ESTIMATING THE COST OF CAPITAL - Simon Benningasimonbenninga.com/benninga_sarig/chap09.pdf ·...

Chapter 9 slides, page 1

ESTIMATING THE COST OF CAPITAL

General approach

� Find levered cost of equity re(L).

� Find cost of debt rD

� Calculated WACC:

� �WACC r LE

D Er t

D

D Ee D C�

�

� �

�

( ) 1

� Discount FCFs at WACC to get total value offirm

� Derive cost of shares by subtracting value ofmore senior claims (Debt, Preferred Stock,Warrants, etc.)


3 METHODS FOR CALCULATING THECOST OF CAPITAL

1. CAPM: Capital Asset Pricing Model

2. Use Gordon model and variations.

3. P/E model

��

��


In all 3 cases the discount rate for the firm’s FreeCash Flows is the WACC. Either :

� Estimate the firm’s cost of debt rD andcalculate the WACC in the ordinary way:

� �WACC r LE

E Dr t

D

E De D c�

�

� �

�

( ) 1

� Unlever the cost of equity to get r(U) andassume that this gives the WACC:

� ��

� �

r L r U r U r tD

E

r Ur L r t

D

ED

E

WACC

e D c

e D c

assumed to be

( ) ( ) ( )

( )( )

� � � �

� �

� �

�

�

1

1

1

� Calculate the WACC using the CAPM bycalculating an asset beta. (Illustrated later.)


SOME IMPORTANT THINGS TOREMEMBER

� Calculate the firm’s cost of capital, not thecost of equity.

� Be consistent in treatment of inflation.

� Use industry data to estimate the cost ofcapital for the firm you value, not just thefirm’s own data.


��

��

��

1. Estimate the equity �e

2. Estimate the market risk-free rate on debt rfdebt .

3. Estimate the firm’s corporate tax rate tc.


4. a. Estimate the expected return on the marketE(rm ).

In this case the SML slope is

[E(rm) - rfdebt(1-tc )]

or

b. Estimate the market risk premium

� = E(rm ) - rfdebt

In this case, the SML slope is [ � + tc rfdebt ]


5. Estimate the firm’s cost of debt rD and calculatethe WACC:

� �WACC r LE

E Dr t

D

E De D c�

�

� �

�

( ) 1

6. Estimate the firm’s debt beta �e and use it tocalculate the firm’s asset beta:

� �� asset e debt c

E

D E

D

D Et�

�

�

�

�1

7. Use the asset beta, �asset , and the WACC SML toestimate the WACC:

WACC = rfdebt (1-tc ) + �asset [E(rm) - rfdebt(1-tc )]

Note: If you assume that the debt beta, �debt = 0,then the asset �asset:

� �� asset e debt c eE

D E

D

D Et

E

D E�

�

�

�

� �

�

1






EXAMPLE: WHAT’S THE WACC OF THE AUTOCOMPANIES?

SML Parametersrfdebt 6.69% <-- 10 year AAA industrial bond yield, December 1996

corporate tax rate, tc 36% <-- Value Line, average tax rate of 3 auto firms

market risk premium 8.40% <-- Ibbotsen-Sinequefield (from Brealey/Myers)slope of SML, E(rm)-rf*(1-tc) 10.81%

GeneralMotors Ford Chrysler

equity beta 1.1 1.1 1.25 <-- Value Linedebt beta 0 0 0 <-- Guess!debt 81,300,000,000 153,500,000,000 13,200,000,000 <-- Value Line figure for total firm debtnumber of shares 756,035,101 1,114,618,895 713,533,304share price 58 33 35 <-- share price, December 13, 1996equity/value 35.04% 19.33% 65.42%(debt/equity, as a check) 1.85 4.17 0.53

asset beta 0.385 0.213 0.818

WACC 8.45% 6.58% 13.12%


INCORPORATING DEBT �Implied debt beta's

LT Debt ($ billion) 2.8 6.3 0.725LT Interest ($ billion) 31.3 103.5 8.5Implied firm cost of debt, rD 8.95% 6.09% 8.53%

Implied debt beta =(rD-rfdebt)/(E(Rm)-rfdebt*(1-tc)) 0.21 -0.06 0.17 <-- debt SML: RADR = rfdebt + �debt[E(rm)-rfdebt*(1-tc) ]

Note : Clearly there's a problem with Ford's debt beta! Perhaps the cause is that I've used the average cost of debt instead of the marginal.

