ESTIMATING THE COST OF CAPITAL
General approach
Find levered cost of equity re(L).
Find cost of debt rD
Calculated WACC:
WACC re ( L)
E
D
rD 1 t C D E
D E
Discount FCFs at WACC to get total value of
firm
Derive cost of shares by subtracting value of
more senior claims (Debt, Preferred Stock,
Warrants, etc.)
Chapter 9 slides, page 1
3 METHODS FOR CALCULATING THE
COST OF CAPITAL
1. CAPM: Capital Asset Pricing Model
2. Use Gordon model and variations.
3. P/E model
Chapter 9 slides, page 2
In all 3 cases the discount rate for the firm’s Free
Cash Flows is the WACC. Either:
Estimate the firm’s cost of debt rD and
calculate the WACC in the ordinary way:
WACC re ( L)
E
D
rD 1 t c ED
ED
Unlever the cost of equity to get r(U) and
assume that this gives the WACC:
re ( L) r (U ) r (U ) rD 1 t c r (U ) re ( L) rD 1 t c 1
D
E
D
E
D
E
assumed to be
WACC
Calculate the WACC using the CAPM by
calculating an asset beta. (Illustrated later.)
Chapter 9 slides, page 3
SOME IMPORTANT THINGS TO
REMEMBER
Calculate the firm’s cost of capital, not the
cost of equity.
Be consistent in treatment of inflation.
Use industry data to estimate the cost of
capital for the firm you value, not just the
firm’s own data.
Chapter 9 slides, page 4
1. Estimate the equity e
2. Estimate the market risk-free rate on debt rfdebt .
3. Estimate the firm’s corporate tax rate tc.
Chapter 9 slides, page 5
4. a. Estimate the expected return on the market
E(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 ]
Chapter 9 slides, page 6
5. Estimate the firm’s cost of debt rD and calculate
the WACC:
WACC re ( L)
E
D
rD 1 t c ED
ED
6. Estimate the firm’s debt beta e and use it to
calculate the firm’s asset beta:
asset
E
D
e debt 1 t c D E
D E
7. Use the asset beta, asset , and the WACC SML to
estimate 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
D
E
e debt 1 t c e
D E
DE
D E
Chapter 9 slides, page 7
Chapter 9 slides, page 8
Chapter 9 slides, page 9
Chapter 9 slides, page 10
Chapter 9 slides, page 11
EXAMPLE: WHAT’S THE WACC OF THE AUTO
COMPANIES?
SML Parameters
rfdebt
corporate tax rate, tc
market risk premium
slope of SML, E(rm)-rf*(1-tc)
6.69% <-- 10 year AAA industrial bond yield, December 1996
36% <-- Value Line, average tax rate of 3 auto firms
8.40% <-- Ibbotsen-Sinequefield (from Brealey/Myers)
10.81%
General
Motors
equity beta
debt beta
debt
number of shares
share price
equity/value
(debt/equity, as a check)
asset beta
WACC
Chapter 9 slides, page 12
Ford
Chrysler
1.1
1.1
1.25 <-- Value Line
0
0
0 <-- Guess!
81,300,000,000 153,500,000,000 13,200,000,000 <-- Value Line figure for total firm debt
756,035,101
1,114,618,895
713,533,304
58
33
35 <-- share price, December 13, 1996
35.04%
19.33%
65.42%
1.85
4.17
0.53
0.385
0.213
0.818
8.45%
6.58%
13.12%
INCORPORATING DEBT Implied debt beta's
LT Debt ($ billion)
LT Interest ($ billion)
Implied firm cost of debt, rD
2.8
31.3
8.95%
6.3
103.5
6.09%
Implied debt beta =
(rD-rfdebt)/(E(Rm)-rfdebt*(1-tc))
0.21
-0.06
0.725
8.5
8.53%
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 FIRMS
incorporating implied debt betas
SML Parameters
rfdebt
corporate tax rate, tc
market risk premium
slope of SML, E(rm)-rf*(1-tc)
6.69% <-- 10 year AAA industrial bond yield, December 1996
36% <-- Value Line, average tax rate of 3 auto firms
8.40% <-- Ibbotsen-Sinequefield (from Brealey/Myers)
10.81% <-- This is the tax-adjusted market risk premium
General
Motors
equity beta
debt beta
debt
number of shares
share price
equity/value
(debt/equity, as a check)
asset beta
WACC
Chapter 9 slides, page 13
Ford
Chrysler
1.1
1.1
1.25 <-- Value Line
0.21
-0.06
0.17
81,300,000,000 153,500,000,000 13,200,000,000 <-- Value Line figure for total firm debt
756,035,101
1,114,618,895
713,533,304
58
33
35 <-- share price, December 13, 1996
35.04%
19.33%
65.42%
1.85
4.17
0.53
0.472
0.184
0.855
9.39%
6.27%
13.53%
SOME PROBLEMS
Each of the above steps has problems. Here are a
few:
1. What’s the actual equity? Value Line says Ford’s
beta 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?
