Crystal Ball (a commercially available add
-in). The LCC analysis models both the uncertainty and the variability in the model ' s inputs using Monte Carlo simulation and probability distributions. The LCC results are displayed as distributions of impacts compared to specified baseline conditions. Results are presented later and are based on 10 ,000 samples per Monte Carlo simulation run. The conventional CAC product LCC analysis and spreadsheet model are detailed in the Residential Central Air Conditioner and Heat Pump Technical Support Document (TSD) under Chapter 5, Life-Cycle Cost and Payback Period Analysis'.

1.2 INPUTS TO LCC ANALYSIS
The LCC analysis for SDHV products utilizes the same inputs as those used in the LCC analysis conducted for conventional CAC products but with the following exceptions: 1) consumer equipment prices for baseline and standard-level SDHV products are based on a
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### detailed engineering analysis conducted specifically for these products; 2) inclusion of an

additional consumer price for the installation of the duct work; 3) electricity price trends are based on projections from the Annual Energy Outlook 2002 (AE02002); and 4) repair costs are based on SDHV consumer equipment prices. All prices used in the SDHV LCC analysis are in 2001 dollars. Prices carried over from the conventional CAC product analysis to the SDHV analysis were converted from 1998 dollars to 2001 dollars using the annual consumer price indices (CPI) for all urban consumersa from the Bureau of Labor Statistics2.

• 1.2.1 Baseline and Standard -Level Consumer Equipment Prices
Table 1.2.1 presents the weighted-average baseline and standard-level consumer equipment prices for SDHV products. Incremental equipment price increases due to an efficiency increase are actually characterized with normal probability distributions. Refer to the Residential Central Air-Conditioner, Small Duct, High Velocity (SDHV) Systems Standards Rulemaking: Engineering Analysis for more details. The consumer equipment prices were determined with markups and sales taxes different from those used for the conventional CAC product analysis. The prices in Table 1.2.1 are for the equipment only. The installation prices of the equipment and the duct work are not included.

8 The 1998 and 2001 annual CPIs equal 163.0 and 177.1, respectively. 

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### Table 1.2.1 Weighted-Average Baseline and Standard-Level SDHV Consumer Equipment Prices (2001$) SEER Incremental Price Increase Total Consumer Equipment Price 10.0 - $2,067 10.15 $26.35 $2,093 10.29 $52.70 $2,120 10.41 $79.05 $2,146 10.51 $105.40 $2,172 10.59 $131.75 $2,199 10.65 $158.10 $2,225 10.71 $184.45 $2,251 10.77 $210.80 $2,278 10.82 $237.15 $2,304 10.87 $263.50 $2,330 10.92 $289.85 $2,357 10.97 $316.20 $2,383 11.0 $325.76 $2,393 11.5 $431.16 $2,498 12.0 $668.31 $2,735 12.5 $835.25 $2,902 13.0 $1,072.40 $3,139 13.4 $1,283.20 $3,350



### 1.2.2 Duct Total Installed Cost

The total installed cost of the duct work was included in the SDHV LCC analysis. The total installed cost is the cost to the consumer of the labor and materials needed to install the duct work and was determined to be $2720
. Refer to the EngineeringAnalysis of SDHV Central AirConditioning Systems for more details on how the installed cost for the duct work was determined.

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### 1.2.3 Electricity Price Trend

In order to forecast electricity prices, a projected price trend in national average electricity prices is applied to each household ' s and commercial building's energy prices. The SDHV LCC analysis allows for the following scenarios to be analyzed:
• Constant energy prices
• Energy Information Administration AEO 2002, High Economic Growth3
• Energy Information Administration AEO 2002, Reference Case4
• Energy Information Administration AEO 2002, Low Economic Growths
• Gas Research Institute (GRI) 1998 Baseline Projection6
Figure 1.2.1 shows the trends for the last four of the above projections. The values in later years (i.e. after 2015 for GRI and after 2020 for AEO 2002) are extrapolated from their relative sources. Extrapolation is needed because the sources used do not forecast beyond 2015 for GRI and 2020 for AEO 2002. For the AEO 2002 trends, extrapolations are based on the average growth rate from 2010 to 2020 . For the GRI trend, the extrapolation is based on the



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### average growth rate from 2005 to 2015. LCC results presented later are based on the AEO 2002

Reference Case price trend.

