2011 7-1
McGraw-Hill/Irwin
Copyright by the McGraw-Hill Companies, Inc. All rights reserved.
Cash Flows for Stockholders
If you own a share of stock, you can
receive cash in two ways
The company pays dividends
You sell your shares, either to another
investor in the market or back to the company
As with bonds, the price of the stock is the
present value of these expected cash
flows
Dividends cash income
Selling capital gains
7-2
One Period Example
Suppose you are thinking of purchasing
the stock of Moore Oil, Inc.
You expect it to pay a $2 dividend in one year
You believe you can sell the stock for $14 at
that time.
You require a return of 20% on investments of
this risk
What is the maximum you would be willing to
pay?
7-3
One Period Example
D1 = $2 dividend expected in one year
R = 20%
P1 = $14
CF1 = $2 + $14 = $16
Compute the PV of the expected cash
flows
(2 + 14)
P0 =
= $13.33
1.20
7-4
Two Period Example
What if you decide to hold the stock for two
years?
D1 = $2.00
D2 = $2.10
CF1 = $2.00
CF2 = $2.10 + $14.70 = $16.80
P2 = $14.70
Now how much would you be willing to pay?
2
(2.10 + 14.70)
P0 =
+
= $13.33
2
1.20
(1.20)
7-5
Three Period Example
What if you decide to hold the stock for three
years?
D1 = $2.00
CF1 = $2.00
D2 = $2.10
CF2 = $2.10
D3 = $2.205
CF3 = $2.205 + $15.435 = $17.640
P3 = $15.435
Now how much would you be willing to pay?
2
2.10
(2.205 + 15.435 )
P0 =
+
+
= $13.33
2
3
1.20 (1.20 )
(1.20)
7-6
Three Period Example
Using TI BAII+ Cash Flow Worksheet
Display
Cash Flows:
CF0
=
0
CF1
=
2.00
CF2
=
2.10
CF3
=
17.64
You Enter
C00
C01
F01
C02
F02
C03
F03
I
NPV
0
2
1
2.10
1
17.64
1
20
13.33
7-7
Developing The Model
You could continue to push back
when you would sell the stock
You would find that the price of
the stock is really just the present
value of all expected future
dividends
7-8
Stock Value = PV of Dividends
^
P0 =
D1
(1+R)1
+
D2
(1+R)2
+
D3
(1+R)3
++
D
(1+R)
Dt
P0 =
t
t =1 (1 + R )
How can we estimate all future dividend payments?
7-9
Estimating Dividends:
3 Special Cases
Zero Growth
Firm will pay a constant dividend forever
Like preferred stock
Price is computed using the perpetuity formula
Constant dividend growth
Firm will increase the dividend by a constant
percent every period
Nonconstant growth
Dividend growth is not consistent initially, but settles
down to constant growth eventually
7-10
1. Zero Growth
Dividends expected at regular intervals
forever = perpetuity
P0 = D / R
Suppose stock is expected to pay a
$0.50 dividend every quarter and the
required return is 10% with quarterly
compounding. What is the price?
0.50
P0 =
= $20
.10
4
7-11
2. Constant Growth Stock
One whose dividends are expected to
grow forever at a constant rate, g.
D1 = D0(1+g)1
D2 = D0(1+g)2
Dt = Dt(1+g)t
D0 = Dividend JUST PAID
D1 Dt = Expected dividends
7-12
Projected Dividends
D0 = $2.00 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
=
7-13
Dividend Growth Model
(1 + g)
P0 = D0
t
t =1 (1 + R )
^
D0(1+g)
P0 =
R-g
t
D1
=
R-g
Gordon Growth Model
7-14
DGM Example 1
Suppose Big D, Inc. just paid a dividend of $.50.
It is expected to increase its dividend by 2% per
year. If the market requires a return of 15% on
assets of this risk, how much should the stock be
selling for?
D0= $0.50
D0 (1 + g)
P0 =
Rg
g = 2%
R = 15%
0.50(1 + .02)
P0 =
= $3.92
.15 .02
7-15
DGM Example 2
Suppose TB Pirates, Inc. is expected to pay a $2
dividend in one year. If the dividend is expected
to grow at 5% per year and the required return is
20%, what is the price?
D1
D1 = $2.00
P0 =
g = 5%
Rg
r = 20%
2.00
P0 =
= $13.33
.20 .05
7-16
Stock Price Sensitivity to Dividend
Growth, g
250
D1 = $2; R = 20%
Stock Price
200
150
100
50
0
0
0.05
0.1
0.15
0.2
Growth Rate
7-17
Stock Price Sensitivity to Required
Return, R
250
D1 = $2; g = 5%
Stock Price
200
150
100
50
0
0
0.05
0.1
0.15
0.2
0.25
0.3
Growth Rate
7-18
Example 7.3
Gordon Growth Company - I
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 =
Rg
4.00
P0 =
= $40
.16 .06
7-19
Example 7.3
Gordon Growth Company - II
What is the price expected to be in year
4?
