Stocks (Equity) Characteristics and Valuation

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Stocks (Equity)Characteristics and Valuation

What is equity?What factors affect stock prices?How are stock prices determined?How are stock returns determined?What techniques do investors use to value stocks?

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Basic Types of Stock

Preferred stock: hybrid Common stock

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Preferred Stock FeaturesPar valueThe nominal or face value of a stock or bond

DividendsGenerally fixed, like debt; based on the par value

Cumulative dividendsPreferred dividends not paid in previous periods must be

paid before common dividends can be paidMaturityNo specific maturity date

Priority to assets and earningsPreferred stockholders are paid before common

stockholders

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Preferred Stock FeaturesControl of the Firm (Voting Rights)Most preferred stock is nonvoting, unless dividends are

not paid for a particular number of periodsConvertibilityCan be converted to common stock

Call provisionFirm has the right to call in preferred stock for

redemptionSinking fundA fund used to retire a given amount of the stock each

yearParticipatingShares earnings with common stockholders

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Common Stock FeaturesPar valueStockholders’ minimum financial obligation

DividendsNo legal obligation to pay dividends

MaturityNo specific maturity date

Priority to assets and earningsReceive distributions last

Preemptive rightRight to buy new issues

Control of the firmVote on board of directors, stockholder proposals, etc.

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Types of Common Stock

Classified StockSpecial designations, such as Class A, Class B,

etc., used to meet special needs of the company

Founder’s SharesClassified stockA class of stock owned by the firm’s founders

who have sole voting rights for a particular time period

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Equity Instruments in International Markets

American Depository ReceiptsCertificates that represent ownership in

stocks of foreign companiesForeign EquityYankee stock—issued by foreign firm and

traded in the United StatesEuro stock—traded outside of “home”

country, excluding the United States

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Stock Valuation

Stock value = Present value of the dividends that the company is expected to pay during its life.If the stock never pays a dividend—whether a regular dividend or a liquidating dividend—then its value is $0.

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Stock Valuation—Terms

tD̂ = dividend expected in Period t, such that 1D̂ = the dividend expected in Period 1

D0 = the most recently paid dividend

tP̂ = stock price expected in Period t, such that

1P̂ = the price expected in Period 1P0 = current market price

g = growth raters = the rate of return investors require to

purchase the firm’s common stock

^ (hat) = an expected value—that is, a value that is forecasted to occur in the future.

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Stock ValuationStock ownership entitles the investor to the future cash flows, called dividends, that are paid by the firm 1

…0 2 3 ∞

1D̂ 2D̂ 3D̂ D̂1D ofPV ˆ

2D ofPV ˆ

3D ofPV ˆ

D ofPV ˆ

...

0t P ValueStock D ofPV ˆˆ

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Stock Valuation

dividends future expected ofPV P V valueStock 0s ˆ

)r (1D

)r (1D

)r (1D P

s2

s2

1s

10

ˆˆˆˆ

)r (1

D 1t

ts

t

ˆ

rs = required return on stock

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Stock ValuationConstant Growth, g

Required: g = constant rs > g

1t

ˆt

s

t0

s0

2s

20

1s

10

0 )r (1g) (1D

)r (1g) (1D

)r (1g) (1D

)r (1g) (1D P

If growth is constant such that g = g1 = g2 = … = g∞ 1

01 g) (1D D ˆ 202 g) (1D D ˆ …

g) (1D D 0ˆ

g - rg) (1D

s

10

g - rD s

1ˆ Value of a constant-

growth stock

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Stock Valuation—Constant Growth, g

The most recent dividend paid (D0) by a firm was $2; the firm is expected to grow at a constant rate (g) equal to 4 percent; and the required rate of return (rs) on similar risk investments is 12 percent.

g - rg) (1D P

s

10

0

ˆ0.04 - 0.12

$2(1.04) 1

$26.00 0.08$2.08

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Stock Valuation—Constant Growth, gD0 = $2; g = 4%; rs = 12%

26.00 25.9831 D100

1tt

ˆ

PV of @ 12%

= $2.00(1.04)tDividend, Year tD̂tD̂ tD̂1 $2.0800 = $2.00(1.04)1 $1.85712 2.1632 = 2.00(1.04)2 1.72453 2.2497 = 2.00(1.04)3 1.60135 2.4333 = 2.00(1.04)5 1.3807

10 2.9605 = 2.00(1.04)10

0.9532

50 14.2134 = 2.00(1.04)50

0.0492

100 101.0099 = 2.00(1.04)100

0.0012

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Stock Valuation—Constant Growth, g=0

)r(1D

)r(1D

)r(1DP

s2

s

21

s

10

ˆˆˆˆ

DDDD 21 ˆˆˆ

g = 0

srD

s2

s1

s0 )r(1

D)r(1

D)r(1

DP

ˆ

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Stock Valuation—Constant Growth, g=0

s0 r

D P ˆ

The preferred stock of a company pays a constant dollar dividend equal to $4 per share. The required rate of return on similar risk investments is 8 percent.

