### APPENDIX P. DISTRIBUTIONS USED FOR DISCOUNT RATES TABLE OF CONTENTS P.1 DISTRIBUTION OF MORTGAGE INTEREST RATES .................... P.1-1 P.2 DISTRIBUTION OF RATES FOR TYPES OF DEBT AND EQUITY USED TO FINANCE REPLACEMENT FURNACES ............................... P.1-2 P.3 DISTRIBUTION OF RATES FOR TYPES OF EQUITY USED TO FINANCE REPLACEMENT FURNACES ......................................... P.1-5 LIST OF FIGURES Figure P.1.1 Distribution of New Home Mortgage Interest Rates ................... P.1-1 

### Figure P.2.1 Distribution of Home Equity Loan Interest Rates ..................... P.1-2 

### Figure P.2.2 Distribution of Credit Card Interest Rates ........................... P.1-3 

### Figure P.2.3 Distribution of Installment Loan Interest Rates ....................... P.1-3 

### Figure P.2.4 Distribution of Other Residence Loan Interest Rates .................. P.1-4 

### Figure P.2.5 Distribution of Other Lines of Credit Loan Interest Rates .............. P.1-4 

### Figure P.3.1 Distribution of Annual Rate of Return on CD 's ....................... P.1-5 

### Figure P.3.2 Distribution of Annual Rate of Return on Savings Bonds ............... P.1-6 

### Figure P.3.3 Distribution of Annual Rate of Return on Corporate AAA Bonds ........ P.1-6 

### Figure P.3.4 Distribution of Annual Rate of Return on Savings Accounts

............ 

### P.1-7 Figure P.3.5 Distribution of Annual Rate of Return on S&P 500

................... P.1-7 

### Figure P.3.6 Distribution of Annual Rate of Return on Mutual Funds ............... P.1-8 

### APPENDIX P. DISTRIBUTIONS USED FOR DISCOUNT RATES TABLE OF CONTENTS P.1 DISTRIBUTION OF MORTGAGE INTEREST RATES

.................... P.l-l P.2 DISTRIBUTION OF RATES FOR TYPES OF DEBT AND EQUITY USED TO FINANCE REPLACEMENT FURNACES

.......... .... ................. P.1-2 P.3 DISTRIBUTION OF RATES FOR TYPES OF EQUITY USED TO FINANCE REPLACEMENT FURNACES

........ . .................. ... ..... . ..... P.l-S

Figure P.1.l Figure P.2.l Figure P.2.2 Figure P.2.3 Figure P.2.4 Figure P.2.S Figure P.3.l Figure P.3.2 Figure P.3.3 Figure P.3.4 Figure P.3.S Figure P.3.6 LIST OF FIGURES Distribution of New Home Mortgage Interest Rates

....... .. .......... P.l-l Distribution of Home Equity Loan Interest Rates

....... .. ............ P.1-2 Distribution of Credit Card Interest Rates

........................... P.1-3 Distribution of Installment Loan Interest Rates

.......... .. ....... .... P.1-3 Distribution of Other Residence Loan Interest Rates

... .... .... .. . ... . P .1-4 Distribution of Other Lines of Credit Loan Interest Rates

.............. P.1-4 Distribution of Annual Rate of Return on CD's

....................... P.l-S Distribution of Annual Rate of Return on Savings Bonds

... . . . ......... P.1-6 Distribution of Annual Rate of Return on Corporate AAA Bonds

........ P .1-6 Distribution of Annual Rate of Return on Savings Accounts

............ P.1-7 Distribution of Annual Rate of Return on S&P SOO

................... P.1-7 Distribution of Annual Rate of Return on Mutual Funds

............... P.1-8

P-i

### APPENDIX P. DISTRIBUTIONS USED FOR DISCOUNT RATES
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.

P.1 DISTRIBUTION OF MORTGAGE INTEREST RATES Figure P.1.1 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 , 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.



### Figure P.1.1 Distribution of New Home Mortgage Interest Rates

P-1 

### APPENDIX P. DISTRIBUTIONS USED FOR DISCOUNT RATES

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 us e d

.