Figure 1.2 . 1 Electricity Price Trends 1.2.4 Repair Costs
The repair cost is the cost to the consumer for replacing or repairing components which have failed in the SDHV product. The assumed annualized repair cost for baseline ( 10 SEER) efficient SDHV products (i.e., the cost the consumer pays annually for repairing equipment) is based on the following expression:
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## RC=

Where, 

## 0.5 • EQP LIFE RC = repair cost, EQP = equipment price (consumer price for only the equipment), and LIFE = the average lifetime of the equipment ( 18.4 years).
If the efficiency of the condensing unit packaged with the SDHV unit has a seasonal energy efficiency ratio (SEER) rating of 13 or less, than the SDHV product is assumed to incur a one percent increase in repair cost over the baseline efficient equipment . If the condensing unit has an SEER rating greater than 13, the assumed annualized repair cost of the SDHV product is based on the equation presented above.
The rationale for assuming essentially flat repair costs for SDHV units that are coupled with condensing units that have efficiency ratings of up to and including 13 SEER pertains to the level of technology being used in the condensing units. For condensing units with ratings up through 13 SEER, system technology generally does not incorporate sophisticated electronic components which are believed to incur higher repair costs. Increases in condensing unit SEER are generally achieved through more efficient single-speed compressors or more efficient and/or larger heat exchanger coils. Condensing units with efficiencies beyond 13 SEER start to incorporate compressors which are generally believed to be more susceptible to failure.

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### Table 1.2.2 shows the weighted-average repair costs by standard-level. Since equipment

prices are a function of variables which are represented by distributions rather than single pointvalues, repair costs are actually represented by a distribution of values rather than just the weighted-average values shown in Table 1.2.2.

Table 1.2.2 SDHV Weighted-Average Annualized Repair Costs (2001$)

SDHV SEER Annualized Repair Cost a 10.0 through 10.99 11.0 through 12.2 greater than 13.4 $61 $62 $86 SDHV SEERs of 10 to 10.99 based on 12 SEER condensing units; SDHV SEERS of 11 to 12.13 based on 13 SEER condensing units; SDHV SEERs greater than 12.13 SEER based on 14 SEER condensing units.



### 1.2.5 Summary of Conventional CAC Product Weighted
-Average Inputs

Table 1.2.3 lists the weighted-average values for the various LCC inputs (other than consumer equipment prices and repair costs) taken from the conventional CAC product analysis that are being used in the SDHV LCC analysis. Note that although the weighted-average values are being provided, for most inputs, probability distributions are used to characterize the input. The sections of the conventional CAC product TSD from which the data are being drawn are also presented in Table 1.2.3.

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### Table 1.2.3 Weighted-Average LCC Input Values taken from the Conventional CAC

LCC Input Weighted
-Average Value Source Percent of units used in commercial applications a 10% CAC TSD, Section 5.1.4 Equipment Installation Cost (2001$) $1390 CAC TSD, Section 5.2.2.8 Residential = 1947 Baseline (10 SEER) Energy Use (kWh/yr)b Commercial = 5824 CAC TSD, Section 5.2.3.1 Combined = 2305 Residential = 9.46 Average Electricity Price (cents/kWh) Commercial = 8.49 CAC TSD, Section 5.2.3.5 Combined = 9.36 Residential = 9.16 Marginal Electricity Price (cents/kWh) Commercial = 8.64 CAC TSD, Section 5.2.3.6 Combined = 9.11 Maintenance Cost (2001$) $40 CAC TSD, Section 5.2.3.9 Lifetime (years) 18.4 CAC TSD, Section 5.2.3.10 10 - 10.99 SEER= $3630 Compressor Replacement Cost (2001$) 11- 12.13 SEER= $391d CAC TSD, Section 5.2.3.10 >12.13 SEER= $498e Discount Rate 5.6% CAC TSD, Section 5.2.3.11 a Value is a single-point value. b Standard-level energy use values are based on the ratio of the baseline efficiency (10 SEER) to the standard-level efficiency. Refer to TSD, Section 5.2.3.2 for more details.
' Range of SEERs based on 12 SEER condensing unit. As a result, 12 SEER conventional unit replacement cost is used. d Range of SEERs based on 13 SEER condensing unit. As a result, 13 SEER conventional unit replacement cost is used. Range of SEERS based on 14 SEER condensing unit. As a result, 18 SEER conventional unit replacement cost is used.



