APPENDIX 8-D. DISTRIBUTIONS USED FOR DISCOUNT RATES 

TABLE OF CONTENTS 

8-D.1 INTRODUCTION .................................................................................................8-D-1 

8-D.2 DISTRIBUTION OF MORTGAGE INTEREST RATES ....................................8-D-1 

8-D.3 DISTRIBUTION OF RATES FOR TYPES OF DEBT AND EQUITY USED 

TO FINANCE REPLACEMENT HEATING PRODUCTS .................................8-D-2 

8-D.4 DISTRIBUTION OF RATES FOR TYPES OF EQUITY USED TO 

FINANCE REPLACEMENT HEATING PRODUCTS .......................................8-D-5
 

LIST OF FIGURES 

Figure 8-D.2.1 Distribution of New Home Mortgage Interest Rates .................................8-D-1
 

Figure 8-D.3.1 Distribution of Home Equity Loan Interest Rates .....................................8-D-2
 

Figure 8-D.3.2 Distribution of Credit Card Interest Rates .................................................8-D-3
 

Figure 8-D.3.3 Distribution of Installment Loan Interest Rates.........................................8-D-3
 

Figure 8-D.3.4 Distribution of Other Residence Loan Interest Rates ................................8-D-4
 

Figure 8-D.3.5 Distribution of Other Lines of Credit Loan Interest Rates ........................8-D-4
 

Figure 8-D.4.1 Distribution of Annual Rate of Return on CDs .........................................8-D-5
 

Figure 8-D.4.2 Distribution of Annual Rate of Return on Savings Bonds.........................8-D-6
 

Figure 8-D.4.3 Distribution of Annual Rate of Return on Corporate AAA Bonds............8-D-6
 

Figure 8-D.4.4 Distribution of Annual Rate of Savings Accounts.....................................8-D-7
 

Figure 8-D.4.5 Distribution of Annual Rate of Return on S&P 500..................................8-D-7
 

Figure 8-D.4.6 Distribution of Annual Rate of Return on Mutual Funds ..........................8-D-8
 

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APPENDIX 8-D. DISTRIBUTIONS USED FOR DISCOUNT RATES 

8-D.1 INTRODUCTION 

DOE derived discount rates for the LCC analysis using data on interest or return rates for 

various types of debt and equity. To account for variation among households in rates for each of 

the types, DOE sampled a rate for each household from a distribution of rates for each debt and 

equity type. This appendix describes the distributions used. 

8-D.2 DISTRIBUTION OF MORTGAGE INTEREST RATES 

Figure 8-D.2.1 shows the distribution of real interest rates for new home mortgages. 

The data source DOE used for mortgage interest rates is the Federal Reserve Board’s Survey of 

Consumer Finances (SCF) in 1989, 1992, 1995, 1998, 2001, 2004, and 2007.1 Using the 

appropriate SCF data for each year, DOE adjusted the nominal mortgage 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 below the inflation rate (resulting in a negative real interest 

rate), DOE set the real effective interest rate to zero. 

0%

5%

10%

15%

20%

25%

30%

35%

0.5%1.6%2.5%3.5%4.4%5.4%6.4%7.4%8.5%9.5%

10.5%11.6%12.4%13.5%14.4%16.7%22.9%

Real Interest Rate 

Probability 

Figure 8-D.2.1 Distribution of New Home Mortgage Interest Rates
 

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8-D.3	 DISTRIBUTION OF RATES FOR TYPES OF DEBT AND EQUITY USED 

TO FINANCE REPLACEMENT HEATING PRODUCTS 

Figure 8-D.3.1 through Figure 8-D.3.5 show the distribution of real interest rates for 

different types of debt used to finance replacement heating products. The data source for the 

interest rates for home equity loans, credit cards, installment loans, other residence loans, and 

other lines of credit is the Federal Reserve Board’s SCF in 1989, 1992, 1995, 1998, 2001, 2004, 

and 2007.1 DOE adjusted the nominal rates to real rates using the annual inflation rate in each 

year. For home equity loans, DOE calculated effective interest rates in a similar manner as for 

mortgage rates, since interest on such loans is tax deductible. 

