Security Analysis Part I

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Security AnalysisSecurity AnalysisPart IPart I


Basic Types of Models Balance Sheet Models Dividend Discount Models Price/Earning Ratios

Estimating Growth Rates and Opportunities

Fundamental Analysis: Models of Equity Valuation


Intrinsic Value Self assigned Value Variety of models are used for estimation

Market Price Consensus value of all potential traders

Trading Signal IV > MP Buy IV < MP Sell or Short Sell IV = MP Hold or Fairly Priced

Intrinsic Value and Market Price


1 (1 )

to

tt

DV

k

1 (1 )

to

tt

DV

k

V0 = Value of Stock

Dt = Dividendk = required return

Dividend Discount Models (DDM):General Model


No growth: Stocks that have earnings and dividends that are expected to remain constant Preferred Stock

Example

EPS1 = D1 = $5.00 k = .15

V0 = $5.00 / .15 = $33.33

Special Cases


00

(1 )D gV

k g

0

0

(1 )D gV

k g

g = constant perpetual growth rate

Constant Growth Model


0 10

(1 )D g DV

k g k g

0 1

0

(1 )D g DV

k g k g

EPS1 = $5.00 b = 40% k = 15%

(1-b) = 60% D1 = $3.00 g = 8%

V0 = 3.00 / (.15 - .08) = $42.86

Constant Growth Model: Example


Model-Building Assumptions

k > g (otherwise denominator would be negative, leading to a negative stock price)

Both k and g represent long-run averages

Ignores taxes, external financing and options Allowing for taxes and debt financing is relatively easy Allowing for executive stock options and warrants is more difficult


Structural Changes in Cash Dividend Payments

Corporate earnings will be used for Cash dividends paid to owners (shareholders) Retained earnings reinvested in firm Share buybacks to repurchase outstanding shares

Recently firms have decreased cash dividend growth rates and begun buying back stock

Examples: IBM, American Express, Coca-Cola


Restating Present Value Models in Terms of Earnings

The retention ratio, or plowback ratio, b represents the portion of earnings not paid as dividends

Therefore, it is retained earnings The payout ratio is (1 –b) Thus, a firm’s dividend can be rewritten as

Dt = (1 – b)*EPSt

A firm can use retained earnings to either repurchase shares or to reinvest and earn the firm’s ROE

Reinvested earnings can finance internal growth at a periodic rate of g = b*ROE

Therefore, EPSt = EPS0 * (1+g)t = EPS0 [1 + b*(ROE)]t


Restating Present Value Models in Terms of Earnings

Profitable firms can earn ROE > 0 by reinvesting RE in profitable projects or repurchasing shares

Share repurchases can increase EPS because the firm’s earnings are now spread out over fewer shares (called reverse dilution)

If the b>0, then the following equations are equivalent Dt = (1 – b) EPSt

Dt = (1 – b) (1 + g)t EPS0

Dt = (1 – b) [1 + b*(ROE)]t EPS0


Reformulated Present Value Model

Substituting the basic discounted dividend model

If D1 is replaced with EPS1 (1 – b) in the constant DDM, we obtain:

This allows us the ability to examine how dividend policy impacts share value

Dividend policy is reflected in the retention rate b

¥

0

01

(1 – ) [1 ( )]

1

t

tt

b b ROE EPSP

k

1

0

1 -

-

bEPSk gP


Dividend Policy Irrelevance

Since g = b*(ROE) 1

0

1

bEPSk b ROEP

If a firm has an ROE on new investments equal to the risk-adjusted discount rate then

1 1

0

1

(1- )

bEPS EPSk b kP

Thus, regardless of a firm’s initial EPS or riskiness, the firm’s value is unaffected by dividend policy, as RR is no longer in the equation So, when ROE = k dividend policy is irrelevant


Dividend Policy and Growth Firms

The relationship between a firm’s ROE and its discount rate determine the impact of dividend policy on firm value A firm earning an ROE > discount rate is considered a

growth firm Declining firms have ROE below the discount rate, or

ROE < k When ROE = k dividend policy is irrelevant


Example

Assume a firm has An ROE of 15% A discount rate, k, of 15% A retention rate b of 66.67%

Leads to a growth rate of 0.6667 x .15 = 10% Cash dividends growth rate of 10%

If these assumptions hold, the firm’s value will remain a constant $50 (in present value terms)


