8C-i

APPENDIX 8C. DISTRIBUTIONS USED FOR DISCOUNT RATES

TABLE OF CONTENTS

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

8C.2 DISTRIBUTION OF RATES FOR DEBT CLASSES CONSIDERED FOR 

REPLACEMENT PRODUCTS ..............................................................................8C-1

8C.3 DISTRIBUTION OF RATES FOR EQUITY CLASSES CONSIDERED FOR 

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

LIST OF FIGURES

Figure 8C.2.1 Distribution of Home Equity Loan Interest Rates .......................................8C-1

Figure 8C.2.2 Distribution of Credit Card Interest Rates...................................................8C-2

Figure 8C.2.3 Distribution of Installment Loan Interest Rates...........................................8C-3

Figure 8C.2.4 Distribution of Other Residence Loan Interest Rates..................................8C-4

Figure 8C.2.5 Distribution of Other Lines of Credit Loan Interest Rates ..........................8C-5

Figure 8C.3.1 Distribution of Annual Rate of Return on CDs ...........................................8C-6

Figure 8C.3.2 Distribution of Annual Rate of Return on Savings Bonds...........................8C-7

Figure 8C.3.3 Distribution of Annual Rate of Return on Corporate AAA Bonds..............8C-8

Figure 8C.3.4 Distribution of Annual Rate of Savings Accounts.......................................8C-9

Figure 8C.3.5 Distribution of Annual Rate of Return on S&P 500..................................8C-10

Figure 8C.3.6 Distribution of Annual Rate of Return on Mutual Funds..........................8C-11
8C-1

APPENDIX 8C. DISTRIBUTIONS USED FOR DISCOUNT RATES

8C.1 INTRODUCTION

DOE derived consumer 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.

8C.2 DISTRIBUTION OF RATES FOR DEBT CLASSES CONSIDERED FOR 

REPLACEMENT PRODUCTS

Figure 8C.2.1 through Figure 8C.2.5 show the distribution of real interest rates for 

different types of debt used to finance replacement 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, 2007, and 

2010.

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 8C.2.1 Distribution of Home Equity Loan Interest Rates

0%

5%

10%

15%

20%

25%

30%

Probability

Real Interest Rate
8C-2

Figure 8C.2.2 Distribution of Credit Card Interest Rates

0%

1%

2%

3%

4%

5%

6%

7%

8%

9%

Probability

Real Interest Rate
8C-3

Figure 8C.2.3 Distribution of Installment Loan Interest Rates

0%

5%

10%

15%

20%

25%

30%

35%

40%

Probability

Real Interest Rate
8C-4

Figure 8C.2.4 Distribution of Other Residence Loan Interest Rates

0%

2%

4%

6%

8%

10%

12%

14%

16%

18%

Probability

Real Interest Rate
8C-5

Figure 8C.2.5 Distribution of Other Lines of Credit Loan Interest 

Rates

8C.3 DISTRIBUTION OF RATES FOR EQUITY CLASSES CONSIDERED 

FOR REPLACEMENT PRODUCTS

Figure 8C.3.1 through Figure 8C.3.6 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 2012. 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 2012.

5 The 

rates for stocks are the annual returns on the Standard and Poor’s (S&P) 500 from 1977 to 2012.

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 2012. DOE adjusted the nominal rates to real 

rates using the annual inflation rate in each year.

0%

2%

4%

6%

8%

10%

12%

Probability

Real Interest Rate
8C-6

Figure 8C.3.1 Distribution of Annual Rate of Return on CDs

-2%

0%

2%

4%

6%

8%

Annual Rate of Return

Year
8C-7

Figure 8C.3.2 Distribution of Annual Rate of Return on Savings 

Bonds

-2%

0%

2%

4%

6%

8%

Annual Rate of Return

Year
8C-8

Figure 8C.3.3 Distribution of Annual Rate of Return on Corporate 

AAA Bonds

-2%

0%

2%

4%

6%

8%

Annual Rate of Return

Year
8C-9

Figure 8C.3.4 Distribution of Annual Rate of Savings Accounts

-2%

0%

2%

4%

6%

8%

Annual Rate of Return

Year
8C-10

Figure 8C.3.5 Distribution of Annual Rate of Return on S&P 500

-40%

-30%

-20%

-10%

0%

10%

20%

30%

40%

Annual Rate of Return

Year
8C-11

Figure 8C.3.6 Distribution of Annual Rate of Return on Mutual 

Funds

-30%

-20%

-10%

0%

10%

20%

30%

Annual Rate of Return

Year
8C-12

REFERENCES

1. The Federal Reserve Board, Survey of Consumer Finances 1989, 1992, 1995, 1998, 

2001, 2004, 2007, 2010. <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, 2013.

<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, 2013.

<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, 

2013. <www.federalreserve.gov/releases/H15/data.htm>

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

History, 2013. <http://mortgage-x.com/general/indexes/default.asp>

6. Damodaran Online Data Page, The Data Page: Historical Returns on Stocks, Bonds and 

Bills - United States, 2013. Damodaran. <http://pages.stern.nyu.edu/~adamodar/>