Chapter 9 slides, page 14
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 * 1 g g
P/E
where
b dividend payout ratio
g growth rate of dividends and earnings
P / E current price / earnings ratio
Chapter 9 slides, page 15
Chapter 9 slides, page 16
Chapter 9 slides, page 17
Chapter 9 slides, page 18
HERE’S AN EVEN MORE PROBLEMATIC EXAMPLE
Manhattan Bagel is, by anyone’s definition, a “high risk” company, but …
Chapter 9 slides, page 19
WHAT’S THE POINT?
depends on:
the time period
the adjustment procedure (follows from
Blume’s “Regression Tendencies of Beta”);
s which are higher than m = 1 in one period
tend to go down in a subsequent period
s which are lower than m = 1 in one period
tend to increase in a subsequent period
(regression towards the mean?)
Bloomberg uses the adjustment procedure:
adjusted 2
1
raw 3
3
m
(pretty arbitrary, but no real standards)
Chapter 9 slides, page 20
ESTIMATING THE MARKET RISK PREMIUM FROM P/E DATA
Median P/E of stocks with earnings
Median dividend yield over next 12 months
Growth potential, 3-5 years
Estimated annual growth
Estimated payout ratio
16.7
2%
40%
0.2
6.96% <-- (1.40) - 1
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 CALCULATIONS
SML Parameters
rfdebt
corporate tax rate, tc
market risk premium
slope of SML, E(rm)-rf*(1-tc)
6.69% <-- 10 year AAA industrial bond yield, December 1996
36% <-- Value Line, average tax rate of 3 auto firms
2.41% <-- number derived above
4.82%
General
Motors
equity beta
debt beta
debt
number of shares
share price
equity/value
asset beta
WACC
Ford
Chrysler
1.1
0.43
81,300,000,000
756,035,101
58
35.04%
1.1
0.17
153,500,000,000
1,114,618,895
33
19.33%
1.25
0.39
13,200,000,000
713,533,304
35
65.42%
0.565
0.299
0.905
7.00%
5.72%
8.64%
<-- Value Line
<-- Calculated previously
<-- Value Line figure for total firm debt
<-- share price, December 13, 1996
Note: Implied payout ratio is consistent with average for 750 industrials, as in Value Line handout.
Chapter 9 slides, page 21
1. Analyze historical dividend growth rates to arrive
at an estimated future real dividend growth rate, g.
2. Estimate the real cost of equity, rereal L by using
the Gordon model:
rereal L D0 1 g g
P0
where
P0 current share price
D0 current dividend
3. Estimate the future anticipated inflation rate to
arrive at a nominal cost of equity, renominal L :
renominal L 1 rereal L 1 anticipated inflation 1
Chapter 9 slides, page 22
4. Calculate the firm’s cost of debt rd and then its
WACC:
WACC reno min al L
E
D
rD
1 t c ED
ED
Alternatively: Unlever the nominal cost of equity
to get to the firm’s unlevered cost of capital, r(U):
r U renominal L rf debt 1 tc Chapter 9 slides, page 23
1
D
E
D
E
General Motors (GM)
year-end
dividend
stock
per
year
price
share
1986
2.50
1987
2.50
1988
2.50
1989
3.00
1990
3.00
1991
1.60
1992
1.40
1993
0.80
1994
0.80
1995
1.10
1996
58.00
1.60
CPI
328.4
340.4
354.3
371.3
391.4
408.0
420.3
432.7
444.0
456.5
469.9
dividend
real
in 1996 dividend
dollars
growth
3.58
3.45
-3.53%
3.32
-3.92%
3.80
14.51%
3.60
-5.14%
1.84 -48.84%
1.57 -15.06%
0.87 -44.49%
0.85
-2.55%
1.13
33.73%
1.60
41.31%
average
-3.40% <-- 10-year average
2.59% <-- 5-year average
Step 1: Take 5-year average dividend growth as
expected future growth.
