Valuing Common Stocks
Expected Return - The percentage yield that an
investor forecasts from a specific investment over
a set period of time. Sometimes called the market
capitalization rate.
Div1  P1  P0
Expected Return  r 
P0
Valuing Common Stocks
Example: If Fledgling Electronics is selling for $100
per share today and is expected to sell for $110
one year from now, what is the expected return if
the dividend one year from now is forecasted to be
$5.00?
5  110  100
Expected Return 
 .15
100
Valuing Common Stocks
Another Example: You purchase an ownership
share in the Indianapolis Colts for $50,000, who
just won the Super Bowl. In one year you expect
the Colts to repeat as Super Bowl champions
and pay you a dividend of $3,000. You think
you will be able to sell your share for $58,000 at
that time. What is your expected return?
3,000  58,000  50,000
Expected Return 
 .22
50,000
Valuing Common Stocks
Capitalization Rate can be estimated using the
perpetuity formula, given minor algebraic
manipulation.
Div1
Capitaliza tion Rate  P0 
rg
Div1
r
g
P0
Valuing Common Stocks
The formula can be broken into two parts.
Dividend Yield + Capital Appreciation
Div1 P1  P0
Expected Return  r 

P0
P0
Valuing Common Stocks
Dividend Discount Model - Computation of today’s
stock price which states that share value equals the
present value of all expected future dividends.
Div1
Div2
Div H  PH
P0 


...

1
2
H
(1  r ) (1  r )
(1  r )
H - Time horizon for your investment.
Valuing Common Stocks
Example
Current forecasts are for XYZ Company to pay
dividends of $3, $3.24, and $3.50 over the next
three years, respectively. At the end of three years
you anticipate selling your stock at a market price
of $94.48. What is the price of the stock given a
12% expected return?
Valuing Common Stocks
Example
Current forecasts are for XYZ Company to pay dividends of $3, $3.24,
and $3.50 over the next three years, respectively. At the end of three
years you anticipate selling your stock at a market price of $94.48.
What is the price of the stock given a 12% expected return?
3.00
3.24
350
.  94.48
PV 


1
2
3
(1.12) (1.12)
(1.12)
PV  $75.00
Valuing Common Stocks
Valuing Common Stocks
Return Measurements
Div1
Dividend Yield 
P0
Div1
Restated P0 
rg
Div1
r
g
P0
Return on Equity  ROE
EPS
ROE 
Book Equity Per Share
Valuing Common Stocks
If we forecast no growth, and plan to hold out
stock indefinitely, we will then value the stock as
a PERPETUITY.
Div1 EPS1
Perpetuity  P0 
or
r
r
Assumes all earnings are
paid to shareholders.
Valuing Common Stocks
Constant Growth DDM - A version of the dividend
growth model in which dividends grow at a
constant rate (Gordon Growth Model).
Valuing Common Stocks
Example
If a stock is selling for $100 in the stock market,
what might the market be assuming about the
growth in dividends?
$3.00
$100 
.12  g
g .09
Answer
The market is
assuming the dividend
will grow at 9% per
year, indefinitely.
Valuing Common Stocks
If a firm elects to pay a lower dividend, and
reinvest the funds, the stock price may increase
because future dividends may be higher.
Payout Ratio - Fraction of earnings paid out as
dividends
Plowback Ratio - Fraction of earnings retained by
the firm.
Valuing Common Stocks
Growth can be derived from applying the
return on equity to the percentage of
earnings plowed back into operations.
g = return on equity X plowback ratio
Valuing Common Stocks
Example
Our company forecasts to pay a $8.33
dividend next year, which represents
100% of its earnings. This will
provide investors with a 15% expected
return. Instead, we decide to plow
back 40% of the earnings at the firm’s
current return on equity of 25%.
What is the value of the stock before
and after the plowback decision?
Valuing Common Stocks
Example
Our company forecasts to pay a $8.33 dividend next year, which
represents 100% of its earnings. This will provide investors with a
15% expected return. Instead, we decide to plow back 40% of the
earnings at the firm’s current return on equity of 25%. What is the
value of the stock before and after the plowback decision?
No Growth
8.33
P0 
 $55.56
.15
With Growth
g  .25  .40  .10
5.00
P0 
 $100.00
.15  .10
Valuing Common Stocks
Example - continued
If the company did not plowback some earnings, the stock
price would remain at $55.56. With the plowback, the
price rose to $100.00.
The difference between these two numbers is called the
Present Value of Growth Opportunities (PVGO).
PVGO  100.00  55.56  $44.44
Valuing Common Stocks
Present Value of Growth Opportunities
(PVGO) - Net present value of a firm’s
future investments.
Sustainable Growth Rate - Steady rate at
which a firm can grow: plowback ratio X
return on equity.
Valuing a Business
Valuing a Business or Project
The value of a business or Project is usually
computed as the discounted value of FCF out to a
valuation horizon (H).
The valuation horizon is sometimes called the
terminal value and is calculated like PVGO.
FCF1
FCF2
FCFH
PVH
PV 

