# 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

8-D-i

# 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%

1 2.

4 %

1 3.

5 % 14.4% 16.7% 22.9%

Real Interest RateProbability



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

8-D-1

# 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%

1 3.

7 % 14.7% 16.7%

1 7.

5 % 42.5%

Real Interest RateProbability



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

8-D-20% 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%

1 0.

6 % 11.5% 12.6%

1 3.

6 %

1 4.

7 % 15.6% 16.4%

1 7.

6 % 18.5% 19.4% 20.5% 21.4% 22.5% 23.6%

2 4.

6 % 25.5% 26.3%

2 7.

3 %

Real Interest RateProbability



## 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%

1 2.

5 %

1 4.

7 % 16.5% 18.5% 20.5%

2 2.

3 % 24.6% 26.6% 28.5%

3 4.

1 % 43.6% 47.2%

Real Interest RateProbability



# Figure 8-D.3.3 Distribution of Installment Loan Interest Rates0. 2 % 1.5% 2.5%

3

. 5%

4. 5 % 5.5% 6.5% 7.5%

8

. 6%

9. 4 % 10.6% 11.6%

1 2.

6 %

1 4.

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%

1 8.

5 %

19.1% 20.2%

2 1. 5 %

22.1% 23.5%

Real Interest RateProbability



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

Rates

8-D-4197 7 1979 1981 198 3 1985 1987

1 989 199 1 1993

1 995 199 7 1999

2 001 200 3

2 007 

# 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 bonds 4 

# 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

8-D-5-2% 0% 2% 4% 6% 8%

197

7 1979 1981 198 3 1985 1987

1 989 199 1 1993

1 995 199 7 1999

2 001 200 3 2005

2 007

YearAnnual Rate of Return



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

Bonds

-2% 0% 2% 4% 6% 8%

197

7 1979 1981 198 3 1985 1987

1 989 199 1 1993

1 995 199 7 1999

2 001 200 3 2005

2 007

YearAnnual Rate of Return



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

AAA Bonds

8-D-6-2% 0% 2% 4% 6% 8%1984198519861987198819891990199119921993199419951996199719981999200020012002200320042005200620072008

YearAnnual Rate of Return



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

-30% -20% -10%

0% 10% 20% 30% 40%

1977 197 9 1981 1983

1 985 1987 1989

1 991 199 3 1995

1 997 199 9 2001

2 003 200 5 2007

YearAnnual Rate of Return



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

8-D-7-15% -10% -5% 0% 5% 10% 15% 20% 25%

1 977

1 97

9

1 981

1 983 1985

1 987

1 989 1991

1 99

3

1 995 1997

1 99

9

2 001 2003

2 00

5

2 007

YearAnnual Rate of Return



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

Funds

8-D-8

# 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 / >

8-D-9