CHAPTER 7
Stocks, Stock Valuation, and
Stock Market Equilibrium
1
Topics in Chapter






Features of common stock
Valuing common stock
Preferred stock
Stock market equilibrium
Efficient markets hypothesis
Implications of market efficiency for
financial decisions
2
EQUITIES

Why?
Key to understanding
valuations


What is investment worth
today?
Value of:



Enterprise
Entity
Company/Firm
Business Application

For Investor:


Determine value of
asset/business/company
For Firm:


Determine cost of
attracting investors &
raising equity capital
Selling ownership stake to
raise $
3
Equities


Valuing companies that don’t pay
dividends
Alternative valuation methods
4
The Big Picture:
The Intrinsic Value of Common Stock
Free cash flow
(FCF)
Dividends (Dt)
ValueStock =
D2
D1
D∞
... +
+
+
(1 + rs )1 (1 + rs)2
(1 + rs)∞
Market interest rates
Cost of
Market risk aversion
equity (rs)
Firm’s debt/equity mix
Firm’s business risk
Common Stock: Owners,
Directors, and Managers






Represents ownership.
Ownership implies control.
Stockholders elect directors.
Directors hire management.
Preemptive right.
Since managers are “agents” of
shareholders, their goal should be:
Maximize stock price.
6
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.
Prior to an IPO, shares are typically
owned by the firm’s managers, key
employees, and, in many situations,
venture capital providers
7
What is a seasoned equity
offering (SEO)?
A seasoned equity offering occurs when
a company with public stock issues
additional shares.
After an IPO or SEO, the stock trades in
the secondary market, such as the
NYSE or Nasdaq.
8
Classified Stock



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.
9
Tracking Stock

The dividends of tracking stock are tied to a
particular division, rather than the company
as a whole.



Investors can separately value the divisions.
Its easier to compensate division managers with
the tracking stock.
But tracking stock usually has no voting
rights, and the financial disclosure for the
division is not as regulated as for the
company.
10
Bonds
Issuer
(company)

vs.


Cost
Cost
(dividends pd out
Cap gains
int. paid out (i)
Bond value or price today

Stocks
Discount the CFs by (i)
(reqr’d return)
Cfs = Int pmts; principal
PV, PMT,FV,N,i

Stock value or price today


Discount the CFs by (R)
(reqr’d return)
Cfs = Dividends
11
Bonds
vs.
Stocks
Bond’s Value
or Price Today

= sum of the PVs of the
future CFs;


That is – discount CFs (int
Pmts (PMT) & Principal
(FV)) by i% over some
period (N) to get PV
PMT,FV,N,I known; solve
for PV
Stock’s Value
or Price Today

= sum of the PVs of the
future CFs;

Discount CFs (divids) by
(R) (reqr’d return) to get Po
(PV)
12
Different Approaches for
Valuing Common Stock

Dividend growth model




Constant growth stocks
Nonconstant growth stocks
Free cash flow method
Using the multiples of comparable firms
13
Why Invest in Stock?

For Growth in Value

From Dividends & Cap Gains

Generating Total Return = R

Stock Price


= Growth = g
Dividend Return or Yield = Annual divid / Price of stock= D1 / Po
Return on Stock = Return on Divid + Growth (cap gains)

R
=
D1 /Po
+
g
(but want price today)

R–g
=
D1 /Po
 Finally: Po
=
D1 / R - g
14
Constant Growth Approach to
Equity Valuations



Po =
D1 / R – g
Discounting the Divids (or CFs) by R-g (return
adjusted for constant growth)
Constant growth model: works when g is constant
rate (%) & R > g

If g > R, then have supernormal or non-constant growth


If so, then look at PVs of CFs generated the stock to determine its
price today
If we need R (req’d return) to use as disct factor, we can
use SML relationship from CAPM