 ... 

1
2
H
H
(1  r ) (1  r )
(1  r )
(1  r )
Valuing a Business
Valuing a Business or Project
FCF1
FCF2
FCFH
PVH
PV 

 ... 

1
2
H
(1  r ) (1  r )
(1  r )
(1  r ) H
PV (free cash flows)
PV (horizon value)
Valuing a Business
Example
Given the cash flows for Concatenator Manufacturing Division,
calculate the PV of near term cash flows, PV (horizon value), and the
total value of the firm. r=10% and g= 6%
Year
1
2
3
4
5
6
7
8
9
10
10.00
12.00
14.40
17.28
20.74
23.43
26.47
28.05
29.73
31.51
Earnings
1.20
1.44
1.73
2.07
2.49
2.81
3.18
3.36
3.57
3.78
Investment
2.00
2.40
2.88
3.46
2.69
3.04
1.59
1.68
1.78
1.89
Free Cash Flow
- .80
- .96
- 1.15
- 1.39
- .20
- .23
1.59
1.68
1.79
1.89
20
20
20
20
20
13
13
6
6
6
Asset Value
.EPS growth (%)
Valuing a Business
Example - continued
Given the cash flows for Concatenator Manufacturing Division,
calculate the PV of near term cash flows, PV (horizon value), and the
total value of the firm. r=10% and g= 6%
1  1.59 
PV(horizon value) 
  22.4
6 
1.1  .10  .06 
.80 .96
1.15 1.39
.20
.23
PV(FCF)  




