8-G-i

APPENDIX 8-G. DISTRIBUTIONS USED FOR DISCOUNT RATES

TABLE OF CONTENTS

8-G.1 INTRODUCTION ................................................................................................ 8-G-1

8-G.2 DISTRIBUTIONS USED FOR CONSUMER DISCOUNT RATES.................. 8-G-1

8-G.2.1 Distribution of Mortgage Interest Rates ............................................................... 8-G-1

8-G.2.2 Distribution of Rates for Debt Classes Considered for Replacement Products.... 8-G-2

8-G.2.3 Distribution of Rates for Equity Classes Considered for Replacement Products. 8-G-7

8-G.3 DISTRIBUTIONS USED FOR COMMERCIAL DISCOUNT RATES........... 8-G-13

LIST OF FIGURES

Figure 8-G.2.1 Distribution of New Home Mortgage Interest Rates.................................8-G-2

Figure 8-G.2.1 Distribution of Home Equity Loan Interest Rates .....................................8-G-3

Figure 8-G.2.2 Distribution of Credit Card Interest Rates.................................................8-G-4

Figure 8-G.2.3 Distribution of Installment Loan Interest Rates.........................................8-G-5

Figure 8-G.2.4 Distribution of Other Residence Loan Interest Rates................................8-G-6

Figure 8-G.2.5 Distribution of Other Lines of Credit Loan Interest Rates ........................8-G-7

Figure 8-G.2.1 Distribution of Annual Rate of Return on CDs .........................................8-G-8

Figure 8-G.2.2 Distribution of Annual Rate of Return on Savings Bonds.........................8-G-9

Figure 8-G.2.3 Distribution of Annual Rate of Return on Corporate AAA Bonds..........8-G-10

Figure 8-G.2.4 Distribution of Annual Rate of Savings Accounts...................................8-G-11

Figure 8-G.2.5 Distribution of Annual Rate of Return on S&P 500................................8-G-12

Figure 8-G.2.6 Distribution of Annual Rate of Return on Mutual Funds........................8-G-13

Figure 8-G.3.1 Distribution of Commercial Discount Rates: Retail ................................8-G-14

Figure 8-G.3.2 Distribution of Commercial Discount Rates: Medical.............................8-G-14

Figure 8-G.3.3 Distribution of Commercial Discount Rates: Medical.............................8-G-15

Figure 8-G.3.4 Distribution of Commercial Discount Rates: Hotel.................................8-G-15

Figure 8-G.3.5 Distribution of Commercial Discount Rates: Food .................................8-G-16

Figure 8-G.3.6 Distribution of Commercial Discount Rates: Office ...............................8-G-16

Figure 8-G.3.7 Distribution of Commercial Discount Rates: Education .........................8-G-17

Figure 8-G.3.8 Distribution of Commercial Discount Rates: State and Local 

Government..............................................................................................8-G-17
8-G-1

APPENDIX 8-G. DISTRIBUTIONS USED FOR DISCOUNT RATES

8-G.1 INTRODUCTION

The Department of Energy (DOE) estimated discount rate distributions by customer type: 

commercial and consumer (i.e. non-commercial residential end user). This appendix describes 

the distributions used.

8-G.2 DISTRIBUTIONS USED FOR CONSUMER DISCOUNT RATES

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.

8-G.2.1 Distribution of Mortgage Interest Rates

Figure 8-G.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, 2007, and 2010.

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.
8-G-2

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

8-G.2.2 Distribution of Rates for Debt Classes Considered for Replacement Products 

Figure 8-G.2.1 through Figure 8-G.2.5 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, 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.

0%

5%

10%

15%

20%

25%

30%

35%

Probability

Real Interest Rate
8-G-3

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

0%

5%

10%

15%

20%

25%

30%

Probability

Real Interest Rate
8-G-4

Figure 8-G.2.2 Distribution of Credit Card Interest Rates

0%

1%

2%

3%

4%

5%

6%

7%

8%

9%

Probability

Real Interest Rate
8-G-5

Figure 8-G.2.3 Distribution of Installment Loan Interest Rates

0%

5%

10%

15%

20%

25%

30%

35%

40%

Probability

Real Interest Rate
8-G-6

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

0%

2%

4%

6%

8%

10%

12%

14%

16%

18%

Probability

Real Interest Rate
8-G-7

Figure 8-G.2.5 Distribution of Other Lines of Credit Loan Interest 

Rates

8-G.2.3 Distribution of Rates for Equity Classes Considered for Replacement Products

