8E-i

APPENDIX 8E. DISTRIBUTIONS FOR DISCOUNT RATES

TABLE OF CONTENTS

8E-1 INTRODUCTION .........................................................................................................8E-1

8E-2 DISTRIBUTIONS FOR CONSUMER RESIDENTIAL DISCOUNT RATES ...........8E-1

8E-2.1 Distributions of Rates for Debt Classes.............................................................8E-2

8E-2.2 Distributions of Interest Rates for Equity Classes.............................................8E-5

8E-3 DISTRIBUTION OF REAL EFFECTIVE DISCOUNT RATES BY INCOME 

GROUP........................................................................................................................8E-10

8E-4 DISTRIBUTIONS FOR COMMERCIAL APPLICATIONS.....................................8E-14

LIST OF TABLES

Table 8E-2.1 Income Groups.............................................................................................8E-1

Table 8E-3.1 Distribution of Real Discount Rates by Income Group .............................8E-12

LIST OF FIGURES

Figure 8E-2.1 Distribution of Interest Rates on Mortgages................................................8E-2

Figure 8E-2.2 Distribution of Interest Rates on Home Equity Loans.................................8E-3

Figure 8E-2.3 Distribution of Interest Rates on Credit Cards.............................................8E-3

Figure 8E-2.4 Distribution of Interest Rates on Installment Loans....................................8E-4

Figure 8E-2.5 Distribution of Interest Rates on Other Residence Loans............................8E-4

Figure 8E-2.6 Distribution of Interest Rates on Other Lines of Credit...............................8E-5

Figure 8E-2.7 Distribution of Annual Rates of Return on CDs..........................................8E-6

Figure 8E-2.8 Distribution of Annual Rates of Return on Savings Bonds.........................8E-7

Figure 8E-2.9 Distribution of Annual Rates of Return on Corporate AAA Bonds............8E-7

Figure 8E-2.10 Distribution of Annual Rates of Return on Savings Accounts....................8E-8

Figure 8E-2.11 Distribution of Annual Rates of Return on Money Market Accounts.........8E-9

Figure 8E-2.12 Distribution of Annual Rates of Return on the S&P 500 ............................8E-9

Figure 8E-2.13 Distribution of Annual Rates of Return on Mutual Funds.........................8E-10

Figure 8E-3.1 Distribution of Real Discount Rates by Income Group .............................8E-11

Figure 8E-4.1 Probability Distribution of Commercial Discount Rates: Retail ...............8E-14

Figure 8E-4.2 Probability Distribution of Commercial Discount Rates: Property ...........8E-15

Figure 8E-4.3 Probability Distribution of Commercial Discount Rates: Medical............8E-15

Figure 8E-4.4 Probability Distribution of Commercial Discount Rates: Industrial..........8E-16

Figure 8E-4.5 Probability Distribution of Commercial Discount Rates: Lodging ...........8E-16

Figure 8E-4.6 Probability Distribution of Commercial Discount Rates: Food Service....8E-17
8E-ii

Figure 8E-4.7 Probability Distribution of Commercial Discount Rates: Office...............8E-17

Figure 8E-4.8 Probability Distribution of Commercial Discount Rates: State and 

Local Government .....................................................................................8E-18

Figure 8E-4.9 Probability Distribution of Commercial Discount Rates: Federal 

Government................................................................................................8E-18

Figure 8E-4.10 Probability Distribution of Commercial Discount Rates: Other................8E-19
8E-1

APPENDIX 8E. DISTRIBUTIONS FOR DISCOUNT RATES

8E-1 INTRODUCTION

The U.S. Department of Energy (DOE) estimates distributions of discount rates for use in 

its life-cycle cost analysis (chapter 8), as well as in its national impacts analysis (chapter 10). 

DOE develops distributions of discount rates separately for consumers' purchases of residential 

products and for commercial applications. This appendix describes the distributions DOE used in 

its analyses.