SML: Ri = rRF + (RM - rRF)bi .
15
Stock Value = PV of Dividends
^
P0 =
D1
(1 + rs)1
+
D2
(1 + rs)2
+
D3
+…+
(1 + rs)3
D∞
(1 + rs)∞
What is a constant growth stock?
One whose dividends are expected to grow
forever at a constant rate, g.
16
For a constant growth stock:
D1 = D0(1 + g)1
D2 = D0(1 + g)2
Dt = D0(1 + g)t
If g is constant and less than rs, then:
D0(1 + g)
D1
^
P0 =
=
rs – g
rs – g
17
Dividend Growth and PV of
Dividends: P0 = ∑(PV of Dt)
$
0.25
Dt = D0(1 + g)t
Dt
PV of Dt =
(1 + r)t
If g > r, P0 = ∞ !
Years (t)
18
What happens if g > rs?
^
P0 =
D0(1 + g)1 D0(1 + g)2
(1 + rs)1
If g > rs, then
+
(1 + rs)2
(1 + g)t
(1 + rs)t
+…+
D0(1 + rs)∞
(1 + rs)∞
^
> 1, and P0 = ∞
So g must be less than rs for the constant
growth model to be applicable!!
19
Required rate of return: beta = 1.2,
rRF = 7%, and RPM = 5%.
Use the SML to calculate rs:
rs = rRF + (RPM)bFirm
= 7% + (5%)(1.2)
= 13%.
20
Projected Dividends




D0 = $2 and constant g = 6%
D1 = D0(1 + g) = $2(1.06) = $2.12
D2 = D1(1 + g) = $2.12(1.06) = $2.2472
D3 = D2(1 + g) = $2.2472(1.06) = $2.3820
21
Expected Dividends and PVs
(rs = 13%, D0 = $2, g = 6%)
0
g = 6%
1
2.12
1.8761
1.7599
1.6508
2
2.2472
3
2.3820
13%
22
Intrinsic Stock Value:
D0 = $2.00, rs = 13%, g = 6%
Constant growth model:
^
P0 =
=
D0(1 + g)
D1
=
rs – g
rs – g
$2.12
0.13 – 0.06
=
$2.12
0.07
= $30.29.
23
Expected value one year from
now:

D1 will have been paid, so expected
dividends are D2, D3, D4 and so on.
D2
^
$2.2472
P1 =
=
rs – g
0.07
= $32.10
24
Return = Dividend Yield +
Capital Gains Yield
D1
Dividend yield =
P0
^
P1 – P0
CG Yield =
=
P0
New - Old
Old
25
Expected Dividend Yield and
Capital Gains Yield (Year 1)
D1
$2.12
Dividend yield =
=
= 7.0%.
P0
$30.29
^
P1 – P0 $32.10 – $30.29
CG Yield =
=
P0
$30.29
= 6.0%.
26
Total Year 1 Return




Total return = Div yield + Cap gains yield.
Total return = 7% + 6% = 13%.
Total return = 13% = rs.
For constant growth stock:

Capital gains yield = 6% = g.
27
Rearrange model to rate of
return form:
D1
^
P0 =
to
rs – g
D1
^
rs =
+ g.
P0
Then, ^
rs = $2.12/$30.29 + 0.06
= 0.07 + 0.06 = 13%.
28
If g = 0, the dividend stream
is a perpetuity.
0 r = 13% 1
s
2.00
PMT
$2.00
P0 =
=
r
0.13
^
2
3
2.00
2.00
= $15.38.
29
Supernormal Growth Stock I



Supernormal growth of 30% for first three
years, then 6% constant g thereafter. Just
paid dividend of $2.00 /sh, & required return
for investments of this risk is 13%. What’s
the price today (Po)?
Can no longer use constant growth model.
However, growth becomes constant after 3
years.
30
Nonconstant growth followed
by constant growth
0
rs = ? %
g=?%
Do=?(1+g)
1
2
g=?%
D1=?
3
g=?%
D2=?
4
g=?%
D3=?
D4=?
?
?
?
?
^
?? = P
0
D4
^
P3 =
R-g
31
Nonconstant growth followed
by constant growth (D0 = $2):
0
rs = 13%
g = 30%
Do=2.00(1+g)
1
2
g = 30%
D1=2.60
3
g = 30%
D2=3.38
4
g = 6%
D3=4.39
D4=4.66
2.30
2.65
3.05
46.11
54.11 = P0
^
$4.66
^
= $66.54
P3 =
0.13 – 0.06
32
Using Cfs
After Determining:






CFo = Do
CF1 = D1
CF2 = D2
CF3 = D3 + P3
i=R%
Po = NPV = ?
Future Divs & gk
terminal value (price)
 CFo
=0
 CF1 = 2.60
 CF2 = 3.38
 CF3 = 4.39 + 66.54
=70.93
 i = 13 %
 Po = NPV = ? = $54.11
33
Expected Dividend Yield and
Capital Gains Yield (t = 0)
Today (@ t =0):
D1
$2.60
Dividend yield =
=
= 4.81%
P0
$54.11
CG Yield = 13.0% – 4.81% = 8.19%.
34
Expected Divd & Cap Gains Yield
(after t = 3)