### P.l DISTRffiUTION OF MORTGAGE INTEREST RATES Figure P

. 1.1 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 Finan ce s (SCF) 

### in 1989 , 1992 , 1995 , 1998 , 2001 , and 2004. 1 

### Using the appropriate SCF 

### data for each year, DOE adjusted the nominal mortgage interest rate for each rele v ant household in the SCF 

### for mortgage tax deduction and inflation. In cases where the effective int e rest 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. 

# 3O% r- - n -

25%

# ~--- - -

# ~ I PI 20% ,In: 

## It**~** 

### :a**~** 1

- ! 15 % 

## e 1 111: D..**I'I~** 10% 1111 1--

## II~ -**~I: ~II**  5 % 

## Il f- iil**~**

# l~ II I,

# ~ II I

# ~**~.,** Ir-l 1)1. ....,. 0% , =---.- , i i ,**\. \.** **\. .** **~\ .** **. ~\.** **\. .** **. ~\.** **\. ~\** **.** a\.**~\a** a\

. 1\a

1:)
- ' v ",

. n, ' b<
- 

# ,, - <0- 

# ,, - '0 ' C!> ' "I:) ' 

# ,,"

- 

## """ n, '?**~-** <o'!l ",n, ' 

## " 

## " Real Interest Rate 

### Figure P.1.l Distribution of New Home Mortgage Interest Rates

P-l

### P.2 DISTRIBUTION OF RATES FOR TYPES OF DEBT AND EQUITY USED TO FINANCE REPLACEMENT FURNACES Figures P.2.1 through P.2.5 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 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.

Figure P.2.1 Distribution of Home Equity Loan Interest Rates 

### P.2 DISTRIBUTION OF RATES FOR TYPES OF DEBT AND EQUITY USED TO FINANCE REPLACEMENT FURNACES Figures P

. 2.1 through P. 2 .5 show the distribution of real inter e st rates for different types of debt used to finance replac e m e nt furnaces. Th e 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 , and 2004. 1 

### DOE adjusted the nominal rate s 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% iT"" i',

15 % I-**~** Iii I" :0 

## ., 1'1 .c 

## e I I a.. 10% 

### '---- /1'

- r---- 

# - ",

- 

### I'

5 % 

### r-- 

# - PM

# ~ 0%

# ~ I!lI El C=i 

## """ = -r- , , , , , , 0'0 ';; '0 ,;;'0 ';; ' 0 ';;'0**,o ,o**  ';;' 0 ';; '0 ';; '0 ';; '0**,o** 

# of, o**~,o** 

# of ,o**,o ~,o**  ';;'0 

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- b.- 10 ' 

## "'

- '0

- '1l
- "t::)- 

## ,, '" ,,'),

-**,,~** "b.

-**,,~ ~**  ,**~** - Real Interest Rate 

### Figure P.2.1 Distribution of Home 

### Equity Loan Interest Rates

P-2h h 40D 0^° ro^° \° p°\° 3\° .\° p°\° 4.\° 6\° ro\° j\° P\° oP\° p. ^• ^. ^^• p. ^ 14i• ^• ^p. ^^• ^^• ^^• ^^• ^y. ^6 ^^• ^g• ^p. lp• ^^• ^^. ^^• ^p• ^y. gyp. gyp.
Real Interest Rate 

### Figure P.2.2 Distribution of Credit Card Interest Rates

35%

30%

25%

10%

5%

t, rod\° 0c\° OrO \° fi`^\° `t' Real Interest Rate Figure P.2.3 Distribution of Installment Loan Interest Rates

P-3 .. -- ..**~- --.** **--.** ._--_. __ . __ . - -- - - - - . - . .. . 

# __ .. . - 10%

; 8% 

# L

__ 6%
- - - - - ----- -**~** 

### :c


# - co ..Q 

## e

- 11. 4% '-- ._-- - 1

- 

### - - 

# - -

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# - - 1

- 

# - - I
- I
- 

# -

0%

# ~ 

# n In []
""

. A

### *~~***~~~~~**~~~~~~*~~*~~**~**~~~~~ ~~** **~~~~~~ ~~~'~** **~~~~~~** Real Interest Rate 

### Figure P.2.2 Distribution of Credit Card Interest Rates


## 35 % 1**~::: r.**  __ --_- - - -- -- -- -- --- -- ----- - ---------- -- -- -- -- -- --

:c co ..Q o Ii. 15 %

10%

5 % 

# J

<Q\o 0\0**, ~'i;>**  </5\0 '0 ' </5\0**~I:l '**  <Q\o**~", '**  a= r-r-lIIjI j & j--**~\o ~~** **' ~\o** **~~.** <Q\ o**~'O .**  <Q\o**. ~\o**  

