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Principles of Business FinanceFin 510

Dr. Lawrence P. Shao

Marshall University

Spring 2002

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CHAPTER 8Stocks and Their Valuation

Features of common stockDetermining common stock

valuesEfficient marketsPreferred stock

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Represents ownership.

Ownership implies control.

Stockholders elect directors.

Directors elect management.

Management’s goal: Maximize stock price.

Facts about Common Stock

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Social/Ethical Question

Should management be equally concerned about employees, customers, suppliers, “the public,” or just the stockholders?

In enterprise economy, work for stockholders subject to constraints (environmental, fair hiring, etc.) and competition.

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Classified stock has special provisions.

Could classify existing stock as founders’ shares, with voting rights but dividend restrictions.

New shares might be called “Class A” shares, with voting restrictions but full dividend rights.

What’s classified stock? How might classified stock be used?

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When is a stock sale an initial public offering (IPO)?

A firm “goes public” through an IPO when the stock is first offered to the public.

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P

D

k

D

k

D

k

D

ks s s s

01

12

23

31 1 1 1

. . .

One whose dividends are expected togrow forever at a constant rate, g.

Stock Value = PV of Dividends

What is a constant growth stock?

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For a constant growth stock,

t0t

202

101

g1DD

g1DD

g1DD

PD g

k gD

k gs s0

0 11

If g is constant, then:

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t

0t g1DD

tt

tk1

DPVD

!P k,>g If 0 t0 PVDP

$

0.25

Years (t)0

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What happens if g > ks?

If ks< g, get negative stock price, which is nonsense.

We can’t use model unless (1) ks> g and (2) g is expected to be constant forever.

.PD

k gg

s0

1

requires ks

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Assume beta = 1.2, kRF = 6%, and kM = 11%. What is the required rate of

return on the firm’s stock?

ks= kRF + (kM - kRF)bFirm

= 6% + (11% - 6%) (1.2) = 12%.

Use the SML to calculate ks:

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D0 was $0.25 and g is a constant 6%. Find the expected dividends for the

next 3 years, and their PVs. ks = 12%.

0 1

0.2809

2

0.2978

3g=6% 4

0.23660.22390.2120

D0=0.2512%

0.265

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What’s the stock’s market value? D0 = 0.25, ks = 12%, g = 6%.

Constant growth model:

06.012.0

265.0$

gk

DP̂

s

10

.42.4$06.0

265.0$

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What is the stock’s market value one year from now, P1?

D1 will have been paid, so expected dividends are D2, D3, D4 and so on. Thus,

Could also find P1 as follows:

$0.. .

PD

k gs1

2 28090 12 0 06

P P g1 0 1 42 106 68 $4. . $4. .

^

$4. .68

^

^

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Find the expected dividend yield, capital gains yield, and total return

during the first year.

Dividend yD

P

CapP P

Pk

D

P

Total retu

s

ld

gains yld

rn

1

0

1 0

0

1

0

265

426%.

6%.

6% 6% 12%.

$0.

$4.

.

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Rearrange model to rate of return form:

.PD

k g

D

Pg

s0

1 1

0

to ks

Then, ks = $0.265/$4.42 + 0.06= 0.06 + 0.06 = 12%.

^

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What would P0 be if g = 0?

The dividend stream would be a perpetuity.

PPMT

k0

250 12

08 $0.

.$2. .

0.25 0.250.25

0 1 2 312% ...

^

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Can no longer use constant growth model.

However, growth becomes constant after 3 years.

^

If we have supernormal growth of 30% for 3 years, then a long-run constant

g = 10%, what is P0? k is still 12%.

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Nonconstant growth followed by constantgrowth:

0

0.2902

0.3368

0.3910

21.5029

1 2 3 4ks=12%

22.52 = P0

g = 30% g = 30% g = 30% g = 10%

D0 = 0.25 0.3250 0.4225 0.5493 0.6042

.. .

$30.P30 604212 0 10

21

0

...

^

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If g = -6%, would anyone buy the stock? If so, at what price?

Firm still has earnings and still paysdividends, so P0 > 0:

.PD

k g

D g

k gs s0

1 0 1

$0. ( . )

. ( . )

$0.

.$1. .

25 0 94

0 12 0 06

235

0 1831

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What is market equilibrium?

In equilibrium, stock prices are stable.There is no general tendency for people to buy versus to sell.

In equilibrium, expected returns mustequal required returns:

ks = D1/P0 + g = ks = kRF + (kM - kRF)b.^

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How is equilibrium established?

If ks = + g > ks, then

P0 is “too low” (a bargain).

Buy orders > sell orders;

P0 bid up; D1/P0 falls until

D1/P0 + g = ks = ks.

^

^

D1

P0

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Why do stock prices change?

gk

DP̂

i

10

1. ki could change: ki = kRF + (kM - kRF )bi

kRF = k* + IP

2. g could change due to economic or firm situation.

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What’s the Efficient Market Hypothesis?

EMH: Securities are normally in equilibrium and are “fairly priced.” One cannot “beat the market” except through good luck or better information.

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1. Weak-form EMH:

Can’t profit by looking at past trends. A recent decline is no reason to think stocks will go up (or down) in the future. Evidence supports weak-form EMH, but “technical analysis” is still used.

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2. Semistrong-form EMH:

All publicly available information is reflected in stock prices, so doesn’t pay to pore over annual reports looking for undervalued stocks. Largely true, but superior analysts can still profit by finding and using new information.

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3. Strong-form EMH:All information, even inside information, is embedded in stock prices. Not true--insiders can gain by trading on the basis of insider information, but that’s illegal.

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Markets are generally efficient because:

1. 15,000 or so trained analysts; MBAs, CFAs, Technical PhDs.

2. Work for firms like Merrill, Morgan, Prudential, which have much money.

3. Have similar access to data.

4. Thus, news is reflected in P0 almost instantaneously.

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Preferred Stock

Hybrid security.Similar to bonds in that preferred

stockholders receive a fixed dividend which must be paid before dividends can be paid on common stock.

However, unlike interest payments on bonds, companies can omit dividend payments on preferred stock without fear of pushing the firm into bankruptcy.

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What’s the expected return of preferred stock with Vp = $50 and

annual dividend = $5?

%.0.1010.050$

5$k̂

k̂

5$50$V

p

p

p