APPENDIX 8-G. DISTRIBUTIONS USED FOR DISCOUNT RATES

TABLE OF CONTENTS

8-G.1 INTRODUCTION .................................................................................................8-G-1

8-G.2 DISTRIBUTIONS USED FOR COMMERCIAL DISCOUNT RATES..............8-G-1

8-G.3 DISTRIBUTIONS USED FOR RESIDENTIAL CONSUMER DISCOUNT 

RATES...................................................................................................................8-G-6

8-G.3.1 Distribution of Rates for Debt Classes...................................................................8-G-6

8-G.3.2 Distribution of Rates for Equity Classes..............................................................8-G-10

8-G.4 DISTRIBUTION OF REAL EFFECTIVE DISCOUNT RATES BY INCOME 

GROUP................................................................................................................8-G-14

LIST OF TABLES

Table 8-G.4.1 Distribution of Real Discount Rates by Income Group.....................8-G-15

LIST OF FIGURES

Figure 8-G.2.1 Distribution of Commercial Discount Rates: Retail ............................8-G-1

Figure 8-G.2.2 Distribution of Commercial Discount Rates: Property........................8-G-2

Figure 8-G.2.3 Distribution of Commercial Discount Rates: Medical.........................8-G-2

Figure 8-G.2.4 Distribution of Commercial Discount Rates: Industrial ......................8-G-3

Figure 8-G.2.5 Distribution of Commercial Discount Rates: Lodging ........................8-G-3

Figure 8-G.2.6 Distribution of Commercial Discount Rates: Food Service ................8-G-4

Figure 8-G.2.7 Distribution of Commercial Discount Rates: Office ...........................8-G-4

Figure 8-G.2.8 Distribution of Commercial Discount Rates: State and Local 

Government..........................................................................................8-G-5

Figure 8-G.2.9 Distribution of Commercial Discount Rates: Federal Government.....8-G-5

Figure 8-G.2.10 Distribution of Commercial Discount Rates: Other.............................8-G-6

Figure 8-G.3.1 Distribution of Mortgage Interest Rates ..............................................8-G-7

Figure 8-G.3.2 Distribution of Home Equity Loan Interest Rates ...............................8-G-8

Figure 8-G.3.3 Distribution of Credit Card Interest Rates...........................................8-G-8

Figure 8-G.3.4 Distribution of Installment Loan Interest Rates...................................8-G-8

Figure 8-G.3.5 Distribution of Other Residence Loan Interest Rates..........................8-G-9

Figure 8-G.3.6 Distribution of Other Lines of Credit Loan Interest Rates ..................8-G-9

Figure 8-G.3.7 Distribution of Annual Rate of Return on Certificates of Deposit ....8-G-10

Figure 8-G.3.8 Distribution of Annual Rate of Return on Savings Bonds.................8-G-11

Figure 8-G.3.9 Distribution of Annual Rate of Return on Corporate AAA Bonds....8-G-11

Figure 8-G.3.10 Distribution of Annual Rate of Savings Accounts.............................8-G-12

Figure 8-G.3.11 Distribution of Annual Rate of Money Market Accounts .................8-G-12

Figure 8-G.3.12 Distribution of Annual Rate of Return on Standard and Poor’s 500 .8-G-13

Figure 8-G.3.13 Distribution of Annual Rate of Return on Mutual Funds..................8-G-13

Figure 8-G.4.1 Distribution of Real Discount Rates by Income Group.....................8-G-14

8-G-i
APPENDIX 8-G. DISTRIBUTIONS USED FOR DISCOUNT RATES

8-G.1 INTRODUCTION

The U.S. Department of Energy (DOE) estimates discount rate distributions by customer 

type: commercial and consumer (i.e. non-commercial residential end user). This appendix 

describes the distributions used.

8-G.2 DISTRIBUTIONS USED FOR COMMERCIAL DISCOUNT RATES

DOE derives commercial discount rates (i.e. weighted average cost of capital) for the 

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

by Damodaran Online.1 State and local government discount rates are estimated using the rate of 

return on 20-year municipal bonds, as provided by the Federal Reserve Board.2 Separate 

distributions are constructed for each major industry. Figure 8-G.2.1 through Figure 8-G.2.10

show the probability distributions of commercial discount rates by industry.

Figure 8-G.2.1 Distribution of Commercial Discount Rates: Retail

8-G-1
Figure 8-G.2.2 Distribution of Commercial Discount Rates: Property

Figure 8-G.2.3 Distribution of Commercial Discount Rates: Medical

8-G-2
Figure 8-G.2.4 Distribution of Commercial Discount Rates: Industrial

Figure 8-G.2.5 Distribution of Commercial Discount Rates: Lodging

8-G-3
Figure 8-G.2.6 Distribution of Commercial Discount Rates: Food Service

Figure 8-G.2.7 Distribution of Commercial Discount Rates: Office

8-G-4
Figure 8-G.2.8 Distribution of Commercial Discount Rates: State and Local 

Government

Figure 8-G.2.9 Distribution of Commercial Discount Rates: Federal 

Government

8-G-5
Figure 8-G.2.10 Distribution of Commercial Discount Rates: Other 

8-G.3 DISTRIBUTIONS USED FOR RESIDENTIAL CONSUMER DISCOUNT 

RATES

DOE derives consumer discount rates for the life-cycle cost (LCC) analysis using data

about interest or return rates, for various types of debt and equity, to calculate a real effective 

discount rate for each household in the Federal Reserve Board’s Survey of Consumer Finances 

(SCF) in 1995, 1998, 2001, 2004, 2007, and 2010.

