8-C-i

APPENDIX 8-C. DISTRIBUTIONS USED FOR DISCOUNT RATES

TABLE OF CONTENTS

8-C.1 INTRODUCTION ................................................................................................. 8-C-1

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

8-C.3 DISTRIBUTION OF RATES FOR DEBT CLASSES CONSIDERED FOR 

REPLACEMENT PRODUCTS ............................................................................ 8-C-2

8-C.4 DISTRIBUTION OF RATES FOR EQUITY CLASSES CONSIDERED FOR 

REPLACEMENT PRODUCTS ............................................................................ 8-C-5

LIST OF FIGURES

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

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

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

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

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

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

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

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

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

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

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

Figure 8-C.4.6 Distribution of Annual Rate of Return on Mutual Funds.......................... 8-C-8
8-C-1

APPENDIX 8-C. DISTRIBUTIONS USED FOR DISCOUNT RATES

8-C.1 INTRODUCTION

The Department of Energy (DOE) derived discount rates for the life-cycle cost (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-C.2 DISTRIBUTION OF MORTGAGE INTEREST RATES

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

0%

5%

10%

15%

20%

25%

30%

Probability

Real Interest Rate
8-C-2

8-C.3 DISTRIBUTION OF RATES FOR DEBT CLASSES CONSIDERED FOR 

REPLACEMENT PRODUCTS

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

different types of debt used to finance replacement clothes dryers and room air conditioners. 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, because interest on such loans is tax deductible.

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

0%

5%

10%

15%

20%

25%

30%

Probability

Real Interest Rate
8-C-3

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

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

0%

1%

2%

3%

4%

5%

6%

7%

8%

9%

10%

Probability

Real Interest Rate

0%

5%

10%

15%

20%

25%

30%

35%

40%

Probability

Real Interest Rate
8-C-4

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

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

Rates

0%

2%

4%

6%

8%

10%

12%

14%

16%

18%

20%

Probability

Real Interest Rate

0%

2%

4%

6%

8%

10%

12%

14%

Probability

Real Interest Rate
8-C-5

8-C.4 DISTRIBUTION OF RATES FOR EQUITY CLASSES CONSIDERED 

FOR REPLACEMENT PRODUCTS

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

different types of equity used to finance replacement products. 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 2009. 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 2009.5 The 

rates for stocks are the annual returns on the Standard and Poor’s (S&P) 500 from 1977 to 2009.6

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 2009. DOE adjusted the nominal rates to real 

rates using the annual inflation rate in each year.

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

-2%

0%

2%

4%

6%

8%

Annual Rate of Return

Year
8-C-6

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

Bonds

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

AAA Bonds

-2%

0%

2%

4%

6%

8%

Annual Rate of Return

Year

-2%

0%

2%

4%

6%

8%

Annual Rate of Return

Year
8-C-7

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

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

-2%

0%

2%

4%

6%

8%

Annual Rate of Return

Year

-40%

-30%

-20%

-10%

0%

10%

20%

30%

40%

Annual Rate of Return

Year
8-C-8

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

Funds

-30%

-20%

-10%

0%

10%

20%

30%

Annual Rate of Return

Year
8-C-9

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, 2010. (Last accessed 2/25/10, 

<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, 2010. (Last 

accessed 2/25/10, <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, 

2010. (Last accessed 2/25/10, <http://www.federalreserve.gov/releases/H15/data.htm>

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

History, 2010. (Last accessed February 25, 2010.) <http://mortgagex.com/general/indexes/default.asp>

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

States, 2010. Damodaran. (Last accessed February 25, 2010.) 

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