During nonconstant growth, dividend yield
and capital gains yield are not constant.
If current growth is greater than gk, current
capital gains yield is greater than g.
After year 3 (t = 3), gk = constant = 6%, so
CGY = 6%.
Because rs = 13%, after yr 3 div yld =

13% – 6% = 7%.
35
Is stock price based on
short-term growth?
The current stock price is $54.11.
The PV of dividends beyond Year 3 is:
=terminal
or horizon value in year 3 (P3) discounted
^
to present by req’d Return (R=13%) = $46.11
% of stock price due to “longterm” dividends is:
$46.11
= 85.2%.
$54.11
36
Intrinsic Stock Value vs.
Quarterly Earnings

If most of a stock’s value is due to
long-term cash flows, why do so many
managers focus on quarterly earnings?
37
Intrinsic Stock Value vs.
Quarterly Earnings


Sometimes changes in quarterly
earnings are a signal of future changes
in cash flows. This affects current
stock price (Po).
Sometimes managers have bonuses
tied to quarterly earnings.
38
Supernormal Growth Stock II



Supernormal growth of 30% for Year 0
to Year 1, 25% for Year 1 to Year 2,
15% for Year 2 to Year 3, and then
long-run constant g = 6%.
Can no longer use constant growth
model.
However, growth becomes constant
after 3 years.
39
Nonconstant growth followed
by constant growth (D0 = $2):
0
rs = 13%
g = 30%
1
2
g = 25%
2.6000
3
g = 15%
3.2500
4
g = 6%
3.7375
3.9618
2.3009
2.5452
2.5903
39.2246
^
46.6610 = P0
$3.9618
^
= $56.5971
P3 =
0.13 – 0.06
40
Expected Dividend Yield and
Capital Gains Yield (t = 0)
At t = 0:
D1
$2.60
Dividend yield =
=
= 5.6%
P0
$46.66
CG Yield = 13.0% – 5.6% = 7.4%.
(More…)
41
Expected Dividend Yield and
Capital Gains Yield (after t = 3)




During nonconstant growth, dividend yield
and capital gains yield are not constant.
If current growth is greater than g, current
capital gains yield is greater than g.
After t = 3, g = constant = 6%, so the
capital gains yield = 6%.
Because rs = 13%, after t = 3 dividend
yield = 13% – 6% = 7%.
42
Is the stock price based on
short-term growth?
The current stock price is $46.66.
The PV of dividends beyond Year 3 is:
^
P3 / (1+rs)3 = $39.22
The percentage of stock price due
to “long-term” dividends is:
$39.22
= 84.1%.
$46.66
43
Suppose g = 0 for t = 1 to 3, and
then g is a constant 6%.
0
rs = 13%
g = 0%
1.7699
1.5663
1.3861
20.9895
25.7118
1
2
g = 0%
2.00
3
g = 0%
2.00
4
g = 6%
2.00
^ = 2.12
P3
0.07
2.12
= 30.2857
44
Dividend Yield and Capital
Gains Yield (t = 0)

Dividend Yield = D1/P0
Dividend Yield = $2.00/$25.72
Dividend Yield = 7.8%

CGY = 13.0% – 7.8% = 5.2%.


45
Dividend Yield and Capital
Gains Yield (after t = 3)




Now have constant growth, so:
Capital gains yield = g = 6%
Dividend yield = rs – g
Dividend yield = 13% – 6% = 7%
46
Suppose negative growth:
If g = -6%, would anyone buy stock?
If so, at what price?
Firm still has earnings and still pays
dividends, so ^
P0 > 0:
D0(1 + g)
D1
^
P0 =
=
rs – g
rs – g
$2.00(1-.06) $1.88
=
=
= $9.89.
0.13 – (-0.06) 0.19
47
Annual Dividend and Capital
Gains Yields
Capital gains yield = g = -6.0%.
Dividend yield = 13.0% – (-6.0%)
= 19.0%.
Both yields are constant over time, with the
high dividend yield (19%) offsetting the
negative capital gains yield.
48
What if company pays no
dividends?