Step 2: Calculate real cost of equity, rereal L :
1.601 2.59% D 1 g rereal L 0
g
2.59% 5.42%
P0
Chapter 9 slides, page 24
58
Step 3: I estimate future inflation at 4% per year.
Thus I calculate the nominal cost of equity,
renominal L :
renominal L 1 rereal L 1 inflation 1
1 5.42% 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 of
LT debt and $2.8B of LT interest. These
numbers give GM’s rd = 8.95%. (We can
argue about the quality of this estimate …)
Accordingly,
E
D
rD 1 t c ED
ED
.
4385
9.63%
. 813
.
4385
.
813
8.95% 1 0.36
7.10%
. 813
.
4385
WACC renominal L
Chapter 9 slides, page 25
Previously (using E(rm) derived from market
multiple):
GM’s WACC = 7.00%
Now (using Gordon) GM’s WACC = 7.10%
Chapter 9 slides, page 26
General Motors (GM)
year-end
dividend
stock
per
year
price
share
1986
2.50
1987
2.50
1988
2.50
1989
3.00
1990
3.00
1991
1.60
1992
1.40
1993
0.80
1994
0.80
1995
1.10
1996
58.00
1.60
CPI
328.4
340.4
354.3
371.3
391.4
408.0
420.3
432.7
444.0
456.5
469.9
dividend
real
in 1996 dividend
dollars
growth
3.58
3.45
-3.53%
3.32
-3.92%
3.80
14.51%
3.60
-5.14%
1.84 -48.84%
1.57 -15.06%
0.87 -44.49%
0.85
-2.55%
1.13
33.73%
1.60
41.31%
average
anticipated inflation
Gordon model
re(L)
-3.40% <-- 10-year average
2.59% <-- 5-year average
4%
5.42% real cost of equity (uses 5-year average)
9.63% nominal cost
Debt
Equity
Debt/Equity
tax rate
81.30 end of 1995 total debt, Value Line, in billion $
43.85 billions
1.85
0.36
GM LT debt
GM LT interest
rd
31.30 from Value Line
2.80
8.95% <-- Divide two numbers above
WACC
previously
7.10%
7.00% <-- Using E(Rm) derived from market P/E ratio
Chapter 9 slides, page 27
FORD MOTOR (F)
year-end
dividend
stock
per
year
price
share
1986
0.56
1987
0.79
1988
1.15
1989
1.50
1990
1.50
1991
0.98
1992
0.80
1993
0.80
1994
0.91
1995
1.23
1996
33.00
1.47
CPI
328.4
340.4
354.3
371.3
391.4
408.0
420.3
432.7
444.0
456.5
469.9
dividend
real
in 1996 dividend
dollars
growth
0.80
1.09
36.10%
1.53
39.86%
1.90
24.46%
1.80
-5.14%
1.13 -37.32%
0.89 -20.76%
0.87
-2.87%
0.96
10.86%
1.27
31.46%
1.47
16.10%
average
anticipated inflation
Gordon model
re(L)
9.28% <-- 10-year average
6.96% <-- 5-year average
4%
11.72% real cost of equity (uses 5-year average)
16.19% nominal cost
Debt
Equity
Debt/Equity
tax rate
153.50 end of 1995 total debt, Value Line, in billion $
36.78 billions
4.17
36%
Ford LT Debt
Ford LT Interest
rd
103.50 from Value Line
6.30
6.09%
WACC
previously
6.27%
5.72% <-- Using E(Rm) derived from market P/E ratio
Chapter 9 slides, page 28
CHRYSLER CORPORATION (C)
year-end
dividend
stock
per
year
price
share
1986
0.40
1987
0.50
1988
0.50
1989
0.60
1990
0.60
1991
0.30
1992
0.30
1993
0.33
1994
0.45
1995
1.00
1996
35.00
1.40
CPI
328.4
340.4
354.3
371.3
391.4
408.0
420.3
432.7
444.0
456.5
469.9
dividend
real
in 1996 dividend
dollars
growth
0.57
0.69
20.59%
0.66
-3.92%
0.76
14.51%
0.72
-5.14%
