1-1 7-1
Cash Flows to Stockholders
• If you buy 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
1
1-2 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, and you
believe that you can sell the stock for $14
at that time. If you require a return of 20%
on investments of this risk, what is the
maximum you would be willing to pay?
– Compute the PV of the expected cash flows
– Price = (14 + 2) / (1.2) = $13.33
– Or FV = 16; I/Y = 20; N = 1; CPT PV = -13.33
2
1-3 7-3
Two-Period Example
• Now, what if you decide to hold the stock
for two years? In addition to the $2
dividend in one year, you expect a
dividend of $2.10 and a stock price of
$14.70 both at the end of year 2. Now how
much would you be willing to pay?
PV = 2 / (1.2) + (2.10 + 14.70) / (1.2)2 = 13.33
Or CF0 = 0; C01 = 2; F01 = 1; C02 = 16.80;
F02 = 1; NPV; I = 20; CPT NPV = 13.33
3
1-4 7-4
Three-Period Example
• Finally, what if you decide to hold the stock
for three periods? In addition to the dividends
at the end of years 1 and 2, you expect to
receive a dividend of $2.205 and a stock
price of $15.435 both at the end of year 3.
Now how much would you be willing to pay?
PV = 2 / 1.2 + 2.10 / (1.2)2 + (2.205 +
15.435) / (1.2)3 = 13.33
Or CF0 = 0; C01 = 2; F01 = 1; C02 = 2.10;
F02 = 1; C03 = 17.64; F03 = 1; NPV; I = 20;
CPT NPV = 13.33
4
1-5 7-5
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
• So, how can we estimate all future
dividend payments?
5
1-6 7-6
Estimating Dividends: Special Cases
• Constant dividend
– The firm will pay a constant dividend forever
– This is like preferred stock
– The price is computed using the perpetuity
formula
• Constant dividend growth
– The firm will increase the dividend by a
constant percent every period
• Supernormal growth
– Dividend growth is not consistent initially, but
settles down to constant growth eventually
6
1-7 7-7
Zero Growth
• If dividends are expected at regular intervals
forever, then this is like preferred stock and is
valued as a 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?
P0 = .50 / (.1 / 4) = .50 / .025 = $20
7
1-8 7-8
Dividend Growth Model
• Dividends are expected to grow at a
constant percent per period.
P0 = D1 /(1+R) + D2 /(1+R)2 + D3 /(1+R)3 +
…
P0 = D0(1+g)/(1+R) + D0(1+g)2/(1+R)2 +
D0(1+g)3/(1+R)3 + …
• With a little algebra, this reduces to:
D 0 (1 g) D1
P0
R-g R-g
8
1-9 7-9
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?
• P0 = .50(1+.02) / (.15 - .02) = $3.92
9
7-10
1-10
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?
P0 = 2 / (.2 - .05) = $13.33
Why isn’t the $2 in the numerator
multiplied by (1.05) in this example?
10
Nonconstant Growth Problem 7-11
1-11
Statement
• 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.
11
7-12
1-12
Nonconstant Growth – Example
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
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
12
7-13
1-13
Using the DGM to Find R
• Start with the DGM:
D 0 (1 g) D1
P0
R-g R-g
rearrange and solve for R
D 0 (1 g) D1
R g g
P0 P0
13
7-14
1-14
Finding the Required Return -
Example
• Suppose a firm’s stock is selling for
$10.50. It just paid a $1 dividend and
dividends are expected to grow at 5% per
year. What is the required return?
R = [$1(1.05)/$10.50] + .05 = 15%
• What is the dividend yield?
$1(1.05) / $10.50 = 10%
• What is the capital gains yield?
g =5%
14
7-15
1-15
Table 7.1
15
7-16
1-16
Features of Common Stock
• Voting Rights
• Proxy voting
• Classes of stock
• Other Rights
– Share proportionally in declared dividends
– Share proportionally in remaining assets
during liquidation
– Preemptive right – first shot at new stock
issue to maintain proportional ownership if
desired
16
7-17
1-17
Dividend Characteristics
• Dividends are not a liability of the firm until a
dividend has been declared by the Board
• Consequently, a firm cannot go bankrupt for
not declaring dividends
• Dividends and Taxes
– Dividend payments are not considered a
business expense; therefore, they are not tax-
deductible
– Dividends received by individuals have
historically been taxed as ordinary income
– Dividends received by corporations have a
minimum 70% exclusion from taxable income
17
7-18
1-18
Features of Preferred Stock
• Dividends
– Stated dividend that must be paid before
dividends can be paid to common
stockholders
– Dividends are not a liability of the firm and
preferred dividends can be deferred
indefinitely
– Most preferred dividends are cumulative –
any missed preferred dividends have to be
paid before common dividends can be paid
• Preferred stock does not generally
carry voting rights
18
7-19
1-19
Stock Market
• Dealers vs. Brokers
• New York Stock Exchange (NYSE)
– Members
– Operations
– Floor activity
• NASDAQ
– Not a physical exchange, but a computer-
based quotation system
– Large portion of technology stocks
19
