 Fundamental
Analysis – looks at
financials, product, mgt., history, etc.
• PE ratio – Price / E.P.S.
• Zero-Growth Dividend (preferred stock)
• Constant Growth Dividend (DCF)
• Nonconstant Growth
 Technical
Analysis – uses charts to
predict future prices
 Industry
Average PE X Company’s EPS
• If company EPS = $2.20 and industry average
PE = 20, stock should sell around $_____.
• Factors affected a company’s PE include:
 Risk
 Expected future growth
 Management
 Dividends
 Preferred
has preference in claims to
assets and dividends – must be paid
before common.
 Preferred dividends – fixed
 Common dividends – fluctuate
 Preferred usually have no voting rights
52 Weeks
Hi
Lo Stock
Yld
% PE
Vol
100s
s 42½ 29 QuakerOats OAT 1.14 3.3 24
s 36¼ 25 RJR Nabisco RN .08p ... 12
5067
6263
Sym Div
Hi
Net
Close Chg
Lo
35 34¼ 34¼ -¾
29¾ 285/8 287/8 -¾
2377/88 20 RJR Nab pfB
2.31 9.7
...
966
24
2355/88 23¾ ...
7¼
.60
...
2248
6½
6¼
5½ RJR Nab pfC
0
1
P0=23.75
D1=2.31
9.4
2
D2=2.31
3
D3=2.31
63/8

D=2.31
P0 = Value of Preferred Stock
= PV of ALL dividends discounted at
investor’s Required Rate of Return
-1/8
52 Weeks
Hi
Lo Stock
Yld
% PE
Vol
100s
s 42½ 29 QuakerOats OAT 1.14 3.3 24
s 36¼ 25 RJR Nabisco RN .08p ... 12
5067
6263
Sym Div
Hi
Net
Close Chg
Lo
35 34¼ 34¼ -¾
29¾ 285/8 287/8 -¾
2377/88 20 RJR Nab pfB
2.31 9.7
...
966
24
2355/88 23¾ ...
7¼
.60
...
2248
6½
6¼
5½ RJR Nab pfC
0
1
P0=23.75
D1=2.31
P0 =
2.31
(1+ rp)
9.4
2
+
2.31
(1+ rp )2

3
D2=2.31
D3=2.31
+
D=2.31
2.31
3
(1+ rkp )+···
If an investor expects a 10% return, how much are they
willing to pay for the stock?
63/8

-1/8
52 Weeks
Hi
Lo Stock
Yld
% PE
Vol
100s
s 42½ 29 QuakerOats OAT 1.14 3.3 24
s 36¼ 25 RJR Nabisco RN .08p ... 12
5067
6263
Sym Div
Hi
Net
Close Chg
Lo
35 34¼ 34¼ -¾
29¾ 285/8 287/8 -¾
2377/88 20 RJR Nab pfB
2.31 9.7
...
966
24
2355/88 23¾ ...
7¼
.60
...
2248
6½
6¼
5½ RJR Nab pfC
0
1
P0=23.75
D1=2.31
P0 =
Zero-Growth
Div. Model
2.31
(1+ rp)
9.4
2
+
P0 = D
R

3
D2=2.31
2.31
(1+ rp )2
D3=2.31
+
2.31
=
10%
D=2.31
2.31
3
(1+ rkp )+···
= $23.10
63/8

-1/8
P0 = PV of ALL expected dividends discounted at
investor’s Required Rate of Return
0
1
P0
D1
P0 =
D1
(1+ rs )
2
D2
+

3
D2
(1+ rs )2
D3
+
D3
(1+ rs )3
D
+···
Investors do not know the values of
D1, D2, .... , DN. The future dividends must
be estimated.
0
D0
1
D1=D0 (1+g)
2
3
D2=D0 (1+g)2 D3=D0 (1+g)3

D=D0 (1+g)
Assume that dividends grow at a constant rate (g).
0
1
D0
P0 =
2
D1=D0 (1+g)
D0 (1+ g)
(1+ rs )
+