Example

Future Value at g = 10% Present Value at k = 15%

Time Period Divt Stock Price

PV of cumulative dividend

PV of future price Total

T=0 NA $50 NA $50 $50

T=1 $2.50 55 $2.18 $47.82 50

T=2 $2.75 60.50 4.26 45.74 50

T=3 3.03 66.55 6.25 43.76 50

T=4 3.33 73.20 8.15 41.85 50

T=5 3.66 80.53 9.97 40.03 50

T=10 5.89 129.68 17.94 32.06 50

T=20 15.29 336.37 29.44 20.56 50

T=50 266.80 5869.55 44.58 5.42 50

T=100 31,319.57 689,030.62 49.41 0.59 50

T= 50 0.0 50


1 20 1 2 ...

(1 ) (1 ) (1 )N N

NV D PD Dk k k

PN = the expected sales price for the stock

at time N

N = the specified number of years the

stock is expected to be held

Specified Holding Period Model


0

1

1(1 )

( )

V

o

EPSPVGO

kD g EPS

PVGOk g k

0

1

1(1 )

( )

V

o

EPSPVGO

kD g EPS

PVGOk g k

PVGO = Present Value of Growth Opportunities

E1 = Earnings per share for period 1

Partitioning Value: Growth and No Growth Components


ROE = 20% d = 60% b = 40%

EPS1 = $5.00 D1 = $3.00 k = 15%

Partitioning Value: Example

g = .20 x .40 = .08 or 8%


52.9$33.33$86.42$

33.33$15.

5

86.42$)08.15(.

3

PVGO

NGV

V

o

o

52.9$33.33$86.42$

33.33$15.

5

86.42$)08.15(.

3

PVGO

NGV

V

o

o

Vo = value with growth

NGVo = no growth component value

PVGO = Present Value of Growth

Opportunities

Partitioning Value: Example (cont’d)


Two Stages of Growth DDM

A firm’s common stock may have one of the following growth patters in dividends

Two stages of positive growth (g1 and g2) One constant positive growth rate Zero growth One constant negative growth rate


Example

Battel Corporation has the following attributes: Paid an annual dividend of $2 per share Cost of equity capital is 10% Cash dividends are growing at 2% annually

What is Battel’s stock worth?

0

0

1 $2 1.02 $2.04 $25.50 per share

- 0.10 - 0.02

0.08

D g

k gP


Example

Battel is now considering international expansion with the following adjustments

Same dividend as above, but now the expected growth rate is 4%, not 2%, and the increased risk is expected to increase the cost of equity to 11%

Battel’s value should increase to:

00

1 $2 1.04 $29.71

0.11 0.02

g

k gDP


Example

Example Initial stock price: $25.50 With international expansion: $29.71

What if the international expansion caused Battel's growth rate to rise to 4% for only four years and then the growth rate dropped to the original estimate of 2% forever?

If the exposure to international risks increases Battel’s cost of equity to 11% permanently

40

$26.516 $6.81576

1.11 $6.81576 $17.4669

$24.282

P

24

52

1 $2.3397 1.02 $26.516

- 0.11- 0.0

2

g

k gDP


DDM Criticism

Critics argue that it is too difficult to accurately forecast future cash dividends This criticism is true for some firms but not others

Example: Coca-Cola’s dividend payment is relatively easy to forecast even though its operations cover over 200 different countries

Critics then argue that, even if earlier dividends are relatively easy to forecast, longer-term dividends (say 50 to 100 years from now) are more difficult to determine These long-range forecasts are unimportant


DDM Criticism

• Because the present value of these amounts are very low

Time

Present Value

Of $1

(i=10%)

Present Value

Of $1

(i=16%)

10 39¢ 23¢

25 9.2¢ 2.5¢

50 < 1¢ 6/100 of 1¢

100 < 1/100 of 1¢ 3/100,000 of 1¢


Implications

It is only essential to accurately forecast cash dividends for 10 years in order to use the DDM

Cash dividends in years 11-30 only need to be forecasted within 40% of their actual values

All cash dividends received from years 31 to infinity have a present value of only $1 or $2

When a higher discount rate is used (as with smaller, riskier firms) it is only necessary to forecast dividends for a few years

Security Analysis Part I

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