7-1
CHAPTER 7
Valuation Models: Stocks
Features of common stock
Determining common stock
values
Security market equilibrium
Efficient markets
Preferred stock
S05
7-2
Facts about Common Stock?
Represents ownership?
Ownership implies control?
Agency problem
Stockholders elect directors?
Directors elect management?
Management’s goal: Maximize
stock price.
7-3
What’s classified stock? How might
classified stock be used?
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.
7-4
What is 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.
7-5
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.
7-6
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.
7-7
ANALYZING STOCKS
7-8
Different Approaches for Valuing
Common Stock
Dividend growth model
Using the multiples of comparable
firms
Free cash flow method (covered in
Chapter 12)
7-9
DIVIDEND GROWTH MODEL
7 - 10
Stock value = PV of dividends
D1
D2
D
^
P0 = (1 + r) + (1 + r)2 + . . . (1 + r) .
ABSOLUTELY FUNDAMENTAL!
7 - 11
Future Dividend Stream:
D1 = D0(1 + g1)
D2 = D1(1 + g2)
.
.
.
7 - 12
WHAT IS A CONSTANT GROWTH
STOCK? HOW ARE CONSTANT
GROWTH STOCKS VALUED?
A stock whose dividends grow at a
constant rate.
In application, doesn’t mean that
each year must have precisely a
growth rate equal to the constant
rate, but rather that our best guess is
that that dividends will grow at a
constant rate.
Slide T7-14.
WHAT IS A CONSTANT GROWTH
STOCK? HOW ARE CONSTANT
GROWTH STOCKS VALUED?
D1 = D0(1+g)
D2 = D1(1+g)=D0(1+g)2
 .
 .
 .
Dn = D0(1+g)n
7 - 13
7 - 14
If growth of dividends g is
constant, then:
^
P0 =
D1
rs - g
D0 (1 + g)
=
.
rs - g
Model requires:
rs > g (otherwise results in negative
price).
g constant forever.
7 - 15
$
D t  D 0 1  g
0.25
PVDt 
P0   PVD t
0
t
Dt
1  r t
If g > k; P0  !
Years (t)
7 - 16
What happens if g > rs?
D1
ˆ
P0 
re quire srs  g .
rs  g
If rs< g, get negative stock price,
which is nonsense.
We can’t use model unless (1) g  rs
and (2) g is expected to be constant
forever. Because g must be a longterm growth rate, it cannot be  rs.
7 - 17
PROOF OF GORDON MODEL
7 - 18
Bon Temps Company: What is the
required rate of return?
 = 1.2.
rRF = 7%.
rM = 12%.
Use SML equation to calculate rs:
rs
= rRF + (rM - rRF)
= 7% + (12% - 7%)(1.2)
rs = 13%.
7 - 19
What is the value of Bon Temps’ stock,
P0, given rs = 13%, D0 = 2.00 ?
Last dividend = $2.00; Dividend is
expected
to grow at 6%, i.e. g = 6%.
.
Hint:
D0 = 2.00 (already paid).
D1 = D0(1.06) = $2.12
D2 = D1(1.06) = $2.247
D3 = D2(1.06) = $2.382
T7-16,7-17.
7 - 20
What’s the stock’s market value?
D0 = 2.00, rs = 13%, g = 6%.
Constant growth model:
D0 1  g 
D1
ˆ
P0 

rs  g
rs  g
$2.12
$2.12
=
=
0.13 - 0.06
0.07
=$30.29.
7 - 21
What is Bon Temps’ value one year
from now?
7 - 22
What is Bon Temps’ value one year
from now?
^
P1 = D2/(rs - g) = 2.247/0.07
= $32.10.
^
Note: Could also find P1 as follows:
^
P1 = D2 /(rs - g) = D1 (1 + g)/(rs - g) =
P0 (1 + g) = $30.29(1.06) = $32.10.
So, price grows at rate = g.
7 - 23
P0 = D1/(rs - g)
P1 = D2/(rs - g)
BUT, D2 = D1( 1+g)
So, P1 = D1( 1+g)
(rs - g)
OR: P1 = P0( 1+g)
7 - 24
Find the expected dividend yield,
capital gains yield, and total return
during the 1st, 2nd and 3rd years.