Figure 8-G.2.1 through Figure 8-G.2.6 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
8-G-8

Figure 8-G.2.1 Distribution of Annual Rate of Return on CDs

-2%

0%

2%

4%

6%

8%

Annual Rate of Return

Year
8-G-9

Figure 8-G.2.2 Distribution of Annual Rate of Return on Savings 

Bonds

-2%

0%

2%

4%

6%

8%

Annual Rate of Return

Year
8-G-10

Figure 8-G.2.3 Distribution of Annual Rate of Return on Corporate 

AAA Bonds

-2%

0%

2%

4%

6%

8%

Annual Rate of Return

Year
8-G-11

Figure 8-G.2.4 Distribution of Annual Rate of Savings Accounts

-2%

0%

2%

4%

6%

8%

Annual Rate of Return

Year
8-G-12

Figure 8-G.2.5 Distribution of Annual Rate of Return on S&P 500

-40%

-30%

-20%

-10%

0%

10%

20%

30%

40%

Annual Rate of Return

Year
8-G-13

Figure 8-G.2.6 Distribution of Annual Rate of Return on Mutual 

Funds

8-G.3 DISTRIBUTIONS USED FOR COMMERCIAL DISCOUNT RATES

DOE derived commercial discount rates (i.e. weighted average cost of capital) for the 

life-cycle cost (LCC) analysis using the capital asset pricing model and firm-level data provided 

by Damodaran Online.7 State and local government discount rates were estimated using the rate 

of return on 20-year municipal bonds, as provided by the Federal Reserve Board.3 Separate 

distributions were constructed for each major industry. Figure 8-G.3.1 through Figure 8-G.3.8

show the probability distributions of commercial discount rates by industry.

-30%

-20%

-10%

0%

10%

20%

30%

Annual Rate of Return

Year
8-G-14

Figure 8-G.3.1 Distribution of Commercial Discount Rates: Retail

Figure 8-G.3.2 Distribution of Commercial Discount Rates: 

Medical

0%

5%

10%

15%

20%

25%

30%

1.8% 2.5% 3.6% 4.5% 5.4% 6.5% 7.4% 8.3% 9.3% 10.7%

Probability

Discount Rate

0%

5%

10%

15%

20%

25%

30%

35%

40%

1.8% 2.5% 3.6% 4.4% 5.4% 6.3% 7.4% 8.1% 9.7% 10.9%

Probability

Discount Rate
8-G-15

Figure 8-G.3.3 Distribution of Commercial Discount Rates: 

Medical

Figure 8-G.3.4 Distribution of Commercial Discount Rates: Hotel

0%

5%

10%

15%

20%

25%

30%

35%

Probability

Discount Rate

0%

5%

10%

15%

20%

25%

30%

35%

40%

1.4% 2.7% 3.7% 4.6% 5.5% 6.5% 7.5% 8.3% 9.4% 10.4%

Probability

Discount Rate
8-G-16

Figure 8-G.3.5 Distribution of Commercial Discount Rates: Food

Figure 8-G.3.6 Distribution of Commercial Discount Rates: Office

0%

5%

10%

15%

20%

25%

30%

35%

3.7% 4.5% 5.4% 6.4% 7.4% 8.6%

Probability

Discount Rate

0%

5%

10%

15%

20%

25%

30%

35%

0.6% 1.6% 2.6% 3.5% 4.5% 5.4% 6.4% 7.3% 8.3% 9.5% 10.1%

Probability

Discount Rate
8-G-17

Figure 8-G.3.7 Distribution of Commercial Discount Rates: 

Education

Figure 8-G.3.8 Distribution of Commercial Discount Rates: State 

and Local Government

0%

5%

10%

15%

20%

25%

30%

35%

40%

45%

50%

1.1% 2.1% 3.4% 4.6% 5.4% 6.4% 7.9%

Probability

Discount Rate

0%

5%

10%

15%

20%

25%

30%

35%

-1.3% 0.7% 1.5% 2.7% 3.6% 4.2% 5.4% 6.1%

Probability

Discount Rate
8-G-18

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/>

7. Damodaran Online, Data Page: Costs of Capital by Industry Sector, 2012. Damodaran. 

(Last accessed July, 2013.) <http://pages.stern.nyu.edu/~adamodar/>