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comm 324 --- W. SuoSlide 1Slide 1
Security Security AnalysisAnalysisPart IIPart II
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Estimating Growth
Balance sheet Historical Analyst forecast
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Year Cal Y EPS % Change Log(EPS)
1 1991 0.42 -0.8675
2 1992 0.41 -2.38 -0.8916
3 1993 0.40 -2.44 -0.9163
4 1994 0.58 45.00 -0.5447
5 1995 0.65 12.07 -0.4308
6 1996 0.72 10.77 -0.3285
7 1997 0.82 13.89 -0.1985
8 1998 0.93 13.41 -0.0726
9 1999 1.07 15.05 -0.0667
10 2000 1.27 18.69 -0.2390
Estimating Historical Growth: GE
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Regression Models
Regression for EPS Regression for log (eps)
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Example
AMA growth rate in earnings per share = 13.79% GMA growth rate in earnings per share = (1.27/0.42)1/9 -1 = 13.08% Linear regression:
EPS = 0.2033 + 0.0952*t R-square = 94.5%
EPS increased 9.52 cent per year Growth rate in earnings per share = Coefficient on linear
regression/Average EPS = 0.0952/0.727 = 13.10% Log Linear regression:
Log(EPS) = -1.1288 + 0.1335*t R-square = 95.8% Coefficient on the time variable can be viewed as a measure of
compound percent growth in earning per share: earning grew at 13.35 per share.
Other more advanced models
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Analyst Estimates of Growth
Who do analysts follow? Market cap Institutional holding Trading volume
Information Firm specific Macro =economic information that might impact future growth Competitors Private information about the firm public information other than earning
Quality of their forecasts?
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P/E Ratios are a function of two factors Required Rates of Return (k) Expected growth in Dividends
Uses Relative valuation Extensive Use in industry
Earnings, Growth and Price-Earnings Ratios
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P/E Ratio
No Growth With growth
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E0 = $2.50 g = 0 k = 12.5%
P0 = D/k = $2.50/.125 = $20.00
PE = 1/k = 1/.125 = 8
Numerical Example: No Growth
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E1 = $2.50 (1 + (.6)(.15)) = $2.73
D1 = $2.73 (1-.6) = $1.09
P0 = 1.09/(.125-.09) = $31.14PE = 31.14/2.73 = 11.4PE = (1 - .60) / (.125 - .09) = 11.4
Numerical Example with Growth
b = 60% ROE = 15% (1-b) = 40%k = 12.5% g = 9%
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The Price Earnings Ratio
The Price-Earnings Ratio (PE) is often used to value stocks by Estimating EPS Estimating a PE ratio Multiplying the two to obtain an estimate of the share
price
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The Price Earnings Ratio
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The Price Earnings Ratio
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Analyzing the P-E Ratio
If the constant growth DDM is divided by EPS1
0 1 1
1
/
P D E
E k g
Thus the P-E ratio has 3 primary determinants A risk-adjusted discount rate of k > g
• As k increases the P-E ratio decreases A growth rate, g
• As g increases the P-E ratio increases
A cash dividend payout ratio of D1/E1 or (1 – b)
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Analyzing the P-E Ratio
As the payout ratio increases, g decreases and the P-E ratio is unaffected
This can also be demonstrated as
1
(1 - ) since g b*ROE
- *
(1 - ) if ROE (a normal firm)
(1 - )
1
P b
E k b ROE
bk
k b
k
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Battel Example
Reconsider the Battel example Battel’s D0 = $2, g = 2%, k = 10% stock price of $25.50 If we expect E1 to be $3, Battel’s P-E ratio is 8.5
0 1 1
0
/ $2.04 / $3 8.5 times
0.10 - 0.02
P D E
E k g
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P-E Ratio
Many fundamental analysts multiply a stock’s EPS by the P-E ratio to estimate the stock’s price
Can even use this method if the firm does not pay a dividend by imputing a payout ratio
Can also use this procedure for stocks that do pay dividends
Can compare a stock price estimate obtained with the P-E ratio approach to the DDM approach
The two methods will probably lead to similar values If the two values differ greatly, further analysis may enable the analyst to obtain
a better estimate
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P-E Ratios of Zero Dividend Stocks
Companies that pay no dividends, such as Microsoft, are problematic for DDM
cash dividends are the only cash flow in the model
By reformulating the DDM in terms of earnings, this problem can be overcome
Example: Microsoft’s average cost of equity is 40% (k); its growth rate is 36% and it has a P-E of 40. Based on this, we can impute a dividend payout ratio