7 - 25
Find the expected dividend yield,
capital gains yield, and total return
during the first year.
Dividend
=
yield in Year n
In 1st year:
Dn
^
P
.
n-1
D1
$2.12
= $30.29 = 7.00%.
^
P
0
7 - 26
Find the expected dividend yield,
capital gains yield, and total return
during the first year.
Dividend
=
yield in Year n
In 2nd
year:
Dn
^
P
.
n-1
D2
$2.247
= $32.10 = 7.00%.
^
P1
7 - 27
So, in CGR models, Dividend and Price
both grow at a rate = g; consequently
the dividend yield is:
?
7 - 28
So, in CGR models, Dividend and
Price both grow at a rate = g;
consequently the dividend yield is:
CONSTANT!
7 - 29
Capital gains yield in any
Year n:
^
^
Pn - Pn - 1
=
.
^
P
n-1
In 1 year:
$32.10 - $30.29
=
6%.
$30.29
In CGR models, Capital gains yield = g
7 - 30
Total yield = Div. yield + Cap. gains yield
= 7% + 6% = 13% = rs.
7 - 31
Find the total return during the
first year.
Total return = Dividend yield +
Capital gains yield.
Total return = 7% + 6% = 13%.
Total return = 13% = rs.
For constant growth stock:
Capital gains yield = 6% = g.
7 - 32
Rearrange model to rate of return form:

D
D1
1
ˆ
P0 
to r s 
 g.
rs  g
P0
^
Then, rs = $2.12/$30.29 + 0.06
= 0.07 + 0.06 = 13%.
7 - 33
Points to Remember
 If a stock is in equilibrium, then:
Price = Value.
^
(P0 = P0)
Required return = Expected return.
(rs = r^s)
7 - 34
 For any stock, the expected total
return in any year equals
dividend yield + capital gains
yield.
7 - 35
For constant growth stocks:
Dividend yield is constant,
D1/P0 = D2/P1 = D3/P2.
Capital gains yield is constant = g.
(P1 - P0)/P0 = (P1/P0) - 1 = (1+g) - 1 =
g.
Stock price grows at constant
rate = g.
7 - 36
DIGRESSION: PRICE-EARNINGS
RATIO
Po = D1/(rs - g)
D1 = E1( 1-b)
Where b = retention ratio, and (1-b) =
payout ratio.
7 - 37
PRICE-EARNINGS RATIO
Po = E1(1-b)/(rs - g)
Po = (1-b)
E1
(rs - g)
A greater g implies a larger P/E.
7 - 38
WHAT WOULD THE STOCK PRICE OF
BON TEMPS BE IF DIVIDENDS HAVE
ZERO GROWTH?
7 - 39
What would P0 be if g = 0?
The dividend stream would be a
perpetuity.
0 r =13%
s
1
2
3
2.00
2.00
2.00
PMT $2.00
P0 =
=
= $15.38.
r
0.13
^
7 - 40
What is Subnormal or Supernormal
Growth
7 - 41
Subnormal or Supernormal Growth
Non-constant growth followed by
constant growth in dividends.
(e.g. after some point, best we can
do is estimate a constant growth
in dividends.)
Cannot use constant growth
model alone
Value the nonconstant & constant
growth periods separately
7 - 42
If we have supernormal growth of 30%
for 3 years, then a long-run constant
^ ?
g = 6%, what is P
0
0 rs=16%
g = 30%
D0 =$2.00
1
2
g = 30%
3
g = 30%
4
g = 6%
7 - 43
Nonconstant growth followed by constant
growth:
0 r =13%
s
1
g = 30%
D0 = 2.00
2
g = 30%
2.60
3
g = 30%
3.38
4
g = 6%
4.394
4.6576
2.3009
2.6470
3.0453
46.1135
54.1067
^
= P0
$4.6576
ˆ
P3 
 $66.5371
0.13  0.06
n.b. P3= D4/(rs - g)
7 - 44
What is the expected dividend and
capital gains yields at t = 0? At t = 4?