$50 0.08$4

Relationship between value and rs

Required Return, rs Stock Value5.0%8.0

12.0


Required Return, rs Stock Value5.0% $80.00


Required Return, rs Stock Value5.0% $80.008.0 50.00


Required Return, rs Stock Value5.0% $80.008.0 50.00

12.0 33.33

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Stock Valuation—Nonconstant Growth

)r (1D

)r (1D

)r (1D P

s2

s2

1s

10

ˆˆˆˆ

)r (1)g (1D

)r (1)g (1D

)r (1)g (1D

s1

2s

211

s

10 ˆˆ N

sNN1N

2s

211

s

10)r (1

P )g (1D )r (1

)g (1D )r (1

)g (1D

ˆˆˆ

norms1N

normsnormN

N g - rD g - r

)g (1D P

ˆˆ

ˆ gnorm = constant, or normal, growth

NP ˆ

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Stock Valuation with Nonconstant Growth—Example

D0 = $1.25g1 = 25%g2 = 20%g3 = 10%g4 = -4%g5 = 5% = g6 = … = g∞

rs =14%

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D0 = $1.25; rs = 14%

25%

-4 1.1723= 2.0625(0.96)

1.9800410 1.3921=

1.8750(1.10)2.06253

20 1.4428= 1.5625(1.20)

1.87502$1.3706=

$1.2500(1.25)$1.56251

Growth rate, g

PV of @ 14% Dividend,

Year tD̂tD̂ )g (1D D t1-tt ˆˆ

= 5.3778


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Because the dividends grow at a constant rate after Year 4, we can apply the constant growth model such that:

nsn4

ns5

4 g - r)g (1D g - r

D P

ˆˆˆ

$23.10 0.09$2.0790 0.05 - 0.14

)$1.98(1.05


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Valuation—Cash Flow Time Line

10 2 3 414%

1.5625 1.8750 2.0625 1.9800

5.3778

tD̂

23.10 4P̂13.677119.0549

$19.05P0 ˆ

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Stock Valuation—Nonconstant Growth

The key to computing the value of a stock that exhibits nonconstant growth is to assume constant growth occurs at some point in the future—it might start in five years, 50 years, or 100 years:Apply the constant growth model to compute the value of

the expected dividends from that point forward. Compute the present value of the stock’s value at the point

where you assume constant growth begins.Prior to the point where constant growth begins:Compute the dividend for each yearFind the present value of each dividend

Sum the PV results.

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Stock Return

g PD̂

r̂0

1s

Expected rateof return

Expecteddividend

yield= +

Expected growthrate (capital gains yield)

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Stock Return

P0 = $30.00; D0 = $1.50; g = 6.0%

g PD r

0

1s ˆ

ˆˆ 0.06 $30

)$1.50(1.06

11.3% 0.06 0.053 0.06 $30$1.59

g - rD g - r

g) (1D Ps

1s

00

ˆˆ

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Stock Return

In one year, the price of the stock is expected to be:

g - rD

)r (1D

)r (1D

)r (1D P

s2

1-s

2s

31

s2

1ˆˆˆˆˆ

$31.80 0.053$1.6854 0.06 - 0.113

)$1.59(1.06

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Stock ReturnBecause the value of the stock is expected to increase from $30.00 to $31.80 during the year,

g PPP

valueBeginning valueBeginning - valueEnding

yieldgainsCapital

0

01

ˆ

0

1PD

yieldDividend ˆ

6.0% 0.06 $30.00$30.00 $31.80

5.3% 0.053 $30.00$1.59

rs = 11.3%^

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Valuation Using P/E Ratios

P/E ratio = Price ÷ EPS = price multiple“Normal” P/EExample: A firm’s P/E is normally 8.0x. If its EPS = $7, then the value of its stock should be $56 = $7 x 8

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Valuation Using EVA

Economic Value Added = EVAEarnings must be sufficient to pay those who provide funds to the firm; otherwise the value of the firm should decrease.

funds) of cost (Dollarrate)Tax EBIT(1funds

of Costincome operatingtaxAfter

EVA

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What is equity?Stock/ownership.

What factors affect stock prices? Investors change their expectations about the

returns the firm will generate in the future.How are stock prices determined?The price is equal to the present value of the

dividends stockholders expect to receive during the company’s life.


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How are stock returns determined?Returns are based on the dividend the

company pays and the change in the market value of the stock during the year

What techniques do investors use to value stocks?P/E RatioEconomic Value Added (EVA)


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Stocks (Equity) Characteristics and Valuation