### 1.3 LCC RESULTS
LCC results are presented here for the standard-levels specified in Table 1.2.1. Results presented here are based on the inputs described above. As has been discussed earlier, the value of most LCC inputs are uncertain and are represented by a distribution of values rather than a single point-value. Thus, the LCC results will also be a distribution of values.

Product Analysis

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### 1.3.1 Baseline LCC

As stated earlier, the Monte Carlo method of analysis relying on Crystal Ball (i.e., random sampling from distributions) was used to conduct the LCC analysis. The following results presented here are based on 10,000 samples per Monte Carlo run.
The first step in developing LCC results is to develop the baseline LCC. Figure 1.3.1 shows the frequency chart for the baseline LCC for SDHV products. A frequency chart shows the distribution of LCCs with its corresponding probability of occurrence. Table 1.3.1 summarizes the baseline distributions depicted in Figures 1.3.1 by showing the mean, median, minimum, and maximum LCCs.

Forecast: LCC 10 SEER

d 10,000 Trials Frequency Chart .036 a

.027

.009 .0001-F $0 55 Outliers -1- 362

271.5

90.50

-0 $5,000 $10,000 $15,000 $20,000 

### Figure 1.3 .1 Baseline LCC Distribution

11Table 1.3.1 Baseline LCC: Mean, Median, Minimum, and Maximum Values (2001$) Minimum Median Mean Maximum Baseline LCC $6,160 $9,159 $9,843 $26,432



### 1.3.2 Change in LCC
The changes in LCC results are presented as differences in the LCC relative to the baseline central air conditioner or heat pump design. The LCC differences are depicted as a distribution of values. The primary results are presented in two types of charts within Crystal Ball: 1) a

frequency chart showing the distribution of LCC differences with its corresponding probability of occurrence and 2) a cumulative chart showing the cumulative distribution of LCC differences along with the corresponding probability of occurrence. In each chart, the mean LCC difference is provided along with the percent of the population for which the LCC will decrease.
In the explanation below, the two charts depicting the case for an 10.51 SEER efficiency level are used (Figures 1.3.2 and 1.3.3). In either chart (frequency or cumulative), the mean change (reduction of $4 in the examples here) is shown in a text box next to a vertical line at that value on the x-axis. The phrase "Certainty is 35.41% from -Infinity to $0" means that 35.41 percent of households will have reduced LCC with the increased efficiency level compared to the baseline efficiency level (i.e., 10 SEER).

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### Figure 1.3.2 is an example of a frequency chart. The y-axes show the number of

households ("Frequency" at right y-axis) and percent of all households ("Probability" at left yaxis). In this example, 10,000 households were examined ("10,000 trials") and all the almost all the results are displayed ("312 outliers"). The x-axis is the difference in LCC between a baseline efficiency level and a higher efficiency level (in this example, 10.51 SEER)., The x-axis begins with negative values on the left, which indicate that standards for those households provide savings (reduced LCC). Reduced LCC occurs when reduced operating expenses more than compensate for increased purchase expense. In Figure 1.3.2, going from the baseline efficiency level (10 SEER) to the 10.51 SEER efficiency level provides buildings with an average LCC reduction of $6, and range from reductions of $300 (at the left) to increases of $126 (at the right) depending upon the building. (The minimum and maximum values cannot be read with precision from the graph, but rather, the program provides them in a statistical summary. It should be noted that in this example, reductions in LCC extend to $1285 but, because they are considered outliers, are not shown.)

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## Forecast : LCC Difference

10,000 Trials Frequency Chart 312 Outliers .037 I -. 11 - 373 .02 - 279.7 - ^p .01 186.5-0 pp ^ I .00 93.25 pp^^ 6 1EII' ^^^ t^ean($6 .000 (6. -0 ($300) ($188) ($75) $38 $150

Certainty is 36.25% from -Infinity to $0 $ 

### Figure 1.3.2 Frequency Chart of Differences for 10.51 SEER The vertical axis in Figure 1.3.3 is the cumulative probability (left axis) or frequency (right axis) that the LCC difference will be less than the value on the horizontal axis. Starting at the left, there is a 0 percent probability that a household will have a reduction in LCC larger than $300 in absolute value (excluding outliers). At the right, there is a 100 percent probability that a household will have either a decrease in LCC or an increase in LCC of less than $126.