3 To account for variation among households 

in rates for each type of debt and equity, DOE samples a rate for each household in its building 

sample from a distribution of discount rates for each of six income groups. This appendix 

describes the distributions used.

8-G.3.1 Distribution of Rates for Debt Classes 

Figure 8-G.3.1 through Figure 8-G.3.6 show the distribution of real interest rates for 

different types of household debt. The data 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 in 1995, 1998, 2001, 2004, 2007, and 2010.

3 DOE adjusts the 

nominal rates to real rates using the annual inflation rate in each year. 

Using the appropriate SCF data for each year, DOE adjusts the nominal mortgage interest 

rate and the nominal home equity loan interest rate for each relevant household in the SCF for 

mortgage tax deduction and inflation. In cases where the effective interest rate is equal to or 

8-G-6
below the inflation rate (resulting in a negative real interest rate), DOE sets the real effective 

interest rate to zero.

Figure 8-G.3.1 Distribution of Mortgage Interest Rates

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

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

8-G-7
Figure 8-G.3.2 Distribution of Home Equity Loan Interest Rates

Figure 8-G.3.3 Distribution of Credit Card Interest Rates

Figure 8-G.3.4 Distribution of Installment Loan Interest Rates

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

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

8-G-8
Figure 8-G.3.5 Distribution of Other Residence Loan Interest Rates

Figure 8-G.3.6 Distribution of Other Lines of Credit Loan Interest Rates

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

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

8-G-9
8-G.3.2 Distribution of Rates for Equity Classes 

Figure 8-G.3.7 through Figure 8-G.3.13 show the distribution of real interest rates for 

different types of equity. Data for equity classes are not available from the Federal Reserve 

Board’s SCF, so DOE derived data for these classes from national-level historical data (1984-

2013). The interest rates associated with certificates of deposit (CDs),4 savings bonds,2 and AAA 

corporate bonds5 are from Federal Reserve Board time-series data. DOE assumes rates on 

checking accounts to be zero. Rates on savings and money market accounts are from Cost of 

Savings Index data.

6 The rates for stocks are the annual returns on the Standard and Poor’s 

(S&P) 500.

7 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 adjusts the nominal rates to real rates 

using the annual inflation rate in each year.

Figure 8-G.3.7 Distribution of Annual Rate of Return on Certificates of 

Deposit

-0.04

-0.02

0

0.02

0.04

0.06

0.08

1984198619881990

1992

1994199619982000200220042006200820102012

Annual Rate of Return (%)

Year

CDs (Average of 12 and 30 month)

8-G-10
Figure 8-G.3.8 Distribution of Annual Rate of Return on Savings Bonds

Figure 8-G.3.9 Distribution of Annual Rate 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%

19841986198819901992

1994

199619982000200220042006200820102012

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%

198419861988199019921994199619982000200220042006200820102012

Annual Rate of Return (%)

Year

AAA Corporate Bonds

8-G-11
Figure 8-G.3.10 Distribution of Annual Rate of Savings Accounts

Figure 8-G.3.11 Distribution of Annual Rate of Money Market Accounts

-0.5%

0.0%

0.5%

1.0%

1.5%

2.0%

2.5%

3.0%

19841986

1988199019921994

19961998200020022004200620082010

2012

Annual Rate of Return (%)

Year

Savings Accounts

-1.0%

0.0%

1.0%

2.0%

3.0%

4.0%

5.0%

6.0%

198419861988199019921994199619982000200220042006200820102012

Annual Rate of Return (%)

Year

Money Market Accounts

8-G-12
Figure 8-G.3.12 Distribution of Annual Rate of Return on

Standard and Poor’s 500

Figure 8-G.3.13 Distribution of Annual Rate of Return on Mutual Funds

-40.0%

-30.0%

-20.0%

-10.0%

0.0%

10.0%

20.0%

30.0%

40.0%

19841986198819901992

1994

199619982000200220042006200820102012

Annual Rate of Return (%)

Year

Stocks (S&P 500)

-30.0%

-20.0%

-10.0%

0.0%

10.0%

20.0%

30.0%

198419861988199019921994199619982000200220042006200820102012

Annual Rate of Return (%)

Year

Mutual Funds

8-G-13
8-G.4 DISTRIBUTION OF REAL EFFECTIVE DISCOUNT RATES BY 

INCOME GROUP

Figure 8-G.4.1 and Table 8-G.4.1 present the distributions of real discount rates for each 

income group.

Figure 8-G.4.1 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

8-G-14
Table 8-G.4.1 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 12.4% 0.002 12.4% 0.002

13-14 13.6% 0.012 13.5% 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 17.5% 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

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

8-G-15
REFERENCES

1. Damodaran Online, Data Page: Costs of Capital by Industry Sector, 2012. Damodaran. 

(Last accessed July, 2013.) <http://pages.stern.nyu.edu/~adamodar/>

2. The Federal Reserve Board, 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.

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

3. The Federal Reserve Board, Survey of Consumer Finances 1989, 1992, 1995, 1998, 

2001, 2004, 2007, 2010. <http://www.federalreserve.gov/pubs/oss/oss2/scfindex.html>

4. The Federal Reserve Board, 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.

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

5. The Federal Reserve Board, 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. <www.federalreserve.gov/releases/H15/data.htm>

6. Mortgage-X - Mortgage Information Service, Cost of Savings Index (COSI) Index 

History, 2013. <http://mortgage-x.com/general/indexes/default.asp>

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

Bills - United States, 2013. Damodaran. (Last accessed June, 2014.) 

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

8-G-16