# APPENDIX 8E. HOUSEHOLD DISCOUNT RATE DISTRIBUTIONS

TABLE OF CONTENTS

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

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

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

TO FINANCE REPLACEMENT EQUIPMENT....................................................8E-2

8E.4 DISTRIBUTION OF RATES FOR TYPES OF EQUITY USED TO

FINANCE REPLACEMENT EQUIPMENT..........................................................8E-5

LIST OF FIGURES

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

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

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

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

Figure 8E.3.4 Distribution of Other Residen ce Loan Interest Rates ..................................8E-4

Figure 8E.3.5 Distribution of Other Lines of Cr edit Loan Interest Rates ..........................8E-4

Figure 8E.4.1 Distribution of Annual Rate of Return on CD’s ..........................................8E-5

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

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

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

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

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

8E-i

# APPENDIX 8E. HOUSEHOLD DISCOUNT RATE DISTRIBUTIONS

8E.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 fo r 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 desc ribes the distributions used.

8E.2 DISTRIBUTION OF MORTGAGE INTEREST RATES

Figure 8E.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 8E.2.1 Distribution of New Home Mortgage Interest Rates

8E-1

# 8E.3 DISTRIBUTION OF RATES FOR TYPES OF DEBT AND EQUITY USED

TO FINANCE REPLACEMENT EQUIPMENT

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

different types of debt used to finance replacement equipment. 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 us ing 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 8E.3.1 Distribution of Home Equity Loan Interest Rates

8E-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



# Figure 8E.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 8E.3.3 Distribution of Installment Loan Interest Rates

8E-30% 5% 10% 15% 20%

0.

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%

Real Interest RateProbability



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

Rates

8E-4

# 8E.4 DISTRIBUTION OF RATES FOR TYPES OF EQUITY USED TO

FINANCE REPLACEMENT EQUIPMENT

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

different types of equity used to finance replacement equipment. Data for equity classes are not

available from the Federal Reserve Board’s SCF , so the Department derived data for these

classes from national-level historical data. The interest rates associated with certificates of

deposit (CDs), 2 

# savings bonds, 3 

# and bonds (AAA corporate bonds) 4 

# are from Federal Reserve

Board time-series data covering 1977–2007. DOE assumed rates on checking accounts to be

zero. Rates on savings and money market accounts ar e from Cost of Savings Index data covering

1984–2007. 5 

# The rates for stocks are the annual return s on the Standard and Poor’s (S&P) 500 in

the 1977–2007 period. 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 of the 1977–2007 period. DOE

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

-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 8E.4.1 Distribution of Annual Rate of Return on CD’s

8E-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 8E.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 8E.4.3 Distribution of Annual Rate of Return on Corporate

AAA Bonds

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

YearAnnual Rate of Return



# 8E-7 Figure 8E.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 8E.4.5 Distribution of Annual Rate of Return on S&P 500-15 % -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 8E.4.6 Distribution of Annual Rate of Return on Mutual

Funds

8E-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 Releas e, 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 Releas e, Selected Interest Rates,

Historical Data, Instrument: State and lo cal 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 Releas e, Selected Interest Rates,

Historical Data, Instrument: Corporat e bonds/Moody's Seasoned AAA, Frequency:

Annual, Description: Moody's yield on seas oned corporate bonds - all industries, AAA,

2008. < http://www.federalreserve.g ov/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 / >

8E-9