0.35 -52.03%
0.34
-2.93%
0.36
6.85%
0.48
32.89%
1.03 116.14%
1.40
36.01%
average
anticipated inflation
Gordon model
re(L)
16.30% <-- 10-year average
37.79% <-- 5-year average
4%
20.95% real cost of equity (uses 10 year average)
25.79% nominal cost
Debt
Equity
Debt/Equity
tax rate
Chrysler LT debt
Chrysler LT interest
rd
WACC
previously
Chapter 9 slides, page 29
13.20 end of 1995 total debt, Value Line, in billion $
24.97 billions
0.53
36%
0.725
8.50
8.53%
18.76%
8.64% <-- Using E(Rm) derived from market P/E ratio
Note: Value LIne 's estimate of future dividend growth for Chrysler is:
Using this estimate, we would get:
Gordon model
re(L)
Debt
Equity
Debt/Equity
tax rate
5.74%
9.97% nominal cost of equity
13.20 end of 1995 total debt, Value Line, in billion $
24.97 billions
0.53
36%
rd
8.53%
WACC
previously
8.41%
8.64% <-- Using E(Rm) derived from market P/E ratio
Chapter 9 slides, page 30
(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).
re L b 1 g g
P/E
Note: Use trailing P/E (see chapter 9).
4. Calculate WACC as before.
Chapter 9 slides, page 31
General Motors (GM)
dividend
payout
year
ratio
1986
56%
P/E ratio
1987
47%
nominal earnings growth
1988
36%
current debt/equity ratio
1989
46%
rd
8.1 <-- trailing P/E
21.47% Value Line estimate
1.85
8.95%
1990
nmf
tc
1991
1992
1993
1994
nmf
nmf
44%
20%
Debt
Equity
re(L)
81.30
43.85
24.92%
1995
1996
19%
19%
WACC
12.45%
average
estimate
Chapter 9 slides, page 32
36%
36%
23% estimated future payout ratio, Value Line
Ford (F)
year
1986
1987
1988
1989
dividend
payout
ratio
18%
17%
21%
33%
P/E ratio
nominal earnings growth
current debt/equity ratio
rd
11.4 <-- trailing P/E
14.42% Value Line estimate
4.17
6.09%
1990
nmf
tc
1991
1992
1993
1994
nmf
nmf
43%
23%
Debt
Equity
re(L)
153.50
36.78
19.44%
1995
1996
38%
43%
WACC
6.90%
average
estimate
Chapter 9 slides, page 33
36%
30%
50% estimated future payout ratio, Value Line
Chrysler (C)
dividend
payout
year
ratio
1986
13%
1987
17%
1988
20%
1989
85%
P/E ratio
nominal earnings growth
current debt/equity ratio
rfdebt
7.0 <-- trailing P/E
7.52% Value Line estimate
13.20
6.63%
1990
nmf
tc
36%
1991
nmf
rd
8.53%
1992
47%
tc
36%
1993
1994
1995
1996
12%
11%
33%
28%
Debt
Equity
re(L)
0.73
8.50
6.63%
WACC
6.54%
average
estimate
Chapter 9 slides, page 34
30%
30% estimated future payout ratio, Value Line
SO WHAT’S THE COST OF CAPITAL?
COST OF CAPITAL ESTIMATES
General Motors
Ford
Chrysler
CAPM
historical "market
risk
based"
premium risk prem.
10.39%
7.00%
7.51%
5.72%
14.06%
8.64%
Gordon
model
7.10%
6.27%
8.41%
P/E
model
12.45%
6.90%
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 are
based on Value Line's estimate of Chrysler's future dividend growth,
Chrysler's cost of capital using the Gordon model and historic
dividend growth would be
18.76%
Chapter 9 slides, page 35
. . . Confucius, The Analects
Chapter 9 slides, page 36