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## Forecast: LCC Difference

10,000 Trials Cumulative Chart 312 Outliers

Z 1.0001
.750 Z .500
Ir 11, 

### 11 I ^ 9NI 16 25 j 10000

= $6 ^Afl Mean .00 & glin 0 ® ($300) ($188) ($75) $38 $150

Certainty is 36.25% from -Infinity to $0 $ 

### Figure 1.3.3 Cumulative Chart of LCC Differences for 10.51 SEER A summary of the change in LCC from the baseline by percentile groupings (i.e., of the distribution of results) is provided below in Table 1.3.2. The mean and the percent of LCCs that are reduced for each standard-level are also shown. As an example of how to interpret the information in Table 1.3.2, the 10.51 SEER efficiency level is reviewed. The 10.51 SEER efficiency level in Table 1.3.2 (row 4) shows that the maximum (zero percentile column) change in LCC is savings of $1285. (Negative values are net savings.) For 90 percent of the cases studied (90th percentile), the change in LCC is a cost of $84 or less. . The largest increase in LCC is $126 (100th percentile). The mean change in LCC is a net savings of $6. The last column shows that 36 percent of the sample have reduced LCC (i.e., change in LCC less than or equal to zero). 1 j f a',R F i^ ^ I

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### The results in Table 1.3.2 indicate that efficiency levels up through 10.51 SEER achieve

mean LCC savings.

Table 1.3.2 Summary of LCC Results Change in LCC from Baseline Shown by Percentiles of the Distribution of Results (values in 2001$) Percent of Buildings with SEER 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Mean reduced LCC 10.15 ($331) ($49) ($25) ($12) ($3) $3 $8 $12 $16 $20 $30 ($8) 45% 10.29 ($716) ($87) ($43) ($17) ($2) $9 $18 $26 $33 $40 $61 ($11) 42% 10.41 ($1,206) ($115) ($53) ($19) $2 $18 $32 $42 $52 $62 $91 ($10) 38% 10.51 ($1,285) ($139) ($60) ($17) $10 $28 $45 $59 $71 $84 $126 ($6) 36% 10.59 ($1,242) ($149) ($59) ($11) $21 $43 $61 $78 $93 $108 $158 $4 33% 10.65 ($1,152) ($147) ($50) $5 $37 $62 $82 $99 $115 $132 $191 $20 29% 10.71 ($1,827) ($148) ($37) $21 $56 $81 $103 $121 $139 $157 $219 $35 26% 10.77 ($1,494) ($142) ($29) $34 $71 $100 $121 $141 $161 $182 $256 $51 24% 10.82 ($1,622) ($141) ($22) $42 $87 $119 $143 $164 $184 $206 $282 $64 23% 10.87 ($1,712 ($133) ($4) $62 $107 $137 $163 $186 $209 $233 $319 $83 21% 10.92 ($1,536 ($130) $5 $75 $122 $157 $185 $209 $232 $256 $348 $98 19% 10.97 ($1,928 ($127) $12 $86 $137 $176 $205 $231 $255 $282 $384 $115 19% 11.0 ($2,426) ($102) $43 $123 $170 $204 $233 $257 $280 $307 $406 $141 16% 11.5 ($2,407) ($182) $27 $131 $199 $248 $290 $326 $358 $396 $530 $161 18% 12.0 ($3,440) ($150) $130 $275 $367 $431 $487 $532 $578 $628 $837 $318 14% 12.5 ($2,860) $238 $533 $678 $773 $843 $908 $970 $1,048 $1,149 $1,648 $749 6% 13.0 ($4,239) $330 $681 $854 $968 $1,050 $1,116 $1,183 $1,261 $1,366 $1,843 $921 6% 13.4 ($2,598) $438 $824 $1,023 $1,140 $1,230 $1,309 $1,383 $1,466 $1,572 $2,175 $1,093 5%



### 1.3.3 LCC Results Based on ±2 Percent Threshold
The results in Table 1.3.3 show, the percent of households with reduced LCC. But considering that the baseline LCC for each product class is significantly greater than the LCC