0 1 1
1
/
P D E
E k g
40 times x (0.40 0.36)=160%Imputed payout ratio
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Microsoft Example
The imputed dividend payout ratio of 160% suggests that market values $1 of Microsoft earnings at $1.60 Perhaps the market places a high value on Microsoft’s
policy of retaining all earnings to finance growth
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Example of Two Approaches
Given Coca-Cola paid a dividend in 1999 of $0.64 per share
1 – b = 65.3% EPS = $0.98
k = 20.7% per year for equity Growth of 19.7% in the annual dividend
Using the DDM, Coca-Cola’s stock is valued at
0
$0.64 $64
0.207 0.197P
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Example of Two Approaches
Using the P-E ratio approach, Coca-Cola is valued at
0 1 1
1
/ $0.64 / $0.98
0.207 - 0.197
65.3 times EPS or 65.3 $0.98 $63.99
P D E
E k g
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The k – g Spread
The denominator (k – g) in both the DDM and the P-E ratio approach plays an important role in stock valuation
For instance, in the Coca-Cola example on the previous slide, k – g was 0.01 or 1%
Regardless of the actual values of k or g, if the difference had been 1%, the value of Coca-Cola would have been the same
Further examination of the constant growth DDM shows that
1
0
- D
k g or the k - g spreadP
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The k – g Spread
This analysis shows that The stock’s k – g spread should equal the stock’s cash dividend
yield (D1/P0) Given that the S&P500 cash dividend yield has steadily decreased since
1983, the k – g spread should narrow, implying higher P-E ratios and a bullish stock market
If S&P500 cash dividend yields continue to fall, the rate of capital gains (or g) must rise in order for k to remain constant
If g rises, the implication is a bullish market
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Analysis of Growth Investing
The DDM can be used to analyze growth stocks Suppose a firm will earn E1 if it doesn’t buy any new assets
If it retains earnings b*E1 and buys a new asset it will grow at ROE In year 2 the new asset will earn (ROE)*b*E1 per year
After the first year the firm will again pay out all EPS as dividends This firm can be valued as
1 1 1 1 10 2 3
1
1 (1 ) (1 )
E b E ROE b E E ROE b EP
k k k
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Analysis of Growth Investing
The earnings in the numerator of that equation can be separated into Perpetual annual earnings from the old assets—EPS1
Perpetual annual earnings from the new assets—ROE x RR x EPS1—that begin in year 2
The previous equation can be rewritten as
1 1 10 2 3
1 1 12 3
1 (1 ) (1 )
+ 1 (1 ) (1 )
E E EP
k k k
E b ROE b E ROE b E
k k k
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Analysis of Growth Investing
The Net Present Value (NPV) of an asset is defined as PVcash flows – cost of asset The NPV (at t=1) of the asset bought in year 1 is the PV of the
perpetual cash flows less the new asset’s cost
11 -
E ROE bb E
k
In time 0 terms the NPV0 is1
11
-
1 1
E ROE bb E
NPV kk k
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Analysis of Growth Investing
Substituting the NPV of the new asset into the previous equation
1 10
1
E NPVP
k k
If a firm buys new assets every year, the equation is reformulated as
1 1 2 32 30
1 (1 ) (1 )
E NPV NPV NPV
k k k kP
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Growth Stock Investing
Growth stocks have high growth rates in sales and earnings, and high P-E ratios Usually also have low cash dividend yields and high ROE
Empirical evidence suggests that in the long-run value stocks (low P-E, below average growth rates and high dividends) tend to outperform growth stocks Perhaps because growth firms retain earnings and invest in zero or
negative NPVsResults in a larger firm, but no growth in PV of stock price
Above analysis suggests that security analysts should try to determine the profitability of firm's investment opportunities
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Pitfalls in P/E Analysis
Use of accounting earnings Historical costs May not reflect economic earnings
Reported earnings fluctuate around the business cycle
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The Free Cash-Flow Approach
Fundamental idea: the intrinsic value of a firm is the present value of all its net cash-flows to shareholders
Estimate the value of the firm as a whole It equals the present value of cash-flows, assuming all-
equity financing plus the net present value of tax shields created by using debt;
Derive the value of equity by subtracting the market value of all non-equity claims