7 - 45
What is the expected dividend yield and
capital gains yield at t = 0? At t = 4?
At t = 0:
D1
$2.60
Dividend yield =
=
= 4.81%.
P0
$54.11
CG Yield = 13.0% - 4.8% = 8.19%.
(More…)
7 - 46
Check on Capital gains yield:
Capital Gains yield = (P1 - P0)/P0
P1= PV(D2) + PV(D3) + PV(P3)
 = 3.38/1.13 + 4.394/(1.13)2 +
66.53/(1.13)2 = $58.53
Capital Gains yield = (P1 - P0)/P0 =
(58.53- 54.11)/54.11 = 8.19%
42
7 - 47
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 t
t = 4 capital gains gains yield = 6%.
 Because rs = 13%, the t = 4 dividend
yield = 13% - 6% = 7%.
7 - 48
At Year 4, stock is constant growth, so
CG yield4 = 6% = g.
Div. yield4 = 7%.
7 - 49
Is the stock price based on
short-term growth?
The current stock price is $54.11
The PV of dividends beyond year 3 is
$66.53/(1.13)^3 (P3 discounted back
to t = 0) =46.11.
The percentage of stock price due to
“long-term” dividends is:
$46.11
$54.11 = 85.2%.
7 - 50
If most of a stock’s value is due to longterm cash flows, why do so many
managers focus on quarterly earnings?
 Sometimes changes in quarterly earnings
are a signal of future changes in cash
flows. This would affect the current stock
price.
 Sometimes managers have bonuses (or
options) tied to quarterly earnings.
7 - 51
Suppose g = 0 for t = 1 to 3, and then g
^
is a constant 6%. What is P0?
0
rs=13%
g = 0%
1
2
g = 0%
2.00
1.7699
1.5663
1.3861
20.9895
25.7118
3
g = 0%
2.00
4
g = 6%
2.00
...
2.12
P  2.12  30.2857
3
0.07
7 - 52
What is dividend yield and capital
gains yield at t = 0 and at t = 3?
D1 2.00
t = 0: P  $25.72 7.8%.
0
CGY = 13.0% - 7.8% = 5.2%.
t = 3: Now have constant growth
with g = capital gains yield = 6% and
dividend yield = 7%.
7 - 53
If g = -6%, no one buy the stock?
Right?
7 - 54
If g = -6%, would anyone buy the
stock? If so, at what price?
Firm still has earnings and still pays
^
dividends, so P0 > 0:
ˆP  D0 1  g   D1
0
rs  g
rs  g
$2.00(0.94) $1.88
=
=
= $9.89.
0.13 - (-0.06) 0.19
7 - 55
What are the annual dividend
and capital gains yield?
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.
7 - 56
Using Free Cash Flows
We will cover this later in
Chapter 12.
7 - 57
Suppose this firm decides to expand:
Finance expansion by borrowing $40
million and halting dividends.
How do we value a firm with no
dividends?
7 - 58
Projected free cash flows (FCF):
Year 1 FCF = -$5 million
Year 2 FCF = $10 million
Year 3 FCF = $20 million
FCF grows at constant rate of 6%
after year 3.
7 - 59
The corporate cost of capital, kc, is
10%.
The company has 10 million shares
of stock.
7 - 60
Free Cash Flows
Recall the definition of free cash
flows:
FCF=NOPAT - Net Capital Investment
where
Net Capital Investment = Net
operating working capital [noninterest bearing CA - CL] - operating
capital
7 - 61
Find the value of operations by
discounting the free cash flows at
the cost of capital.
0 r =10%
c
FCF=
1
2
-5.00
10.00
3 g = 6%
20.00
4
21.2
-4.545
8.264
15.026
Vop at 3
398.197
416.942
=
Vop
$21.2

 $530.
0 .10  0.06
7 - 62
Find the price per share of
common stock.
Value of equity = Value of operations
- Value of debt
= $416.94 - $40
= $376.94 million.