3
D2=D0 (1+g)2 D3=D0 (1+g)3
D=D0 (1+g)
D0 (1+ g)2 D0 (1+ g)3
+ (1+ r )3 +
(1+ rs )2
s
··· + 
Reduces to:
P0 =
D0(1+g)
r– g
=
D1
r– g
Requires
r> g
 Gordon
Growth Company is expected to pay
a dividend of $4 next period and dividends
are expected to grow at 6% per year. The
required return is 16%.
 What is the current price?
D1
P0 
Rg
4.00
P0 
 $40
.16  .06
 What
is the price expected to be in
year 4?
D 4 (1  g) D5
P4 

Rg
R-g
D5  D1(1  g)4
4.00(1  .06)
P4 
 $50.50
.16  .06
4
 Used
with companies that have very high
growth rates.
 Calculate the PV of cash flows or
dividends for the high growth period.
 Solve for the PV of cash flows during the
constant growth period that are a
perpetuity.
 The sum of these two is the stock price.
99
00
01
02
03
04
05
06
07
08
09
10
11
12
Sales
.2M
6M
86M
440M
1.4B
3B
6B
10B
16B
21B
23B
29B
37B
50B
Net
Income
-6M
-15M
7M
100M
105M
400
M
1.4
B
3B
4.2B
4.2B
6.5B
8.5B
9.7B
10.7
B
 Can
no longer only use constant growth
model.
 However, growth becomes constant
after 3 years.
Supernormal growth followed by constant
growth:
0
r=13%
g = 30%
D0 = 2.00
= P0
1
2
g = 30%
2.60
^
3
g = 30%
3.38
4
g = 6%
4.39
4.66
Supernormal growth followed by constant
growth:
0
r =13%
g = 30%
D0 = 2.00
1
2
g = 30%
2.60
3
g = 30%
3.38
Pˆ3 
= P0
^
4
g = 6%
4.39
4.66
$ 4.66
 $66.54
0.13  0.06
Supernormal growth followed by constant
growth:
0
rs=13%
g = 30%
D0 = 2.00
1
2
g = 30%
2.60
3
g = 30%
3.38
4
g = 6%
4.39
4.66
2.30
2.65
3.05
Pˆ3 
46.11
54.11
= P0
^
Do not add in D0
$ 4.66
 $66.54
0.13  0.06
0
rs=13%
g = 0%
1
2
g = 0%
2.00
3
g = 0%
2.00
4
g = 6%
2.00
 
P
3
.
...
2.12

0
rs=13%
g = 0%
1
2
g = 0%
2.00
3
g = 0%
2.00
4
g = 6%
2.00
...
2.12
P  2.12  30.29
3
0.07
0
rs=13%
g = 0%
1
2
g = 0%
2.00
1.77
1.57
1.39
20.99
25.71
3
g = 0%
2.00
4
g = 6%
2.00
...
2.12
P  2.12  30.29
3
0.07
Terminal Value – the (present) value, at
the horizon date, of all future dividends
after that date.
 Suppose
a firm is expected to increase
dividends by 20% in one year and by
15% in two years. After that dividends
will increase at a rate of 5% per year
indefinitely. If the last dividend was $1
and the required return is 20%, what is
the price of the stock?
 Remember that we have to find the PV of
all expected future dividends.
 Compute
the dividends until growth levels off
• D1 = 1(1.2) = $1.20
• D2 = 1.20(1.15) = $1.38
• D3 = 1.38(1.05) = $1.449
 Find
the expected future price at the beginning
of the constant growth period:
• P2 = D3 / (R – g) = 1.449 / (.2 - .05) = 9.66
 Find
the present value of the expected future
cash flows
• P0 = 1.20 / (1.2) + (1.38 + 9.66) / (1.2)2 = 8.67
Nonconstant + Constant growth
D1
D2
P2
P̂0 


1
2
2
1  R  1  R  (1  R )