Discount Free Cash Flows (CFs which can be
returned to investors) instead of dividends
Where FCF = NOPAT – Net Capital Spending
49
Uses of Free Cash Flows





Pay interest on debt
Repay principal on debt
Pay dividends to equityholders
Repurchase stock from equityholders
Buy mrktbl securities or other nonoperating assets
50
Equity Valuation using FCFs

A young firm just recorded a $<1.0> million FCF. It
expects the FCF 1-yr from today to be
$<5.0>million. In yrs 2 & 3, they are expected to
become positive at $10 and $20 million. In the 4th
yr, a constant growth in FCFs is expected to kick-in
at 6%. The required return for investments of this
risk is 10%. The firm has $40 million in debt, and
10 million shares outstanding. What’s the price per
share today?
51
Equity Valuation using FCFs
0
rs = 10%
1
2
3
4
g=6%
FCFo=<1>
FCF1=<5>
FCF2=10
FCF3=20 *(1+g)
FCF4=?
?
?
?
?
^
?? = P
0
FCF4
^
P3 =
R-g
52
Using Cfs for FCFs Equity Valuation
After Determining:






CFo = FCFo
CF1 = FCF1
CF2 = FCF2
CF3 = FCF3 + P3
i=R%
Po = NPV =?= value of firm
Future Divs & gk
terminal value (price)
 CFo
=0
 CF1 = <5>
 CF2 = 10
 CF3 = 20 + 530 =550.00
 i = 10 %
 Po = NPV = ? = $416.94
53
Equity Valuation using FCFs

Value of firm = $416.94
- Debt
40.00
=Value of equity $376.94 / 10 mil shrs

=price per share of $37.69


54
Market Cap (Capitalization)

= Market Value of firm’s equity

= (price/sh)*(#shs outstanding)
55
Enterprise Value

= Value of firm’s underlying business,
unencumbered by Debt, and separate from
cash & marketable securities


Enterprise Value= MV of equity + Debt - cash
Think:: Enterprise Value = Net cost of
acquiring a firm’s equity, taking its cash, and
paying off debt. In essence, it’s equivalent
to owning the unlevered (debt-free)
business.
56
Market Cap & Enterprise Value I

H.J. Heinz has a share price of $46.78,
its shares outstanding were 319.2
million. It has a market-to-book ratio of
8.00, a book debt-equity ratio of 2.62,
and cash of $352 million.


What’s Heinz’s market cap?
What’s its enterprise value?
57
Using Stock Price Multiples to
Estimate Stock Price


Analysts often use the P/E multiple (the
price per share divided by the earnings
per share).
Example:


Estimate the average P/E ratio of
comparable firms. This is the P/E multiple.
Multiply this average P/E ratio by the
expected earnings of the company to
estimate its stock price.
58
Multiples Approach I

Auto Industry
Industry P/E = 5

Pinto Car Co
Pinto EPS = $1.50/sh

Industry




If Pinto trading on NYSE =
$9.00
If $4.00


Pinto
5/1 = P/E = ?/$1.50
So Pinto relative price per
share (P) = $7.50
=overvalued (sell)
=undervalued (buy)
59
Using Entity Multiples

The entity value (V) is:




the market value of equity (# shares of stock
multiplied by the price per share)
plus the value of debt.
Pick a measure, such as EBITDA, Sales,
Customers, Eyeballs, etc.
Calculate the average entity ratio for a sample of
comparable firms. For example,


V/EBITDA
V/Customers
60
Using Entity Multiples
(Continued)

Find the entity value of the firm in question. For
example,





Multiply the firm’s sales by the V/Sales multiple.
Multiply the firm’s # of customers by the V/Customers
ratio
The result is the firm’s total value.
Subtract the firm’s debt to get the total value of its
equity.
Divide by the number of shares to calculate the
price per share.
61
Problems w/ Market Multiple Methods




It is often hard to find comparable firms.
What are relevant multiples?
New Co.’s often lack earnings
Average ratio for sample of comparable firms often
has a wide range.


I.E, ave P/E ratio might be 20, but range from 10 to 50.
How do you know whether firm should be compared to
low, average, or high performers?
Differences between firms in comparables pool

i.e: growth rates, risk, cost of capital
62
What if an equity’s dividend is
fixed? No g !
^
P0 =
D1
rs – g

So, Po = D1 /rs
And return = D1 / Po

It’s a perpetuity

63
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 bonds, preferred stock
dividends can be omitted without fear
of pushing firm into bankruptcy.
64
Expected return =?,
given Preferred stock share trading at $50
& pays annual dividend = $5
Vps
$5
= $50 =
^
rps
$5
^
rps =
= 0.10 = 10.0%
$50
65
A determinant of Growth


Relationship between ROE, Retention Rate, EPS
growth, and Dividends
A firm has an ROE of 25% & Retention Rate of
80%. If the most recent EPS was $3.00, what’s
the expected dividend at the end of the year?
66
Why are stock prices volatile?
^
P0 =

rs – g
rs = rRF + (RPM)bi could change.