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### differences shown in Tables 6, it is more useful to demonstrate which consumers experience

significant net LCC savings or costs due to a higher standard-level. We define significant as those consumers experiencing net LCC savings or costs which are greater than 2 percent of the baseline LCC.b Since for SDHV products the weighted-average baseline LCC is $9843, this translates to an LCC increase or decrease of approximately $197 or an annual expense of approximately $10 over the lifetime of the system.
Table 1.3.3 depicts the LCC results based on the above defined 2 percent threshold. Thetables show the average LCC values for the baseline level (10 SEER) and the various standardlevels analyzed. As presented earlier in Table 1.3.2, Table 1.3.3 also provides the difference in LCC at each efficiency level relative to the baseline. The differences represent either an LCC savings or an LCC cost increase. In addition, each table shows the subset of consumers (both residential and commercial) at each efficiency level who are impacted in one of three ways: consumers who achieve significant net LCC savings (i.e., LCC savings greater than 2 percent of the baseline LCC), consumers who are impacted in an insignificant manner by having either a small reduction or small increase in LCC (i.e., within ±2 percent of the baseline LCC), or consumers who achieve a significant net LCC increase (i.e., an LCC increase exceeding 2 percent of the baseline LCC). Accompanying each percentage value is the average LCC savings or increase that corresponds to each subset of consumers. For example, in the case of the 10.51 SEER efficiency level, the percentage of consumers with significant net savings is 6 percent and the corresponding average LCC savings for those consumers is $326. At 10.51 SEER, an b The use of the ±2 percent threshold to express LCC results was used in the conventional CAC product analysis. Refer to section 5.2.4.4 of the conventional product CAC TSD. 

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### overwhelming majority of the consumers (94 percent) are not impacted significantly by the

efficiency increase. The efficiency level where a majority of consumers (52 percent) begin to incur significant LCC increases is 11 SEER.

Table 1.3.3 Summary of LCC Results based upon ±2 Percent Threshold criterion Percent of Consumers with

EER verage

LCC Average

LCC (Savings) or Costs (2001$) Net

Savings (>2%) Average

LCC (Savings) or Costs (2001$) No

significant impact (<2%) Average

LCC (Savings) or Costs (2001 $) et Costs

(>2%) Average

LCC (Savings) or Costs (2001$) 10.0 $9,843 - - - - - - - 10.15 $9,835 ($8) 0% ($236) 100% ($8) 0% - 10.29 $9,832 ($11) 2% ($272) 98% ($5) 0% - 10.41 $9,833 ($10) 5% ($301) 95% $5 0% - 10.51 $9,837 ($6) 6% ($326) 94% $16 0% - 10.59 $9,847 $4 7% ($342) 93% $31 0% - 10.65 $9,863 $20 7% ($352) 93% $49 0% - 10.71 $9,878 $35 8% ($370) 92% $67 0% $204 10.77 $9,894 $51 7% ($383) 88% $77 5% $211 10.82 $9,907 $64 8% ($395) 79% $82 14% $219 10.87 $9,926 $83 7% ($408) 67% $81 25% $229 10.92 $9,941 $98 8% ($424) 57% $79 35% $241 10.97 $9,958 $115 8% ($419) 50% $74 43% $255 11.0 $9,984 $141 7% ($444) 41% $75 52% $268 11.5 $10,004 $161 10% ($543) 30% $58 60% $325 12.0 $10,161 $318 9% ($624) 15% $35 76% $483 12.5 $10,592 $749 4% ($632) 5% $30 91% $852 13.0 $10,764 $921 4% ($718) 3% $24 92% $1,032 13.4 $10,936 $1,093 4% ($708) 3% $19 93% $1,202



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### 1.4 REFERENCES

1. U.S. Department of Energy-Energy Efficiency & Renewable Energy, Technical Support Document: Energy Efficiency Standards for Consumer Products: Residential Central Air Conditioners and Heat Pumps, May 2002. Washington, DC. <http://www.eren.doe .gov/buildings/codes

_standards/applbrf/central

_air conditioner.htinl> 2. U.S. Department of Labor, Bureau of Labor Statistics, Consumer Price Index - All Urban Consumers (Current Series). Washington, DC. <www.bls.gov> 3. U.S. Department of Energy-Energy Information Administration, Annual Energy Outlook 2002, December, 2001. Washington, DC. Report No. DOE/EIA-0383(2002). 4. U.S. Department of Energy-Energy Information Administration, Annual Energy Outlook 2002, December, 2001. Washington, DC. Report No. DOE/EIA-0383(2002). 5. U.S. Department of Energy-Energy Information Administration, Annual Energy Outlook 2002, December, 2001. Washington, DC. Report No. DOE/EIA-0383(2002). 6. Gas Research Institute, 1998 Edition of the GRI Baseline Projection, 1998. Arlington, VA.

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