CHAPTER 9 Stocks and Their Valuation

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Copyright © 2002 by Harcourt, Inc. All rights reserved.

CHAPTER 9Stocks 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 the stock price.

Facts about Common Stock

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Social/Ethical Question

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

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

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

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

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Issuer Proceeds from sale

AT&T Wireless $9.03 billion

Infineon Technologies $2.72 billion

Metropolitan Life Ins. Co. $2.50 billion

TyCom $2.88 billion

Genuity $1.91 billion

Biggest IPOs of 2000

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Average Initial Returns on IPOs in Various Countries

Mal

aysi

a

100%

75%

50%

25%

Brazil

Portugal

Japan

Sweden

United

State

sCan

ada

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Dividend growth model

Free cash flow method

Using the multiples of comparable firms

Different Approaches for Valuing Common Stock

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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

D1 = D0(1 + g)1

D2 = D0(1 + g)2

Dt = Dt(1 + g)t

P0 = = .

If g is constant, then:

D0(1 + g)ks – g

D1

ks – g^

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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.

0P̂ = requires ks > g.D1

ks – g

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Assume beta = 1.2, kRF = 7%, and kM = 12%. What is the required rate of

return on the firm’s stock?

ks= kRF + (kM – kRF)bFirm

= 7% + (12% – 7%) (1.2) = 13%.

Use the SML to calculate ks:

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D0 was $2.00 and g is a constant 6%. Find the expected dividends for the

next 3 years, and their PVs. ks = 13%.

0 1

2.247

2

2.382

3g = 6%

1.87611.7599

D0 = 2.00

1.6509

13%2.12

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= =

What’s the stock’s market value? D0 = 2.00, ks = 13%, g = 6%.

Constant growth model:

P0 = = D1

ks – g 0.13 – 0.06

$2.12

$2.12

0.07$30.29.

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

Could also find P1 as follows:

ks – g 0.13 – 0.06 P1 = =

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

^

^

^

D2 $2.247^

= $32.10.

P1 = P0(1.06) = $32.10.

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

during the first year.

Dividend yld = = =

Cap gains yld = =

Total return = 7.0% + 6.0% = 13.0%.

D1

P0

P1 – P0

P0

^$30.29$2.12

7.0%.

$32.10 – $30.29$30.29

= 6.0%.

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Rearrange model to rate of return form:

.PD

k g

D

Pg

s0

1 1

0

to k s

Then, ks = $2.12/$30.29 + 0.06= 0.07 + 0.06 = 13%.

^

–

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P0 = = = $15.38.

What would P0 be if g = 0?

The dividend stream would be a perpetuity.

2.00 2.002.00

0 1 2 313% ...

^ PMTk

$2.000.13

^

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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 = 6%, what is P0? k is still 13%.^

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Nonconstant growth followed by constant growth:

0

2.301

2.647

3.045

46.114

1 2 3 4ks = 13%

54.107 = P0

g = 30% g = 30% g = 30% g = 6%

D0 = 2.00 2.600 3.380 4.394 4.658

.. .

$66.54P34.65813 0 06

0

...

^

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

At t = 4?

Div. yield0 = = 4.81%.

Cap. gain0 = 13.00% – 4.81% = 8.19%.

$2.60$54.11

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

After t = 3, g = constant = 6% = capital gains yield; k = 13%; so D/P = 13% – 6% = 7%.

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25.72

Suppose g = 0 for t = 1 to 3, and then g is a constant 6%. What is P0?

0

1.771.571.39

20.99

1 2 3 4ks=13%

g = 0% g = 0% g = 0% g = 6%

2.00 2.00 2.00 2.00 2.12

.P3

2.12

0 0730.29.

^

...

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t = 3: Now have constant growth with g = capital gains yield = 6% and D/P = 7%.

$2.00$25.72

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

t = 0:D1

P0

= = 7.78%.

CGY = 13% – 7.78% = 5.22%.

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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=

=

$2.00(0.94) $1.880.13 – (-0.06) 0.19

= = = $9.89.

– –+

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

Capital gains yield = g = -6.0%,

Dividend yield= 13.0% – (-6.0%) = 19%.

D/P and cap. gains yield are constant,with high dividend yield (19%) offsettingnegative capital gains yield.

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Free Cash Flow Method

The free cash flow method suggests that the value of the entire firm equals the present value of the firm’s free cash flows (calculated on an after-tax basis).

Recall that the free cash flow in any given year can be calculated as:

NOPAT – Net capital investment.

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Once the value of the firm is estimated, an estimate of the stock price can be found as follows:

MV of common stock (market capitalization) = MV of firm – MV of debt and preferred stock.

P = MV of common stock/# of shares.

Using the Free Cash Flow Method

^

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Free cash flow method is often preferred to the dividend growth model--particularly for the large number of companies that don’t pay a dividend, or for whom it is hard to forecast dividends.

Issues Regarding the Free Cash Flow Method

(More...)

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Similar to the dividend growth model, the free cash flow method generally assumes that at some point in time, the growth rate in free cash flow will become constant.

Terminal value represents the value of the firm at the point in which growth becomes constant.

FCF Method Issues (Continued)

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416.942

FCF estimates for the next 3 years are -$5, $10, and $20 million, after which the FCF is expected to grow at 6%.

The overall firm cost of capital is 10%.

0

-4.5458.264

15.026398.197

1 2 3 4k = 10%

g = 6%

-5 10 20 21.20

21.200.04

...

*TV3 represents the terminal value of the firm, at t = 3.

530 = = *TV3

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If the firm has $40 million in debt and has 10 million shares of stock, what is

the price per share?

Value of equity = Total value – Value of debt

= $416.94 – $40

= $376.94 million.

Price per share = Value of equity/# of shares

= $376.94/10

= $37.69.

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Analysts often use the following multiples to value stocks:P/EP/CFP/SalesP/Customer

Example: Based on comparable firms, estimate the appropriate P/E. Multiply this by expected earnings to back out an estimate of the stock price.

Using the Multiples of Comparable Firms to Estimate Stock Price

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What is market equilibrium?

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

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:

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

Expected returns are obtained by estimating dividends and expected capital gains (which can be found using any of the three common stock valuation approaches).

Required returns are obtained from the CAPM.

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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?

1. ki could change: ki = kRF + (kM – kRF )bi. kRF = k* + IP.

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

P0 = . ^ D1

ki – g

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

2. Work for firms like Merrill, Morgan, Prudential, which have a lot of money.

3. Have similar access to data.

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

Markets are generally efficient because:

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Preferred Stock

Hybrid security.Similar to bonds in that preferred

stockholders receive a fixed dividend that 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?

.k

5$50$V

pp

%.0.1010.050$

5$k̂p

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CHAPTER 9 Stocks and Their Valuation