USING THE CAPM TO DERIVE THE WACC FOR THE BIG 3 AUTO FIRMSincorporating implied debt betas

SML Parametersrfdebt 6.69% <-- 10 year AAA industrial bond yield, December 1996


market risk premium 8.40% <-- Ibbotsen-Sinequefield (from Brealey/Myers)slope of SML, E(rm)-rf*(1-tc) 10.81% <-- This is the tax-adjusted market risk premium


equity beta 1.1 1.1 1.25 <-- Value Linedebt beta 0.21 -0.06 0.17debt 81,300,000,000 153,500,000,000 13,200,000,000 <-- Value Line figure for total firm debtnumber of shares 756,035,101 1,114,618,895 713,533,304share price 58 33 35 <-- share price, December 13, 1996equity/value 35.04% 19.33% 65.42%(debt/equity, as a check) 1.85 4.17 0.53

asset beta 0.472 0.184 0.855

WACC 9.39% 6.27% 13.53%


SOME PROBLEMS

Each of the above steps has problems. Here are afew:

1. What’s the actual �equity? Value Line says Ford’sbeta is 1.10. Look at the Bloomberg pages below:

a. Different time periods?

b. Raw versus adjusted beta?

c. What’s the “market portfolio”?

d. Price � versus total return �?

2. rfdebt ? We use AAA industrial. Why not:

a. Treasury rates?

b. T-bill rate?


3. Estimating corporate tax rate tc:

� Marginal tax rate

vs

� Average tax rate

4. Estimating E(rm ):

� Why use historical averages?

� Using P/E model (see page 21)

� �RADR

b g

P Eg

where

b dividend payout ratio

g growth rate of dividends and earnings

P E current price earnings ratio

�

�

�

�

�

�

*

/

/ /

1





HERE’S AN EVEN MORE PROBLEMATIC EXAMPLEManhattan Bagel is, by anyone’s definition, a “high risk” company, but …


WHAT’S THE POINT?

� depends on:

� the time period

� the adjustment procedure (follows fromBlume’s “Regression Tendencies of Beta”);

�s which are higher than �m = 1 in one periodtend to go down in a subsequent period

�s which are lower than �m = 1 in one periodtend to increase in a subsequent period

(regression towards the mean?)

� Bloomberg uses the adjustment procedure:

adjusted rawm

� � �� 2

3

1

3

(pretty arbitrary, but no real standards)


ESTIMATING THE MARKET RISK PREMIUM FROM P/E DATA

Median P/E of stocks with earnings 16.7Median dividend yield over next 12 months 2%Growth potential, 3-5 years 40%

Estimated annual growth 6.96% <-- (1.40)0.2 - 1Estimated payout ratio 33.4% <-- product of div. yld. * median P/E

E(rm) 9.10%

rfdebt 6.69% <-- 10 year AAA industrial bond yield, December 1996

implied market risk premium 2.41% <-- E(rm) - rfdebt

REDOING THE WACC CALCULATIONSSML Parametersrfdebt 6.69% <-- 10 year AAA industrial bond yield, December 1996


market risk premium 2.41% <-- number derived aboveslope of SML, E(rm)-rf*(1-tc) 4.82%


equity beta 1.1 1.1 1.25 <-- Value Linedebt beta 0.43 0.17 0.39 <-- Calculated previouslydebt 81,300,000,000 153,500,000,000 13,200,000,000 <-- Value Line figure for total firm debtnumber of shares 756,035,101 1,114,618,895 713,533,304share price 58 33 35 <-- share price, December 13, 1996equity/value 35.04% 19.33% 65.42%

asset beta 0.565 0.299 0.905

WACC 7.00% 5.72% 8.64%

Note: Implied payout ratio is consistent with average for 750 industrials, as in Value Line handout.