8E-2 DISTRIBUTIONS FOR CONSUMER RESIDENTIAL DISCOUNT RATES 

To derive discount rates for its life-cycle cost analysis of portable air conditioners 

purchased for residential applications, DOE examined data on interest or return rates for various 

types of consumer debt and equity. DOE used those rates to calculate a real effective discount 

rate for each household in the Federal Reserve Board’s Survey of Consumer Finances (SCF) for

1995, 1998, 2001, 2004, 2007, and 2010.

1 To account for variations in rates for each type of debt 

or equity, DOE estimated individual distributions of discount rates for six income groups, 

divided based on income percentile as reported in the Federal Reserve Board’s SCF. 0 lists the 

income groups DOE identified. 

Table 8E-2.1 Income Groups

Income Group Percentile of Income

1 1

st to 20th

2 21st to 40th

3 41st to 60th

4 61st to 80th

5 81st to 90th

6 91th to 99th

Sources: Federal Reserve Board. Survey of Consumer Finances (SCF) for 1995, 1998, 2001, 2004, 2007, and 2010.

DOE sampled a rate for each household in its building sample from a distribution of 

discount rates for each income group. DOE examined the income groups separately because lowand high-income consumers tend to have different proportions of debt and asset types and tend to 

encounter different interest rates on debts and assets. This appendix describes the distributions 

DOE used in its analysis.
8E-2

8E-2.1 Distributions of Rates for Debt Classes 

Figure 8E-2.1 through Figure 8E-2.6 show the distributions of real interest rates for 

various types of household debt. The source for the interest rates for mortgages, home equity 

loans, credit cards, installment loans, other residence loans, and other lines of credit is the 

Federal Reserve Board’s SCF for 1995, 1998, 2001, 2004, 2007, and 2010.

1 DOE adjusted the 

nominal rates to real rates by applying the annual rate of inflation in each year. Using the

appropriate SCF data for each year, DOE also adjusted the nominal interest rates on mortgage 

and home equity loan for mortgage tax deductions. In cases where the effective interest rate was 

equal to or less than the inflation rate (resulting in a negative real interest rate), DOE set the real 

effective interest rate to zero.

Figure 8E-2.1 Distribution of Interest Rates on Mortgages

0%

5%

10%

15%

20%

25%

30%

35% 0.5% 1.6% 2.5% 3.5% 4.4% 5.4% 6.3% 7.4% 8.5% 9.4% 10.4% 11.6% 12.5% 13.2% 14.4% 16.6% 22.8% Probability

Real Interest Rate
8E-3

Figure 8E-2.2 Distribution of Interest Rates on Home Equity Loans

Figure 8E-2.3 Distribution of Interest Rates on Credit Cards

0%

5%

10%

15%

20%

25%

30% 0.4% 1.5% 2.5% 3.5% 4.5% 5.4% 6.4% 7.5% 8.4% 9.4% 10.5% 11.5% 12.5% 13.8% 14.7% 15.7% 16.6% 17.1% 22.0% Probability

Real Interest Rate

0%

1%

2%

3%

4%

5%

6%

7%

8%

9% 0.0% 2.5% 4.5% 6.6% 8.6% 10.5% 12.5% 14.7% 16.4% 18.4% 20.4% 22.7% 24.7% 26.8% 28.5% Probability

Real Interest Rate
8E-4

Figure 8E-2.4 Distribution of Interest Rates on Installment Loans

Figure 8E-2.5 Distribution of Interest Rates on Other Residence Loans

0%

5%

10%

15%

20%

25%

30%

35%

40% 0.0% 2.4% 4.5% 6.6% 8.5% 10.5% 12.5% 14.7% 16.4% 18.4% 20.5% 22.5% 24.6% 26.8% 28.5% Probability

Real Interest Rate

0%

2%

4%

6%

8%

10%

12%

14%

16%

18% 0.2% 1.5% 2.5% 3.5% 4.5% 5.5% 6.5% 7.5% 8.6% 9.4% 10.4% 11.5% 12.5% 13.1% 14.7% 15.7% 16.6% Probability

Real Interest Rate
8E-5

Figure 8E-2.6 Distribution of Interest Rates on Other Lines of Credit

8E-2.2 Distributions of Interest Rates for Equity Classes

Figure 8E-2.7 through Figure 8E-2.13 show the distributions of real interest rates for 

various types of consumer equity. Because data for equity classes are not available from the 

Federal Reserve Board’s SCF, DOE derived the data from national-level historical data (for 

1984–2013). The interest rates associated with certificates of deposit (CDs),2savings bonds,3and 

AAA corporate bonds4derive from Federal Reserve Board time-series data. DOE assumed rates 

on checking accounts to be zero. Rates on savings and money market accounts were obtained 

from Cost of Savings Index data.

