8E-i

APPENDIX 8E. DISTRIBUTION USED FOR DISCOUNT RATES

TABLE OF CONTENTS

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

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

8E.3 DISTRIBUTION OF RATES FOR DEBT CLASSES CONSIDERED FOR 

REPLACEMENT PRODUCTS ..............................................................................8E-1

8E.4 DISTRIBUTION OF RATES FOR EQUITY CLASSES CONSIDERED FOR 

REPLACEMENT PRODUCTS ..............................................................................8E-4

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-2

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

Figure 8E.3.4 Distribution of Other Residence Loan Interest Rates..................................8E-3

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

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

Figure 8E.4.2 Distribution of Annual Rate of Return on Savings Bonds...........................8E-5

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-6

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-7
8E-1

APPENDIX 8E. DISTRIBUTION USED FOR DISCOUNT RATES

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 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.

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.

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

8E.3 DISTRIBUTION OF RATES FOR DEBT CLASSES CONSIDERED FOR 

REPLACEMENT PRODUCTS

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 for residential dishwashers. The data source 

0%

5%

10%

15%

20%

25%

30%

Probability

Real Interest Rate
8E-2

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.

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

Figure 8E.3.2 Distribution of Credit Card Interest Rates

0%

5%

10%

15%

20%

25%

30%

Probability

Real Interest Rate

0%

1%

2%

3%

4%

5%

6%

7%

8%

9%

10%

Probability

Real Interest Rate
8E-3

Figure 8E.3.3 Distribution of Installment Loan Interest Rates

Figure 8E.3.4 Distribution of Other Residence Loan Interest Rates

0%

5%

10%

15%

20%

25%

30%

35%

40%

Probability

Real Interest Rate

0%

2%

4%

6%

8%

10%

12%

14%

16%

18%

20%

Probability

Real Interest Rate
8E-4

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

Rates

8E.4 DISTRIBUTION OF RATES FOR EQUITY CLASSES CONSIDERED 

FOR REPLACEMENT PRODUCTS

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 for residential dishwashers. 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 2010. 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 2010.5 The rates for stocks are the annual returns on the Standard and Poor’s (S&P) 500 from 

1977 to 2010.6 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 2010. DOE adjusted the 

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

0%

2%

4%

6%

8%

10%

12%

14%

Probability

Real Interest Rate
8E-5

Figure 8E.4.1 Distribution of Annual Rate of Return on CDs

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

Bonds

-2%

0%

2%

4%

6%

8%

Annual Rate of Return

Year

-2%

0%

2%

4%

6%

8%

Annual Rate of Return

Year
8E-6

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

AAA Bonds

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

-2%

0%

2%

4%

6%

8%

Annual Rate of Return

Year

-2%

0%

2%

4%

6%

8%

Annual Rate of Return

Year
8E-7

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

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

Funds

-40%

-30%

-20%

-10%

0%

10%

20%

30%

40%

Annual Rate of Return

Year

-30%

-20%

-10%

0%

10%

20%

30%

Annual Rate of Return

Year
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 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, 2011. (Last accessed 2/25/11, 

<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, 2011. (Last 

accessed 2/25/11, <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, 

2011. (Last accessed 2/25/11, 

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

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

History, 2011. (Last accessed February 25, 2011.) <http://mortgagex.com/general/indexes/default.asp>

6. Damodaran Online Data Page, Historical Returns on Stocks, Bonds and Bills-United 

States, 2011. Damodaran. (Last accessed February 25, 2011.) 

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