### ",,,,

. </5\0**.** </5\0**~.** Real Interest Rate 

### Figure P .2.3 Distribution of Installment Loan Interest Rates

P

- 3**~\o** .\

.**~\o ~.** **~'i;> ~.** **~**20%

15%

5%

0% 11 -M, ®I Im-I -m- -^^ i

Real Interest Rate 

### Figure P.2.4 Distribution of Other Residence Loan Interest Rates

14%

12%

10%

4%

2%

0% ^^o ^^o y^o ^^0 600 6^0 ^o^o ^^ 6^0 ^^o y^o 6^0 ^^o ^^o ^o^o ^^o D o^o Do^o ^o^o ^^o ^o^o ^^o ^o^o y^o p. ^• y. g. ^. ^• 6. ^• ^• ^• ^p. ^^. ^^L• ^^• ^R• ^^• ^6. ^1. ^^' ^^' gyp. y^' yL' ^3' Real Interest Rate Figure P.2.5 Distribution of Other Lines of Credit Loan Interest Rates

P-4**.--- ---~--** **----- --** **--- --**  .. _- .- -- ---- --

_ .**~~--~- --** **~---** . . . - 

## 20 % 1

15 % 

### 1-

------- - 1--

- ...-**~** 

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- I- I I, co 

# I t-- ..Q 

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# -**;!\** - - ' 

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# EJ ,'I, 0 % I','**~** c:I F."'I r= 

# - - I;:;;;a , , I 0\0**~\o ~\o ~\o** **~\o \o** **~\o ~\o**  0 \0 0 \ 0 rt;\o 0\0 0\0 0\0**\o** rt; \o**~\o** C)'Y 

# ".
... .**~. .** **.** 10 ' '\

. 'Or,;.**C!>~** "C) , "r,;. " ", r,;.**'? ,,~** **.** ,, 10 '**.** 

## " " Real Interest Rate 

### Figure P.2.4 Distribution of Other Residenc e Loan Interest Rates

14 % 

## I 1 2% 

## I 10 %
- 

### - - ' 0- 

## I**~** 8 %



# - :s co ..Q 

## m 2 6% II. - 

### -- - I-
-

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### ~***~~~~~**~**~~~~*~~~~*

C) , "

. ... .**~.** \><

.**.** 10 ' '\. '0 ' C!> ' " C) , ""

. "...

.**,, .** **~. ~.**  ,,10'**.** ,, '0 ' "C!> '**~** . ... "

. ...... . 0/' Real Interest Rate 

### Figure P .2 . 5 Distribution of Other Lines of Credit Loan Interest Rates

P -4

### P.3 DISTRIBUTION OF RATES FOR TYPES OF EQUITY USED TO FINANCE

REPLACEMENT FURNACES Figures P.3.1 through P.3.6 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 deposit (CDs),2 savings bonds,' and bonds (AAA corporate bonds)' are from Federal Reserve Board time-series data covering 1977-2006. DOE assumed rates on checking accounts to be zero. Rates on savings and money market accounts are from Cost of Savings Index data covering 1984-2006.5 The rates for stocks are the annual returns on the Standard and Poor's (S&P) 500 in the 1977-2006 period.' 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 of the 1977-2006 period. DOE adjusted the nominal rates to real rates using the annual inflation rate in each year.

8% -

6%

d ii 4% d

2% -

0% 00 0 ) N M V ( n (0 N- 00 0) o N M t UL) (C 1, W O ) 0 N 1L) (0

N- n ao W W W W W W W W M 0 ) 0) a) a) 0) 0) M M M o 0 0 0 0 0) 0) 0) 0) Q) 0) 0) 0) 0) 0) 0) 0) 0) 0) 0) rn rn rn rn rn rn rn rn o 0 0 0 0 r r r r r r r r r r r r r r r r r r r r r r N N N N N

