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 WACC
assumed to be
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
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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%
equity beta debt beta debt number of shares share price equity/value (debt/equity, as a check) asset beta WACC
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 8.45% 0.213 6.58% 0.818 13.12%
General Motors
Chapter 9 slides, page 12
INCORPORATING DEBT
Implied debt beta's LT Debt ($ billion) LT Interest ($ billion) Implied firm cost of debt, rD Implied debt beta = (rD-rfdebt)/(E(Rm)-rfdebt*(1-tc)) 2.8 31.3 8.95% 0.21 6.3 103.5 6.09% -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
equity beta debt beta debt number of shares share price equity/value (debt/equity, as a check) asset beta WACC
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 9.39% 0.184 6.27% 0.855 13.53%
General Motors
Chapter 9 slides, page 13
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: vs Average tax rate Marginal 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
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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 E(rm) rfdebt implied market risk premium 16.7 2% 40% 0.2 6.96% <-- (1.40) - 1 33.4% <-- product of div. yld. * median P/E 9.10% 6.69% <-- 10 year AAA industrial bond yield, December 1996 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 1.1 0.43 81,300,000,000 756,035,101 58 35.04% 0.565 7.00%
Ford 1.1 0.17 153,500,000,000 1,114,618,895 33 19.33% 0.299 5.72%
Chrysler 1.25 0.39 13,200,000,000 713,533,304 35 65.42% 0.905 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 1 D E D E
Chapter 9 slides, page 23
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 58
Chapter 9 slides, page 24
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,
WACC renominal L E D rD 1 t c ED ED . 4385 9.63% . . 4385 813 . 813 8.95% 1 0.36 7.10% . . 4385 813
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 -3.40% <-- 10-year average 2.59% <-- 5-year average
anticipated inflation Gordon model re(L)
4%
5.42% real cost of equity (uses 5-year average) 9.63% nominal cost
Debt Equity Debt/Equity tax rate GM LT debt GM LT interest rd WACC previously
81.30 end of 1995 total debt, Value Line, in billion $ 43.85 billions 1.85 0.36 31.30 from Value Line 2.80 8.95% <-- Divide two numbers above 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 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) 4% 9.28% <-- 10-year average 6.96% <-- 5-year average
CPI 328.4 340.4 354.3 371.3 391.4 408.0 420.3 432.7 444.0 456.5 469.9
11.72% real cost of equity (uses 5-year average) 16.19% nominal cost
Debt Equity Debt/Equity tax rate Ford LT Debt Ford LT Interest rd WACC previously
153.50 end of 1995 total debt, Value Line, in billion $ 36.78 billions 4.17 36% 103.50 from Value Line 6.30 6.09% 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 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) 4% 16.30% <-- 10-year average 37.79% <-- 5-year average
CPI 328.4 340.4 354.3 371.3 391.4 408.0 420.3 432.7 444.0 456.5 469.9
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
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
Chapter 9 slides, page 29
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 rd WACC previously
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% 8.53% 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 1990 1991 1992 1993 1994 1995 1996 average estimate nmf nmf nmf 44% 20% 19% 19% tc Debt Equity re(L) WACC
8.1 <-- trailing P/E 21.47% Value Line estimate 1.85 8.95% 36% 81.30 43.85 24.92% 12.45%
36% 23% estimated future payout ratio, Value Line
Chapter 9 slides, page 32
Ford (F) dividend payout ratio 18% 17% 21% 33% nmf nmf nmf 43% 23% 38% 43%
year 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 average estimate
P/E ratio nominal earnings growth current debt/equity ratio rd tc Debt Equity re(L) WACC
11.4 <-- trailing P/E 14.42% Value Line estimate 4.17 6.09% 36% 153.50 36.78 19.44% 6.90%
30% 50% estimated future payout ratio, Value Line
Chapter 9 slides, page 33
Chrysler (C) dividend payout year ratio 1986 13% 1987 17% 1988 20% 1989 85% 1990 1991 1992 1993 1994 1995 1996 average estimate nmf nmf 47% 12% 11% 33% 28%
P/E ratio nominal earnings growth current debt/equity ratio rfdebt tc rd tc Debt Equity re(L) WACC
7.0 <-- trailing P/E 7.52% Value Line estimate 13.20 6.63% 36% 8.53% 36% 0.73 8.50 6.63% 6.54%
30% 30% estimated future payout ratio, Value Line
Chapter 9 slides, page 34
SO WHAT’S THE COST OF CAPITAL?
COST OF CAPITAL ESTIMATES
CAPM historical "market risk based" premium risk prem. 10.39% 7.00% 7.51% 5.72% 14.06% 8.64%
General Motors Ford Chrysler
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