5 The rates for stocks are the annual returns on the Standard and 

Poor’s 500.

6 The mutual fund rates are a weighted average of the stock rates (two-thirds weight) 

and the bond rates (one-third weight) in each year. DOE used the annual rate of inflation in each 

year to adjust the nominal rates to real rates.

0%

2%

4%

6%

8%

10%

12% 0.1% 2.5% 4.5% 6.6% 8.6% 10.5% 12.5% 14.7% 16.4% 18.4% 20.2% 22.6% 25.4% Probability

Real Interest Rate
8E-6

Figure 8E-2.7 Distribution of Annual Rates of Return on CDs

-0.04

-0.02

0

0.02

0.04

0.06

0.08 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 Annual Rate of Return (%)

Year

CDs (Average of 12 and 30 month)
8E-7

Figure 8E-2.8 Distribution of Annual Rates of Return on Savings Bonds

Figure 8E-2.9 Distribution of Annual Rates of Return on Corporate AAA Bonds

0.0%

1.0%

2.0%

3.0%

4.0%

5.0%

6.0%

7.0%

8.0%

9.0% 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 Annual Rate of Return (%)

Year

Savings Bonds

0.0%

1.0%

2.0%

3.0%

4.0%

5.0%

6.0%

7.0%

8.0%

9.0% 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 Annual Rate of Return (%)

Year

AAA Corporate Bonds
8E-8

Figure 8E-2.10 Distribution of Annual Rates of Return on Savings Accounts

-0.5%

0.0%

0.5%

1.0%

1.5%

2.0%

2.5%

3.0% 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 Annual Rate of Return (%)

Year

Savings Accounts

-1.0%

0.0%

1.0%

2.0%

3.0%

4.0%

5.0%

6.0% 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 Annual Rate of Return (%)

Year

Money Market Accounts
8E-9

Figure 8E-2.11 Distribution of Annual Rates of Return on Money Market Accounts

Figure 8E-2.12 Distribution of Annual Rates of Return on the S&P 500

-40.0%

-30.0%

-20.0%

-10.0%

0.0%

10.0%

20.0%

30.0%

40.0% 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 Annual Rate of Return (%)

Year

Stocks (S&P 500)
8E-10

Figure 8E-2.13 Distribution of Annual Rates of Return on Mutual Funds

8E-3 DISTRIBUTION OF REAL EFFECTIVE DISCOUNT RATES BY INCOME 

GROUP

Figure 8E-3.1 presents the distributions of real discount rates for each of the six income 

groups.

-30.0%

-20.0%

-10.0%

0.0%

10.0%

20.0%

30.0% 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 Annual Rate of Return (%)

Year

Mutual Funds
8E-11

Figure 8E-3.1 Distribution of Real Discount Rates by Income Group

0%

5%

10%

15%

20%

25%

0.0% 5.0% 10.0% 15.0% 20.0%

Share of Individuals in Group (%)

Real Effective Discount Rate (%)

Group 1

Group 2

Group 3

Group 4

Group 5

Group 6
8E-12

Table 8E-3.1 Distribution of Real Discount Rates by Income Group

DR Bin*

Income Group 1 Income Group 2 Income Group 3 Income Group 4 Income Group 5 Income Group 6

(1-20 percentile) (21-40 percentile) (41-60 percentile) (61-80 percentile) (81-90 percentile) (90-99 percentile)

Rate % Weight Rate % Weight Rate % Weight Rate % Weight Rate % Weight Rate % Weight

