8 - 1

Lecture TenCost of Capital From Issuing Stocks or

Stocks and Their Valuation

Determining common stock values

Efficient marketsPreferred stock

8 - 2

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?

8 - 3

For a constant growth stock,

D D gD D gD D gt t

t

1 01

2 02

111

PD g

k gD

k gs s0

0 11

If g is constant, then:

8 - 4

D D gtt 0 1

PVD

D

kt

tt

1

If g > k, P0 !P PVDt0

$

0.25

Years (t)0

8 - 5

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. See slide #8-8.

.PD

k gg

s0

1

requires ks

8 - 6

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%.

Also, this is the cost of capital to the firm from issuing common Stk.

Use the SML to calculate ks:

8 - 7

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

8 - 8

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

Constant growth model:

$0.

. .P

D

k gs0

1 265

012 0 06

$0.

.$4. .

265

0 0642

8 - 9

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

^

^

8 - 10

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.

.

8 - 11

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%.

Again, this is the cost of raising fundsfrom the sale of common stock.

^

8 - 12

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% ...

^

8 - 13

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

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

Can no longer use constant growth model.

However, growth becomes constant after 3 years.

^

8 - 14

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

...

^

8 - 15

What is the expected dividend yield and capital gains yield at t = 0?

At t = 4?

Div

Cap

.$0.$22.

.

. . .

yield

gain

0

325052

144%.

12% 144% 10 56%.0

8 - 16

During nonconstant growth, D/P and capital gains yield are not constant, and capital gains yield is less than g.

After t = 3, g = constant = 10% = capital gains yield; k = 12%; so D/P = 12% - 10% = 2%.

8 - 17

Suppose g = 0 for t = 1 to 3, and then g is a constant 11%. What is P0?

0

0.22320.19930.1779

19.7519

1 2 3 4ks=12%

20.3523

g = 0% g = 0% g = 0% g = 11%

0.25 0.25 0.25 0.2775

..

P3

0 27750 01

27.75.

^

...

8 - 18

What is D/P and capital gains yield at t = 0 and at t = 3?

t = 0:D1

P0

CGY

2535

123%.

12% 123% 1077%.

$0.$20.

.

. .

t = 3: Now have constant growth with g = capital gains yield = 11% and D/P = 1%.

8 - 19

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

012 0 06

235

01831

8 - 20

What is the annual D/P and capital gains yield?

Capital gains yield = g = -6.0%,

Dividend yield = 12.0% - (-6.0%)= 18%.

D/P and cap. gains yield are constant,with high dividend yield (18%) offsettingnegative capital gains yield.

8 - 21

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.^

8 - 22

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

8 - 23

Why do stock prices change?

PD

k gi0

1

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

kRF = k* + IP

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

^

8 - 24

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.

8 - 25

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.

8 - 26

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.

8 - 27

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.

8 - 28

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.

8 - 29

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.

8 - 30

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

annual dividend = $5?

Vk

k

psps

ps

$50$5

$5

$50. .010 10 0%.