2% - Year 

### Figure P.3.1 Distribution of Annual Rate of Return on CD's 

### P.3 DISTRIBUTION OF RATES FOR TYPES OF EQUITY USED TO FINANCE 

### REPLACEMENT FURNACES Figures P.3.1 through P.3.6 show the distribution of real interest rates for different types of equity used to finance replacement furnaces. Data for equity classes are not a v ailable from the Federal Reserve Board's 

### SCF , so the Department deri v ed data for the s e classes from national-level historical data. The interest rates associated with certificates of deposit (CDs), 2 savings bonds ,3 and bonds (AAA corporate bonds) 4 are from Federal R e serve Board time-series data covering 1977-2006. DOE assumed rate s on checking accounts to be zero. Rates on savings and money market accounts are from Cost of Savings Index data co v ering 1984-2006. 5 

### The rates for stocks are the annual returns on the Standard and Poor's (S&P) 500 in the 1977-2006 period. 6 

### The mutual fund rates are a weighted average of the stock rates (two-thirds weight) and the bond rat e s (one-third weight) in each year of the 1977

- 2006 p e riod. DOE adjusted the nominal rates to real rates using the annual inflation rate in each year.

8%

6% - - - E :::I li It: '0 4%**~-** 

### - 

# ----**~** It: iii :::I C c 

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### ........ .... .... 

### .... .... 

### .... .... .... .... 

### .... .... .... .... .... .... 

### .... .... .... .... N N N N 0%

-2% Year 

### Figure P.3.1 Distribution of Annual Rate 

### of Return on CD's

P-5Annual Rate of Return
N O N A 0) co a o 0 0 0 0 1977 1978 ii^

1981 ffiffi^ 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 [}gyp Annual Rate of Return
N A 0) 0 0 0 1977 ri 1978 r ,---MM

L 1981 1982 1983 1984 1985 1986 1987 1988 - 1989 1990 1991 go 1992 pm 1993 . - 1994 1995 i

1996 1997 1998 1999 2000 t 2001 2002 2003 p 2004 2005 , 2006 I

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# = 

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1978

# ~**k** 1982 II

- I 1983 

# r 1984 Ii

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## - r'

## ~::~ j : [

# ~::: I:

- I 1990 li e

- I 1991 II 1992 ' I i>

__ 1993 1994 1995 t¥* 1996 fi-.

- l 1997 I

- I 1998

_ I' 1999

_ I ' 2000 U L 2001

- I

# ::**1~**

- I 2005 

## " =

- I 2006 J I , oc>- Annual Rate of Return 

## '" '$.

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.... 

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# =**~ ~**  o '$. 1977**~** 1978 Annual Rate of Return 

## '"**~** o 

### ..,. '$.

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_ 1 ; - 1 1 1983 ..:: ci l

- I 1984 "



### - I I 1985

__**~~~ ~**  1986 

# r l 1987 t --=- v==;**1988 ~**  • 91 1989**1!1 t=** **~==~~** 1990 

### l b tI 1991 1 +_ . I

# ~::: 

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1994 I L 1995

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## - F J 1998 I r-=--.= !

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### re=-== 2003**1!:1 "'** **=~::::::::: ::::::** **::rJ** 2004 "

_ II

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..**~! ==~~**  CX> '$.8%

6%

4%

2%

0%

-2% Year L1 L , 9 O O O I 

# I CO O O O v O N N N N N N



### Figure P.3.4 Distribution of Annual Rate of Return on Savings Accounts
40%

30% - -

20% - - -

10% i

v

,

CO 0) 0 O N- DO 0) N [[' ') Lo (0 E+ cc, 0) O] a) 61 a) m m Y-- [~ m Cr m rn W rn rn 00 l0 CO O O O O U- i 1 ^ ^ - •- - _ _ 0 N N N N 10%
-

-20% - -

30%
- Year Figure P.3.5 Distribution of Annual Rate of Return on S&P 500 u I_l V LO CO N- Co 0) O N M e} u) (O h o0 O) O CO Co Co CO Co Co 0) 0 ) 0) O) 0) 0 ) 0) 0) 0) 0) O 0) 0) 0) 0 ) 0) 0) 0) 0 ) 0) 0) 0) 0) 0) 0) 0) 0) O ^ r ^ ^ ^ r r r r r r r r r r r N