D1
Inflation expectations
Risk aversion
Company risk
g could change.
67
Consider the following
situation.
D1 = $2, rs = 10%, and g = 5%:
P0 = D1/(rs – g) = $2/(0.10 – 0.05) = $40.
What happens if rs or g changes?
68
Stock Prices vs. Changes in rs
and g
rs
9%
4%
$40.00
g
5%
$50.00
10%
$33.33
$40.00
$50.00
11%
$28.57
$33.33
$40.00
6%
$66.67
69
Are volatile stock prices
consistent with rational pricing?



Small changes in expected g and rs
cause large changes in stock prices.
As new information arrives, investors
continually update their estimates of
g and rs.
If stock prices aren’t volatile, then
this means there isn’t a good flow of
information.
70
What is market equilibrium?


In equilibrium, the intrinisic price must equal
the actual price.
If the actual price is lower than the
fundamental value, then the stock is a
“bargain.” Buy orders will exceed sell orders,
the actual price will be bid up. The opposite
occurs if the actual price is higher than the
fundamental value.
(More…)
71
Intrinsic Values and Market Stock Prices
Managerial Actions, the Economic
Environment, and the Political Climate
“True” Expected
“True”
“Perceived” Expected
“Perceived”
Future Cash Flows
Risk
Future Cash Flows
Risk
Stock’s
Intrinsic Value
Stock’s
Market Price
Market Equilibrium:
Intrinsic Value = Stock Price
In equilibrium, expected returns
must equal required returns:
^
rs = D1/P0 + g = rs = rRF + (rM – rRF)b.
73
Expected Return vs. Required Return

16% >
15% reqr’d to invest

:: undervalued

Stock priced too low so buy
b/c bargain

As more people buy it,
Price
& return


10% <

:: then reach equilibrium
level of return
:: overvalued -SELL
74
How is equilibrium established?
^
D1
^
If rs =
+ g > rs, then P0 is “too low.”
P0
If the price is lower than the fundamental
value, then the stock is a “bargain.” Buy
orders will exceed sell orders, the price will
be bid up until:
D1/P0 + g = ^rs = rs.
75
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 inside information.
EMH does not assume all investors are
rational.
EMH assumes that stock market prices
track intrinsic values fairly closely.
(More…)
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EMH (continued)



If stock prices deviate from intrinsic
values, investors will quickly take
advantage of mispricing.
Prices will be driven to new equilibrium
level based on new information.
It is possible to have irrational investors
in a rational market.
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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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Semistrong-form EMH

All publicly available information is
reflected in stock prices, so it doesn’t
pay to pore over annual reports looking
for undervalued stocks. Largely true.
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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:



100,000 or so trained analysts—MBAs,
CFAs, and PhDs—work for firms like
Fidelity, Morgan, and Prudential.
These analysts have similar access to
data and megabucks to invest.
Thus, news is reflected in P0 almost
instantaneously.
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Market Efficiency


For most stocks, for most of the time,
it is generally safe to assume that the
market is reasonably efficient.
However, periodically major shifts can
and do occur, causing most stocks to
move strongly up or down.
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Implications of Market Efficiency
for Financial Decisions

Many investors have given up trying to
beat the market. This helps explain the
growing popularity of index funds,
which try to match overall market
returns by buying a basket of stocks
that make up a particular index.
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Implications of Market Efficiency
for Financial Decisions



Important implications for stock issues,
repurchases, and tender offers.
If the market prices stocks fairly,
managerial decisions based on over- and
undervaluation might not make sense.
Managers have better information but
they cannot use for their own advantage
and cannot deliberately defraud
investors.
84
Rational Behavior vs. Animal Spirits,
Herding, and Anchoring Bias


Stock market bubbles of 2000 and 2008
suggest that something other than pure
rationality in investing is alive and well.
People anchor too closely on recent events
when predicting future events.


When market is performing better than average,
they tend to think it will continue to perform better
than average.
Other investors emulate them, following like a
herd of sheep.
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Conclusions




Markets are rational to a large extent, but at
time they are also subject to irrational behavior.
One must do careful, rational analyses using the
tools and techniques covered in the book.
Recognize that actual prices can differ from
intrinsic values, sometimes by large amounts
and for long periods.
Good news! Differences between actual prices
and intrinsic values provide wonderful
opportunities for those able to capitalize on
them.
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