Price per share = $376.94/10 = $37.69.
7 - 63
In equilibrium, expected returns must
equal required returns:
^
rs = D1/P0 + g = rs = rRF + (rM - rRF)b.
7 - 64
Using multiples of comparable firms
7 - 65
Second Method: Using the Multiples
of Comparable Firms to Estimate Stock
Price (Price Multiples)
 Analysts often use the following multiples
to value stocks:
P/E
P/CF or P/EBITDA
P/Sales
P/margin
P/Customer
.
7 - 66
Using the Stock Price Multiples to
Estimate Stock Price
 Analysts often use the P/E multiple (the price
per share divided by the earnings per share)
or the P/CF multiple (price per share divided
by cash flow per share, which is the earnings
per share plus the dividends per share) to
value stocks (or other multiples).
 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.
7 - 67
Using the Stock Price Multiples to
Estimate Stock Price
 Example: BOH
Estimate the average P/E ratio of
comparable firms. This is the P/E multiple.
The P/E multiple for Pacific Banks is 19.06.
Multiply this average P/E ratio by the
expected earnings of the company to
estimate its stock price.
The EPS(ttm) is 3.22
Consequently, the Implied price is: $61.37
This is 16% greater than the current $52.81
price.
7 - 68
Using Entity Multiples
 The entity value (V) of the comparable firm 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
7 - 69
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 total value of the firm.
 Subtract the firm’s debt to get the total value
of equity.
 Divide by the number of shares to get the
price per share.
7 - 70
Problems with Market Multiple Methods
 It is often hard to find comparable firms.
 The average ratio for the sample of
comparable firms often has a wide range.
For example, the average P/E ratio might
be 20, but the range could be from 10 to 50.
How do you know whether your firm
should be compared to the low, average, or
high performers?
What factors account for the difference in
P/E ratios?
7 - 71
Why are stock prices volatile?
^
D
P  r 1g
0 s
 rs = rRF + (RPM)βi could change.
 Inflation expectations
 Risk aversion
 Company risk
 g could change.
7 - 72
Stock value vs. changes in rs and g
D1 = $2, rs = 10%, and g = 5%:
P0 = D1 / (rs-g) = $2 / (0.10 - 0.05) = $40.
rs
9%
10%
11%
What if rs or g change?
g
g
g
4%
5%
6%
40.00
50.00
66.67
33.33
40.00
50.00
28.57
33.33
40.00
7 - 73
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.
7 - 74
What is market equilibrium?
7 - 75
What is market equilibrium?
In equilibrium, stock prices are
stable. There is no general tendency
for people to buy versus sell.
In equilibrium, expected returns must
equal required returns:
^
r = D1/P0 + g = r = rRF + (rM - rRF)β.
7 - 76
How is equilibrium established?
^
7 - 77
How is equilibrium established?
D1
^
If r = P + g > r, then
0
P0 is “too low,” a bargain.
Buy orders > sell orders; P0 bid up;
D /P falls until D /P + g = ^r = r.
1
0
1
0
7 - 78
Why do stock prices change?
^
D1
P0 
ri  g
 ri = rRF + (rM - rRF )βi could change.
 Inflation expectations
 Risk aversion
 Company risk
 g could change.
7 - 79
What’s the Efficient Market
Hypothesis?
7 - 80
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.
7 - 81
What are the three forms of the EMH?
7 - 82
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. Seems
empirically true, but “technical
analysis” is still used.
7 - 83
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; especially on
smaller stocks.
7 - 84
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.
7 - 85
Markets are generally efficient
because:
1. 100,000 or so trained analysts--MBAs,
CFAs, and PhDs--work for firms like
Fidelity, Merrill, Morgan, and Schwab.
2. These analysts have similar access to
data and megabucks to invest.
3. Thus, news is reflected in P0 almost
instantaneously.
7 - 86
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 the firm into bankruptcy.
7 - 87
What’s the expected return on
preferred stock with Vps = $50 and
annual dividend = $5?
V ps  $50 
$5

r ps

r ps
$5

 0.10  10.0%.
$50
7 - 88
END!