P-7 ----------------------- ------------

8%

6% 

### '" c


### ... 

### " Gi II::



### .... 4% 0**~** S co II:: c;; F 

### " c c 2% 

### «

0%

-2%**~------------------------------------** Year 

### Figure P.3.4 Distribution of Annual Rate 

### of Return on Savings Accounts

20% E

### ~ ... 10%

- -- --

0% ('t) .q- LO co 

### :5 :5 :5 :5 N N N N -10%

-**---- --l** **II II--------------------------1** **II ~-** **r. ---** **---**

-20% 

# --- - -- - - - - ----- --

.. -**~O%~-------------------------------------** Year 

### Figure P.3.S Distribution of Annual Rate 

### of Return on S&P SOO

P-7Annual Rate of Return

N N U1 O 01 O cn O U1 O 01 0 0 0 0 0 0 0 0 0

1978 9 1979 1980 O

1982 1983 1984 1985 1986 1987 1988 1 1989
1991 [ 1992 l 1993 1994 mil 1995 1996 1997 1998 1999 I- I Yfr'r-I

2003 iI 2004 2005 2006 =.1

120%-1--------15%-------------1-1----1I,,lD.,,'"'"CD00 000 0 00'"'"'"'"-5%-10%+-------15%YearFigureP.3.6DistributionofAnnualRateofReturnonMutualFundsP-8

### REFERENCES

1. The Federal Reserve Board, Survey of Consumer Finances (SCF), 1989-2004. (Last accessed December 10, 2006.) 

### <http://www. federalreserve. gov/pubs/oss/oss2/scfindex.html> 2. The Federal Reserve Board, Federal Reserve Statistical Release, Selected Interest Rates. Instruments: 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., 2007. 

### <http://www.bog.frb.fed.us/releases/H 15/data.htm> 3. The Federal Reserve Board, Federal Reserve Statistical Release, Selected Interest Rates. Instruments: State and local bonds. Maturity: 20 year. Frequency: Monthly. Description: Bond buyer go 20-bond municipal bond index., 2007. <http://www.bog.frb.fed.us/ releases /H 1 5/data.htm> 4. The Federal Reserve Board , Federal Reserve Statistical Release, Selected Interest Rates. Instruments : Corporate bonds/Moody's Seasoned AAA. Maturity: 20 year. Frequency: Annual . Description: Moody's yield on seasoned corporate bonds-all industries, AAA., 2007. <http://www.bog.frb. fed.us / releases4 l l5/data.htm> 5. Golden West Financial Corporation (GDW), Cost of Savings Index, 2007. (Last accessed February 10, 2007.) <http://mortgage-x.com/general/indexes/default.asp>
6. Damodaran , A., Damodaran Online: The Data Page, 2007. Stem School of Business at New York University. ( Last accessed February 10, 2007.) <http:// pages.stem .nyu.edu/- adamodar/> 

## REFERENCES 1. The Federal Reserve Board, 

### Survey of Consumer Finances (SCF), 1989-2004. (Last accessed December 10,2006.) <http://www. federalreserve. gov /pubs / oss/ oss2/scfindex

. html > 2. The Federal Reserve Board, 

### Federal Reserve Statistical Release, Selected Interest Rates. Instruments: 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

. , 2007

. <http:/ / www.bog.frb.fed

. us / releases / H15 / data.htm > 3. The Federal Reserve Board, 

### Federal Reserve Statistical Release, Selected Interest Rates. Instruments : State and local bonds. Maturity: 20-year

. Frequenc y : Monthly. Description: Bond buyer go 20-bond municipal bond index., 2007. <http:/ / www.bog.frb.fed.us/releases/H15/data.htm> 4. The Federal Reserve Board, 

### Federal Reserve Statistical Release, Selected Interest Rates. Instruments: Corporate bonds /

Moody's Seasoned AAA

. Maturity : 20-year. Frequency : Annual. Description : Moody's yield on seasoned corporate bonds-all industries, AAA., 2007. <http://www.bog.frb.fed.us/releasesIH15/data.htm> 5. Golden West Financial Corporation (GDW), 

### Cost of Savings Index, 2007. (Last accessed February 10, 2007.) <http://mortgage- x. com! generaVindexes/ default. asp > 6. Damodaran, A., 

### Damodaran Online: The Data Page, 2007. Stem School of Business at New York University. (Last accessed February 10,2007.)**<http://pages.stem.nyu.edu/~adamodar/>**

P-9