1
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?
2
Basic Types of Stock
Preferred stock: hybrid Common stock
3
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
4
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
5
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.
6
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
7
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
8
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.
9
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.
10
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
11
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
12
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
13
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
14
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
15
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
16
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
Relationship between value and rs
Required Return, rs Stock Value5.0% $80.00
Relationship between value and rs
Required Return, rs Stock Value5.0% $80.008.0 50.00
Relationship between value and rs
Required Return, rs Stock Value5.0% $80.008.0 50.00
12.0 33.33
17
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
18
Stock Valuation with Nonconstant Growth—Example
D0 = $1.25g1 = 25%g2 = 20%g3 = 10%g4 = -4%g5 = 5% = g6 = … = g∞
rs =14%
19
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
Stock Valuation with Nonconstant Growth—Example
20
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
Stock Valuation with Nonconstant Growth—Example
21
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
22
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.
23
Stock Return
g PD̂
r̂0
1s
Expected rateof return
Expecteddividend
yield= +
Expected growthrate (capital gains yield)
24
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
25
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
26
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%^
27
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
28
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
29
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.
Stocks (Equity)Characteristics and Valuation
30
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)
Stocks (Equity)Characteristics and Valuation