0-1 0.5 0.238 0.6 0.152 0.6 0.104 0.6 0.077 0.6 0.056 0.6 0.057

1-2 1.6 0.110 1.6 0.120 1.6 0.105 1.6 0.146 1.6 0.142 1.6 0.185

2-3 2.5 0.087 2.5 0.112 2.6 0.131 2.5 0.205 2.5 0.219 2.5 0.207

3-4 3.5 0.117 3.5 0.137 3.5 0.164 3.5 0.173 3.5 0.200 3.5 0.178

4-5 4.5 0.097 4.5 0.113 4.5 0.136 4.5 0.129 4.5 0.153 4.5 0.144

5-6 5.5 0.083 5.5 0.084 5.5 0.100 5.5 0.093 5.5 0.098 5.5 0.120

6-7 6.5 0.058 6.5 0.062 6.5 0.075 6.5 0.067 6.5 0.063 6.4 0.079

7-8 7.5 0.036 7.5 0.051 7.6 0.054 7.4 0.041 7.4 0.029 7.3 0.011

8-9 8.5 0.036 8.4 0.039 8.4 0.034 8.5 0.015 8.4 0.012 8.5 0.005

9-10 9.5 0.017 9.5 0.018 9.5 0.017 9.5 0.010 9.5 0.008 9.6 0.005

10-11 10.5 0.014 10.5 0.019 10.5 0.013 10.5 0.011 10.6 0.004 10.7 0.004

11-12 11.5 0.010 11.5 0.015 11.5 0.014 11.5 0.007 11.4 0.004 11.7 0.001

12-13 12.5 0.011 12.5 0.012 12.5 0.009 12.4 0.005 12. 0.002 12.4 0.002

13-14 13.6 0.012 13. 0.008 13.5 0.009 13.5 0.004 13.5 0.002 13.3 0.001

14-15 14.6 0.016 14.6 0.014 14.6 0.009 14.5 0.005 14.6 0.003 14.2 0.001

15-16 15.5 0.011 15.5 0.010 15.5 0.006 15.6 0.004 15.6 0.002 15.3 0.000

16-17 16.5 0.013 16.5 0.009 16.5 0.004 16.5 0.003 16.5 0.001 0.0 0.000

17-18 17.5 0.009 17.6 0.006 17. 0.005 17.5 0.003 17.6 0.001 17.7 0.001

18-19 18.4 0.005 18.5 0.005 18.6 0.003 18.4 0.001 18.2 0.000 0.0 0.000

19-20 19.4 0.006 19.4 0.004 19.4 0.002 19.7 0.000 19.7 0.000 19.4 0.000

20-21 20.6 0.004 20.4 0.002 20.5 0.001 20.3 0.001 20.5 0.000 20.3 0.000

21-22 21.4 0.003 21.4 0.002 21.4 0.001 21.5 0.001 0.0 0.000 21.4 0.000

22-23 22.5 0.002 22.4 0.001 22.6 0.001 22.9 0.000 22.8 0.000 22.3 0.000

23-24 23.6 0.001 23.4 0.001 23.6 0.001 0.0 0.000 0.0 0.000 24.0 0.000

24-25 24.6 0.001 24.5 0.000 24.6 0.000 24.1 0.000 24.3 0.000 0.0 0.000
8E-13

DR Bin*

Income Group 1 Income Group 2 Income Group 3 Income Group 4 Income Group 5 Income Group 6

(1-20 percentile) (21-40 percentile) (41-60 percentile) (61-80 percentile) (81-90 percentile) (90-99 percentile)

Rate % Weight Rate % Weight Rate % Weight Rate % Weight Rate % Weight Rate % Weight

