# 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 FURNACES....................................................8-D-2 8-D.4 DISTRIBUTION OF RATES FOR TYPES OF EQUITY USED TO

FINANCE REPLACEMENT FURNACES ..........................................................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 CD’s ........................................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-i0.4 % 1. 6% 2.5% 3.5 % 4. 4% 5.4% 6. 4% 7. 4% 8.5% 9. 4% 10.5% 11. 7% 12. 4% 13.3% 14. 4% 16. 9% 23.2% 

# 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

1 

# Consumer Finances (SCF) in 1989, 1992, 1995, 1998, 2001, and 2004. 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.

30%

25 %

20 %

1 5 %

1 0 %

5 %

0 %Probability



## Real Interest Rate



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

8-D-10. 4% 1. 5% 2.5 % 3.5% 4.5% 5. 4% 6. 4% 7. 5% 8. 5% 9.5% 10.5% 11.8% 12 .7% 13. 4% 14. 7% 15. 0 % 17.0% 17.5% 42.7% 

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

TO FINANCE REPLACEMENT FURNACES

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 furnaces. The data source for the interest rates for home equity loans, credit cards, installment loans, other residence loans, and other lines of

1 

# credit is the Federal Reserve Board’s SCF in 1989, 1992, 1995, 1998, 2001, and 2004. 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.

25%

20%

15%Probability



## 10%

5%

0%

Real Interest Rate



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

8-D-2123456 

## 0% 2% 4 % 6 % 8 % 1 0 %0.0%1.4%2.6%3.5%4.5%5.5%6.6%7.4%8.6%9.6%10.6%11.5%12.5%13.6%14.7%15.6%16.4%17.6%18.4%19.3%20.4%2.4%2.5%2.6%2.6%2.5%2.3%36.9%



## Real Interest RateProbability



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

0% 5% 1 0 % 1 5 % 2 0 % 2 5 % 3 0 % 3 5 %

0.0% 2. 4% 4. 5% 6.6% 8. 6% 10. 6% 12.5% 14 .7% 16.4% 18.5% 20. 5% 22.2% 24 .6% 26. 6% 28.4% 43. 6% 47. 2 %



## Real Interest RateProbability



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

8-D-3

## 0% 5% 1 0 % 1 5 % 2 0 %

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% 14.8% 15. 7% 16. 6% 17.9%



## Real Interest RateProbability



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

0% 2% 4 % 6 % 8 % 1 0 % 1 2 % 1 4 %

0.1% 1.5% 2.

5% 3. 5% 4.6% 5.6% 6.7% 7.

6% 8. 6% 9.5% 10.

5%

11.

6%

12.5% 13.5% 14.

7%

15.

6%

16.4% 17.4% 18.

5%

19.

1%

20.2% 21.1% 22.

1%

23.

5%



## Real Interest RateProbability



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

Rates

8-D-4

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

FINANCE REPLACEMENT FURNACES

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 the Department derived data for these

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

2 3 4 

# deposit (CDs), savings bonds, and bonds (AAA corporate bonds) 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 are from Cost of Savings Index data covering

5 

# 1984–2007. The rates for stocks are the annual returns on the Standard and Poor’s (S&P) 500 in

6

# the 1977–2007 period. The mutual fund rates are a weighted average of the stock rates (twothirds 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 %

1977 1979 1981 1983 1985 198 7 1989 199 1 199 3 1995 19 9 7 1999 2001 2003 2005 2007



## YearAnnual Rate of Return



# Figure 8-D.4.1 Distribution of Annual Rate of Return on CD’s

8-D-5

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

1977 1979 1981 1983 1985 198 7 1989 199 1 199 3 1995 19 9 7 1999 2001 2003 2005 2007



## YearAnnual Rate of Return



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

Bonds

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

1977 1979 1981 1983 1985 198 7 1989 199 1 199 3 1995 19 9 7 1999 2001 2003 2005 2007



## YearAnnual Rate of Return



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

AAA Bonds

8-D-61234567



## -2% 0% 2 % 4 % 6 % 8 %19841985198619871988198919901991199219931994199519961997199819992000200200200200200200200



## YearAnnual Rate of Return



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

-30% -2 0% - 1 0%

0% 1 0 % 20 % 3 0 % 4 0 %

197

7 1979 1981 1983 198 5 1987 1989 1991 19 9 3 1995 1997 1999 2001 200 3 2005 2007



## YearAnnual Rate of Return



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

8-D-7

## -15% -1 0% -5 % 0% 5% 1 0 % 15 % 20 % 25 %

197

7 1979 1981 1983 198 5 1987 1989 1991 19 9 3 1995 1997 1999 2001 200 3 2005 2007



## 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 . < 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