D 4 (1 + g) D5
P4 =
=
Rg
R-g
D5 = D1(1 + g)4
4.00(1 + .06 )
P4 =
= $50.50
.16 .06
4
7-20
Example 7.3
Gordon Growth Company - II
What is the implied return given the
change in price during the four year
period?
50.50 = 40(1+return)4; return = 6%
4 ; 40 ; 50.50 ; 0 ; = 6%
The price grows at the same rate as
dividends
7-21
ConstantGrowthModelConditions
1.
2.
3.
4.
Dividend expected to grow at g forever
Stock price expected to grow at g forever
Expected dividend yield is constant
Expected capital gains yield constant
and is equal to g
5. Expected total return, R, must be > g
6. Expected total return (R):
= expected dividend yield (DY)
+ expected growth rate (g)
= dividend yield + g
7-22
3. Nonconstant Growth
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.
7-23
Nonconstant Growth Solution
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
7-24
Nonconstant + Constant
growth
Basic PV of all Future Dividends Formula
P0 =
D1
(1 + R
)
1
D2
+
(1 + R
)
2
D3
+
(1 + R
)
3
D
+. . . +
(1 + R )
Dividend Growth Model
= D t +1
Pt
R g
7-25
Nonconstant + Constant growth
P0 =
D1
(1 + R )
1
Because
+
D2
(1 + R )
2
P2
+
2
(1 + R)
Dt
P2 =
(1 + R)t
t =3
If g constant after t = 2, then
D3
P2 =
Rg
7-26
Nonconstant growth followed by
constant growth:
0 rs=20%
g = 20%
D0 = 1.00
1
2
g = 15%
1.20
3
g = 5%
1.38
1.449
1.0000
0.9583
^
P2 =
6.7083
8.6667
$1.449 = $9.66
0.20 0.05
= P0
7-27
Quick Quiz: Part 1
What is the value of a stock that is expected to
pay a constant dividend of $2 per year if the
required return is 15%?
2.00
P0 =
= $13.33
.15
What if the company starts increasing
dividends by 3% per year beginning with the
next dividend? The required return remains at
15%.
2.00(1.03 )
P0 =
= $17.17
.15 .03
7-28
Features of Common Stock
Voting Rights
Stockholders elect directors
Proxy voting
Classes of stock
Founders shares
Class A and Class B shares
7-29
Features of Common Stock
Other Rights
Share proportionally in declared
dividends
Share proportionally in remaining assets
during liquidation
Preemptive right
Right of first refusal to buy new stock issue
to maintain proportional ownership if
desired
7-30
Dividend Characteristics
Dividends are not a liability of the firm until
declared by the Board of Directors
A firm cannot go bankrupt for not declaring
dividends
Dividends and Taxes
Dividends are not tax deductible for firm
Taxed as ordinary income for individuals
Dividends received by corporations have a
minimum 70% exclusion from taxable income
7-31
Features of Preferred Stock
Dividends
Must be paid before dividends can be paid to
common stockholders
Not a liability of the firm
Can be deferred indefinitely
Most preferred dividends are cumulative
Missed preferred dividends have to be paid before
common dividends can be paid
Preferred stock generally does not carry
voting rights
7-32
The Stock Markets
Primary vs. Secondary Markets
Primary = new-issue market
Secondary = existing shares traded among
investors
Dealers vs. Brokers
Dealer: Maintains an inventor
Ready to buy or sell at any time
Think Used car dealer
Broker: Brings buyers and sellers together
Think Real estate broker
7-33
New York Stock Exchange
NYSE Euronext (merged 2007)
Members (Historically)
NYSE Specialist:
Assigned broker/dealer
Each stock has one assigned specialist
All trading in that stock occurs at the
specialists post
7-34
NASDAQ
NASDAQ OMX (merged 2007)
Dealer-based quotation system
Multiple market makers
Large portion of technology stocks
7-35
ECNs
Electronic
Communications
Networks provide direct
trading among
investors
Developed in late
1990s
ECN orders transmitted
to NASDAQ
Observe live trading
online at
Batstrading.com
7-36
Reading Stock Quotes
What information is provided in the stock
quote?
7-37
Quick Quiz: Part 2
What are some of the major
characteristics of common stock?
What are some of the major
characteristics of preferred stock?
7-38
Practice Problems Ch. 7
1.
The Pancake House pays a constant annual dividend of $1.25 per
share. How much are you willing to pay for one share if you
require a 15 percent rate of return?
2.
Healthy Foods just paid its annual dividend of $1.45 a share. The
firm recently announced that all future dividends will be increased
by 2.8 percent annually. What is one share of this stock worth to
you if you require a 14 percent rate of return?
7-39
Practice Problems Ch. 7
3.
Atlas Home Supply has paid a constant annual dividend of $2.40 a
share for the past 15 years. Yesterday, the firm announced the
dividend will increase next year by 10 percent and will stay at the
level through year three, after which time the dividends will
increase by 2 percent annually. The required return on this stock is
12 percent. What is the current value per share?
7-40
Chapter 7
END