25-26 25.4 0.001 25.4 0.001 25.5 0.000 0.0 0.000 0.0 0.000 0.0 0.000

26-27 26.5 0.001 26.5 0.000 26.4 0.000 0.0 0.000 0.0 0.000 0.0 0.000

27-28 27.8 0.000 27.6 0.000 27.8 0.000 0.0 0.000 0.0 0.000 0.0 0.000

28-29 28.2 0.000 0.0 0.000 0.0 0.000 0.0 0.000 0.0 0.000 0.0 0.000

29-23 29.9 0.000 29.3 0.000 0.0 0.000 0.0 0.000 0.0 0.000 0.0 0.000

>30 59.1 0.001 142.7 0.002 0.0 0.000 53.3 0.000 0.0 0.000 0.0 0.000

DR = discount rate.
8E-14

8E-4 DISTRIBUTIONS FOR COMMERCIAL APPLICATIONS

DOE derived commercial discount rates (i.e., weighted average costs of capital) for the 

life-cycle cost analysis using the capital asset pricing model and firm-level data provided by 

Damodaran Online.7 DOE constructed separate distributions for each major commercial sector. 

DOE presents the results as probability distributions showing the probability that a company in a 

given commercial sector will encounter a given discount (interest) rate. Figure 8E-4.1through 

Figure 8E-4.10 show the probability distributions for commercial discount rates by sector. The 

figures present rates for the following sectors: retail, property (real estate), medical, industrial, 

lodging, food service, office, and other.

Figure 8E-4.1 Probability Distribution of Commercial Discount Rates: Retail
8E-15

Figure 8E-4.2 Probability Distribution of Commercial Discount Rates: Property

Figure 8E-4.3 Probability Distribution of Commercial Discount Rates: Medical
8E-16

Figure 8E-4.4 Probability Distribution of Commercial Discount Rates: Industrial

Figure 8E-4.5 Probability Distribution of Commercial Discount Rates: Lodging
8E-17

Figure 8E-4.6 Probability Distribution of Commercial Discount Rates: Food Service

Figure 8E-4.7 Probability Distribution of Commercial Discount Rates: Office
8E-18

Figure 8E-4.8 Probability Distribution of Commercial Discount Rates: State and Local 

Government

Figure 8E-4.9 Probability Distribution of Commercial Discount Rates: Federal 

Government
8E-19

Figure 8E-4.10 Probability Distribution of Commercial Discount Rates: Other 
8E-20

REFERENCES

1. Board of Governors of the Federal Reserve System. Survey of Consumer Finances. 1995, 

1998, 2001, 2004, 2007, and 2010. (Last accessed September 12, 2014.) 

<http://www.federalreserve.gov/econresdata/scf/scf-previous-surveys.htm>

2. Board of Governors of the Federal Reserve System. Federal Reserve Statistical Release, 

Selected Interest Rates, Historical Data, Instrument: CDs (secondary market), Maturity: 

6-month, Frequency: Annual, Description: Average rate on 6-month negotiable 

certificates of deposit (secondary market), quoted on an investment basis. 2013. (Last 

accessed September 12, 2014.) <www.federalreserve.gov/releases/H15/data.htm>

3. Board of Governors of the Federal Reserve System. Federal Reserve Statistical Release, 

Selected Interest Rates, Historical Data, Instrument: State and local bonds,Maturity: 20-

year, Frequency: Monthly, Description: Bond buyer go 20-bond municipal bond index.

2013. (Last accessed September 12, 2014.) 

<www.federalreserve.gov/releases/H15/data.htm>

4. Board of Governors of the Federal Reserve System. Federal Reserve Statistical Release, 

Selected Interest Rates, Historical Data, Instrument: Corporate bonds/Moody’s Seasoned 

AAA, Frequency: Annual, Description: Moody’s yield on seasoned corporate bonds—all 

industries, AAA. 2013. (Last accessed September 12, 2014.) 

<www.federalreserve.gov/releases/H15/data.htm>

5. Mortgage-X–Mortgage Information Service. Cost of Savings Index (COSI) Index History.

2013. (Last accessed September 12, 2014.) <http://mortgagex.com/general/indexes/default.asp>

6. Damodaran Online Data Page. The Data Page: Historical Returns on Stocks, Bonds and 

Bills–United States. 2013. Damodaran. (Last accessed September 12, 2014.) 

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

7. Damodaran Online Data Page. The Data Page: Historical Returns on Stocks, Bonds and 

Bills–United States. 2013. Damodaran. (Last accessed September 12, 2014.)

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