0%

5%

10%

15%

20%

25%

30%

35%

0.4%1.5%2.6%3.5%4.5%5.4%6.4%7.5%8.5%9.5%

10.6%11.8%12.7%13.7%14.7%16.7%17.5%42.5%

Real Interest Rate 

Probability 

Figure 8-D.3.1 Distribution of Home Equity Loan Interest Rates
 

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0%

2%

4%

6%

8%

10%

12%

0.0%1.4%2.5%3.5%4.5%5.6%6.7%7.5%8.7%9.6%

10.6%11.5%12.6%13.6%14.7%15.6%16.4%17.6%18.5%19.4%20.5%21.4%22.5%23.6%24.6%25.5%26.3%27.3%

Real Interest Rate 

Probability 

8-D-3 

Figure 8-D.3.2 Distribution of Credit Card Interest Rates 

0%

5%

10%

15%

20%

25%

30%

35%

0.0%2.4%4.5%6.7%8.6%

10.6%12.5%14.7%16.5%18.5%20.5%22.3%24.6%26.6%28.5%34.1%43.6%47.2%

Real Interest Rate 

Probability 

Figure 8-D.3.3 Distribution of Installment Loan Interest Rates 

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0.2%1.5%2.5%3.5%4.5%5.5%6.5%7.5%8.6%9.4%

10.6%11.6%12.6%14.7%15.7%16.6%17.9%

Probability 

20%

15%

10%

5%

0%

Real Interest Rate 

Figure 8-D.3.4 Distribution of Other Residence Loan Interest Rates 

0%

2%

4%

6%

8%

10%

12%

14%

16%

0.1%1.4%2.5%3.5%4.5%5.5%6.7%7.6%8.7%9.5%

10.5%11.6%12.5%13.5%14.7%15.6%16.5%17.3%18.5%19.1%20.2%21.5%22.1%23.5%

Real Interest Rate 

Probability 

Figure 8-D.3.5	 Distribution of Other Lines of Credit Loan Interest 

Rates 

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19771979198119831985

1987

1989

1991

1993

199519971999

2001

2003

2007

8-D.4	 DISTRIBUTION OF RATES FOR TYPES OF EQUITY USED TO 

FINANCE REPLACEMENT HEATING PRODUCTS 

Figure 8-D.4.1 through Figure 8-D.4.6 show the distribution of real interest rates for 

different types of equity used to finance replacement furnaces. 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. The interest rates associated with certificates of deposit (CDs),2 

savings bonds,3 and AAA corporate bonds4 are from Federal Reserve Board time-series data 

covering 1977 to 2007. DOE assumed rates on checking accounts to be zero. Rates on savings 

and money market accounts are from Cost of Savings Index data covering 1984 to 2007.5 The 

rates for stocks are the annual returns on the Standard and Poor’s (S&P) 500 from 1977 to 2007.6 

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 from 1977 to 2007. DOE adjusted the nominal rates to real 

rates using the annual inflation rate in each year. 

8%

6%

Annual Rate of Return 

4%

2%

0%

5 200

-2%

Year 

Figure 8-D.4.1 Distribution of Annual Rate of Return on CDs 

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-2%

0%

2%

4%

6%

8%

19771979198119831985

1987

1989

1991

1993

199519971999

2001

20032005

2007

Year 

Annual Rate of Return 

Figure 8-D.4.2 Distribution of Annual Rate of Return on Savings 

Bonds 

-2%

0%

2%

4%

6%

8%

19771979198119831985

1987

1989

1991

1993

199519971999

2001

20032005

2007

Year 

Annual Rate of Return 

Figure 8-D.4.3	 Distribution of Annual Rate of Return on Corporate 

AAA Bonds 

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-2%

0%

2%

4%

6%

8%

1984198519861987198819891990199119921993199419951996199719981999200020012002200320042005200620072008

Year 

Annual Rate of Return 

Figure 8-D.4.4 Distribution of Annual Rate of Savings Accounts
 

-30%

-20%

-10%

0%

10%

20%

30%

40%

1977197919811983

1985

1987

1989

1991

1993

1995

1997

19992001

2003

20052007

Year 

Annual Rate of Return 

Figure 8-D.4.5 Distribution of Annual Rate of Return on S&P 500
 

8-D-7 

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-15%

-10%

-5%

0%

5%

10%

15%

20%

25%

1977197919811983198519871989199119931995199719992001200320052007

Year 

Annual Rate of Return 

Figure 8-D.4.6 Distribution of Annual Rate of Return on Mutual 

Funds 

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REFERENCES
 

1.	 The Federal Reserve Board, Survey of Consumer Finances 1989, 1992, 1995, 1998, 2001, 

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

2.	 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, 2008. 

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

3.	 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, 2008. 

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

4.	 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, 

2008. <http://www.federalreserve.gov/releases/H15/data.htm> 

5.	 Wachovia, Cost of Savings Index (COSI) Index History, 2008. (Last accessed March 10, 

2008.) <http://mortgage-x.com/general/indexes/default.asp> 

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

Bonds, and Bills - United States), 2008. Stern School of Business, New York University. 

(Last accessed March 10, 2008.) <http://pages.stern.nyu.edu/~adamodar/> 

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