comm 324 --- w. suo slide 1. comm 324 --- w. suo slide 2 estimating growth balance sheet ...

comm 324 --- W. SuoSlide 1Slide 1

Security Security AnalysisAnalysisPart IIPart II


Estimating Growth

Balance sheet Historical Analyst forecast


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


Regression Models

Regression for EPS Regression for log (eps)


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


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?


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


P/E Ratio

No Growth With growth


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


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%


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


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)


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


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


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


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


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


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


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


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


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


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



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



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



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


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


Pitfalls in P/E Analysis

Use of accounting earnings Historical costs May not reflect economic earnings

Reported earnings fluctuate around the business cycle


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

comm 324 --- w. suo slide 1. comm 324 --- w. suo slide 2 estimating growth balance sheet ...

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