Because
Dt
P2  
t
(
1

R
)
t 3
If g constant after t  2, then
D3
P2 
Rg
0 R = 20% 1
g = 20%
D0 = 1.00
2
g = 15%
1.20
3
g = 5%
1.38
1.449
1.00
0.96
6.71
8.67 = P0
^
P2 =
$1.449 = $9.66
0.20 – 0.05
The Jones Company has decided to
undertake a large project. Consequently,
there is a need for additional funds. The
financial manager plans to issue
preferred stock with a perpetual annual
dividend of $5 per share.
If the required return on this stock is
currently 20 percent, what should be the
stock's market value?
The Jones Company has decided to
undertake a large project. Consequently,
there is a need for additional funds. The
financial manager plans to issue
preferred stock with a perpetual annual
dividend of $5 per share. If the required
return on this stock is currently 20
percent, what should be the stock's
market value?
5 ∕ .20 = 25
A share of preferred stock pays a
quarterly dividend of $2.50. If the price of
this preferred stock is currently $50, what
is the nominal annual rate of return?
A share of preferred stock pays a
quarterly dividend of $2.50. If the price of
this preferred stock is currently $50, what
is the nominal annual rate of return?
2.5 X 4 = 10/year
10/50 = 20%
McKenna Motors is expected to pay a
$1.00 per-share dividend at the end of
the year (D1 = $1.00). The stock sells for
$20 per share and its required rate of
return is 11 percent. The dividend is
expected to grow at a constant rate, g,
forever. What is the growth rate, g, for this
stock?
P0 =
D1
R– g
McKenna Motors is expected to pay a $1.00
per-share dividend at the end of the year (D1 =
$1.00). The stock sells for $20 per share and its
required rate of return is 11 percent. The
dividend is expected to grow at a constant rate,
g, forever. What is the growth rate, g, for this
stock?
D1/(R-g) = 20
1/(.11-g) = 20
1 = 2.2 – 20g
-1.2 = -20g
-1.2/-20 = g
.06 = g
A share of common stock has just paid a
dividend of $2.00. If the expected longrun growth rate for this stock is 15%, and
if investors require a 19% rate of return,
what is the price of the stock?
A share of common stock has just paid a
dividend of $2.00. If the expected longrun growth rate for this stock is 15%, and
if investors require a 19% rate of return,
what is the price of the stock?
2.00 X (1.15) = 2.30 = D1
P = 2.30 / (.19 - .15)
P = 2.30 / .04
P = $57.5
A
firm’s stock is selling for $10.50.
They just paid a $1 dividend and
dividends are expected to grow at
5% per year.
What is the required return?
 P0
= $10.50.
 D0 = $1
 g = 5% per year.
 What is the required return?
D0 (1  g)
D1
R
g
g
P0
P0
1.00(1.05)
R
 .05  15%
10.50
 P0
= $10.50
 D0 = $1
 g = 5% per year
 What is the dividend
yield?
1(1.05) / 10.50 = 10%
 What
is the capital
gains yield?
g = 5%
D0 (1  g)
R
 g
P0
R
D1
P0
 g
1.00(1.05)
R
 .05  15%
10.50
Dividend
Yield
Capital Gains
Yield
 Primary vs. Secondary Markets
• Primary = new-issue market
• Secondary = existing shares traded among
investors
 Dealers vs. Brokers
• Dealer: Maintains an inventory
Ready to buy or sell at any time
Think “Used car dealer”
• Broker: Brings buyers and sellers together
Think “Real estate broker”
 NYSE
• Merged with Euronext in 2007
• NYSE Euronext merged with the American
Stock Exchange in 2008
 Members (Historically)
• Buy a trading license (own a seat)
• Designated market makers, DMMs (formerly
known as “specialists”)
• Floor brokers
 Operational
goal = attract order flow
 NYSE DMMs:
• Assigned broker/dealer
 Each stock has one assigned DMM
 All trading in that stock occurs at the
“DMM’s post”
• Trading takes place between customer
orders placed with the DMMs and “the
crowd”
• “Crowd” = Floor brokers
 Index
funds outperform active funds
80 – 90% of the time.