��

��

��

1. Analyze historical dividend growth rates to arriveat an estimated future real dividend growth rate, g.

2. Estimate the real cost of equity, � �r Lereal by using

the Gordon model:

� ��

r LD g

Pg

where

P current share price

D current dividend

ereal

�

�

�

�

�

0

0

0

0

1

3. Estimate the future anticipated inflation rate toarrive at a nominal cost of equity, � �r Le

nominal :� � � �� r L r L anticipated inflatione

nominalereal

� � � � �1 1 1


4. Calculate the firm’s cost of debt rd and then itsWACC:

� � � �WACC r LE

E Dr

D

E Dte

no alD c�

�

�

�

�min 1

Alternatively : Unlever the nominal cost of equityto get to the firm’s unlevered cost of capital, r(U):

� ��

r Ur L rf t

D

ED

E

enominal

debt c�

� �

�

1

1


��

��General Motors (GM)

year-end dividend dividend realstock per in 1996 dividend

year price share CPI dollars growth1986 2.50 328.4 3.581987 2.50 340.4 3.45 -3.53%1988 2.50 354.3 3.32 -3.92%1989 3.00 371.3 3.80 14.51%1990 3.00 391.4 3.60 -5.14%1991 1.60 408.0 1.84 -48.84%1992 1.40 420.3 1.57 -15.06%1993 0.80 432.7 0.87 -44.49%1994 0.80 444.0 0.85 -2.55%1995 1.10 456.5 1.13 33.73%1996 58.00 1.60 469.9 1.60 41.31%

average -3.40% <-- 10-year average2.59% <-- 5-year average

Step 1: Take 5-year average dividend growth asexpected future growth.

Step 2: Calculate real cost of equity, � �r Lereal :

� ��

r LD g

Pge

real�

�

� �

�

� �0

0

1 160 1 2 59%

582 59% 542%

. .. .


Step 3: I estimate future inflation at 4% per year.Thus I calculate the nominal cost of equity,

� �r Lenominal :

� � � ��

� � � �

r L r L inflationenominal

ereal

� � � � �

� � � � � �

1 1 1

1 542% 1 4% 1 9 63%. .

Step 4:

� GM’s debt/equity ratio is currently 1.85.

� The corporate tax rate is tc = 36%.

� According to Value Line, GM has $31.3B ofLT debt and $2.8B of LT interest. Thesenumbers give GM’s rd = 8.95%. (We canargue about the quality of this estimate …)

� Accordingly,

� � � �

� �

WACC r LE

E Dr t

D

E Denominal

D c�

�

� �

�

�

�

�

�

�

�

1

9 63%4385

4385 813

8 95% 1 0 36813

4385 813710%

..

. .

. ..

. ..


��

��

Previously (using E(rm) derived from marketmultiple): GM’s WACC = 7.00%

Now (using Gordon) GM’s WACC = 7.10%

��


General Motors (GM)year-end dividend dividend real

stock per in 1996 dividendyear price share CPI dollars growth1986 2.50 328.4 3.581987 2.50 340.4 3.45 -3.53%1988 2.50 354.3 3.32 -3.92%1989 3.00 371.3 3.80 14.51%1990 3.00 391.4 3.60 -5.14%1991 1.60 408.0 1.84 -48.84%1992 1.40 420.3 1.57 -15.06%1993 0.80 432.7 0.87 -44.49%1994 0.80 444.0 0.85 -2.55%1995 1.10 456.5 1.13 33.73%1996 58.00 1.60 469.9 1.60 41.31%

average -3.40% <-- 10-year average2.59% <-- 5-year average

anticipated inflation 4%

Gordon modelre(L) 5.42% real cost of equity (uses 5-year average)

9.63% nominal cost

Debt 81.30 end of 1995 total debt, Value Line, in billion $Equity 43.85 billionsDebt/Equity 1.85tax rate 0.36

GM LT debt 31.30 from Value LineGM LT interest 2.80rd 8.95% <-- Divide two numbers above

WACC 7.10%previously 7.00% <-- Using E(Rm) derived from market P/E ratio


��

FORD MOTOR (F)year-end dividend dividend real

stock per in 1996 dividendyear price share CPI dollars growth

1986 0.56 328.4 0.801987 0.79 340.4 1.09 36.10%1988 1.15 354.3 1.53 39.86%1989 1.50 371.3 1.90 24.46%1990 1.50 391.4 1.80 -5.14%1991 0.98 408.0 1.13 -37.32%1992 0.80 420.3 0.89 -20.76%1993 0.80 432.7 0.87 -2.87%1994 0.91 444.0 0.96 10.86%1995 1.23 456.5 1.27 31.46%1996 33.00 1.47 469.9 1.47 16.10%

average 9.28% <-- 10-year average6.96% <-- 5-year average


Gordon modelre(L) 11.72% real cost of equity (uses 5-year average)

16.19% nominal cost

Debt 153.50 end of 1995 total debt, Value Line, in billion $Equity 36.78 billionsDebt/Equity 4.17tax rate 36%

Ford LT Debt 103.50 from Value LineFord LT Interest 6.30rd 6.09%



��

CHRYSLER CORPORATION (C)year-end dividend dividend real

stock per in 1996 dividendyear price share CPI dollars growth

1986 0.40 328.4 0.571987 0.50 340.4 0.69 20.59%1988 0.50 354.3 0.66 -3.92%1989 0.60 371.3 0.76 14.51%1990 0.60 391.4 0.72 -5.14%1991 0.30 408.0 0.35 -52.03%1992 0.30 420.3 0.34 -2.93%1993 0.33 432.7 0.36 6.85%1994 0.45 444.0 0.48 32.89%1995 1.00 456.5 1.03 116.14%1996 35.00 1.40 469.9 1.40 36.01%

average 16.30% <-- 10-year average37.79% <-- 5-year average


Gordon modelre(L) 20.95% real cost of equity (uses 10 year average)

25.79% nominal cost


Chrysler LT debt 0.725Chrysler LT interest 8.50rd 8.53%



Note : Value LIne 's estimate of future dividend growth for Chrysler is: 5.74%Using this estimate, we would get:

Gordon modelre(L) 9.97% nominal cost of equity


rd 8.53%



��

��

��

(isn’t it about time for an end to this “easy step”business?!)

1. Estimate the dividend payout ratio, b.

2. Estimate the growth of future earnings, g.

3. Calculate the cost of equity re(L).

� ��

r Lb g

P Ege �

�

�

1

/

Note: Use trailing P/E (see chapter 9).

4. Calculate WACC as before.


��

General Motors (GM)dividendpayout

year ratio1986 56% P/E ratio 8.1 <-- trailing P/E1987 47% nominal earnings growth 21.47% Value Line estimate1988 36% current debt/equity ratio 1.851989 46% rd 8.95%

1990 nmf tc 36%

1991 nmf1992 nmf Debt 81.301993 44% Equity 43.851994 20% re(L) 24.92%

1995 19% WACC 12.45%1996 19%

average 36%estimate 23% estimated future payout ratio, Value Line


��

Ford (F)dividendpayout

year ratio1986 18% P/E ratio 11.4 <-- trailing P/E1987 17% nominal earnings growth 14.42% Value Line estimate1988 21% current debt/equity ratio 4.171989 33% rd 6.09%

1990 nmf tc 36%

1991 nmf1992 nmf Debt 153.501993 43% Equity 36.781994 23% re(L) 19.44%

1995 38% WACC 6.90%1996 43%

average 30%estimate 50% estimated future payout ratio, Value Line


��

Chrysler (C)dividendpayout

year ratio1986 13% P/E ratio 7.0 <-- trailing P/E1987 17% nominal earnings growth 7.52% Value Line estimate1988 20% current debt/equity ratio 13.201989 85% rfdebt 6.63%

1990 nmf tc 36%

1991 nmf rd 8.53%

1992 47% tc 36%

1993 12%1994 11% Debt 0.731995 33% Equity 8.501996 28% re(L) 6.63%

WACC 6.54%average 30%estimate 30% estimated future payout ratio, Value Line


SO WHAT’S THE COST OF CAPITAL?

COST OF CAPITAL ESTIMATES

CAPMhistorical "market

risk based" Gordon P/Epremium risk prem. model model

General Motors 10.39% 7.00% 7.10% 12.45%Ford 7.51% 5.72% 6.27% 6.90%Chrysler 14.06% 8.64% 8.41% 6.54%

Note : All estimates are for WACC.

Note : The CAPM estimates use the implied debt beta

Note: The Gordon model estimates of Chrysler's WACC arebased on Value Line's estimate of Chrysler's future dividend growth,Chrysler's cost of capital using the Gordon model and historicdividend growth would be 18.76%


��

��

��

��

��

. . . Confucius, The Analects

Date post:	17-Mar-2018
Category:	Documents
Upload:	dinhquynh
View:	213 times
Download:	0 times

ESTIMATING THE COST OF CAPITAL - Simon Benningasimonbenninga.com/benninga_sarig/chap09.pdf ·...

Documents