2
3
4
5
1.1 1.1 1.1 1.1 1.1 1.16
 3.6
Valuing a Business
Example - continued
Given the cash flows for Concatenator Manufacturing Division,
calculate the PV of near term cash flows, PV (horizon value), and the
total value of the firm. r=10% and g= 6%
PV(busines s)  PV(FCF)  PV(horizon value)
 -3.6  22.4
 $18.8
Payout Policy
Topics Covered
How Companies Pay Cash to Shareholders
Dividend Payments
Stock Repurchases
How Do Companies Decide on The Payout?
Why Payout Policy Should Not Matter
Why Dividends May Increase Firm Value
Why Dividends May Reduce Firm Value
Dividend Payments
Cash Dividend - Payment of cash by the firm
to its shareholders.
Ex-Dividend Date - Date that determines
whether a stockholder is entitled to a dividend
payment; anyone holding stock before this
date is entitled to a dividend.
Record Date - Person who owns stock on this
date received the dividend.
Dividend Payments
Stock Dividend - Distribution of additional
shares to a firm’s stockholders.
Stock Splits - Issue of additional shares to
firm’s stockholders.
Stock Repurchase - Firm buys back stock
from its shareholders.
Dividend & Stock Repurchases
U.S. Data 1980 - 2003
700
600
Repurchases
Dividends
400
300
200
100
0
-100
19
80
19
81
19
82
19
83
19
84
19
85
19
86
19
87
19
88
19
89
19
90
19
91
19
92
19
93
19
94
19
95
19
96
19
97
19
98
19
99
20
00
20
01
20
02
20
03
$ Billions
500
Earnings less repurchases & dividends
Dividend Payments
Jan 13
Feb 2
Declaration
date
Withdividend
date
Feb 3
Ex-dividend
date
Share
price
falls
Feb 4
Record
date
Feb 28
Payment
date
Dividend Payments
Stock Dividend
Example - Amoeba Products has 2 million shares
currently outstanding at a price of $15 per share.
The company declares a 50% stock dividend. How
many shares will be outstanding after the dividend
is paid?
Answer
2 mil x .50 = 1 mil + 2 mil = 3 mil shares
Stock Repurchase
Example - Cash dividend versus share repurchase
Assets
Liabilities & Equity
A. Original balance sheet
Cash
Other assets
$150,000
850,000
Value of Firm 1,000,000
Debt
Equity
0
1,000,000
Value of Firm 1,000,000
Shares outstanding = 100,000
Price per share = $1,000,000 / 100,000 = $10
Stock Repurchase
Example - Cash dividend versus share repurchase
Assets
Liabilities & Equity
B. After cash dividend
Cash
$50,000
Debt
Other assets
850,000
Equity
Value of Firm 900,000
0
900,000
Value of Firm 900,000
Shares outstanding = 100,000
Price per share = $900,000 / 100,000 = $9
Stock Repurchase
Example - Cash dividend versus share repurchase
Assets
Liabilities & Equity
C. After stock repurchase
Cash
$50,000
Debt
Other assets
850,000
Equity
Value of Firm 900,000
0
900,000
Value of Firm 900,000
Shares outstanding = 90,000
Price per share = $900,000 / 90,000 = $10
The Dividend Decision
Lintner’s “Stylized Facts”
(How Dividends are Determined)
1. Firms have longer term target dividend payout
ratios.
2. Managers focus more on dividend changes than on
absolute levels.
3. Dividends changes follow shifts in long-run,
sustainable levels of earnings rather than short-run
changes in earnings.
4. Managers are reluctant to make dividend changes
that might have to be reversed.
Dividend Policy is Irrelevant
Since investors do not need dividends to
convert shares to cash they will not pay
higher prices for firms with higher dividend
payouts. In other words, dividend policy
will have no impact on the value of the firm.
Dividend Policy is Irrelevant
Example - Assume Rational Demiconductor has no extra cash, but declares a
$1,000 dividend. They also require $1,000 for current investment needs.
Using M&M Theory, and given the following balance sheet information,
show how the value of the firm is not altered when new shares are issued
to pay for the dividend.
Record Date
Cash
1,000
Asset Value 9,000
Total Value 10,000 +
New Proj NPV
2,000
# of Shares
1,000
price/share
$12
Dividend Policy is Irrelevant
Example - Assume Rational Demiconductor has no extra cash, but declares a
$1,000 dividend. They also require $1,000 for current investment needs.
Using M&M Theory, and given the following balance sheet information,
show how the value of the firm is not altered when new shares are issued
to pay for the dividend.
Record Date
Cash
1,000
Asset Value 9,000
Total Value 10,000 +
New Proj NPV
2,000
# of Shares
1,000
price/share
$12
Pmt Date
0
9,000
9,000
2,000
1,000
$11
Dividend Policy is Irrelevant
Example - Assume Rational Demiconductor has no extra cash, but declares a
$1,000 dividend. They also require $1,000 for current investment needs.
Using M&M Theory, and given the following balance sheet information,
show how the value of the firm is not altered when new shares are issued
to pay for the dividend.
Record Date
Cash
1,000
Asset Value 9,000
Total Value 10,000 +
New Proj NPV
2,000
# of Shares
1,000
price/share
$12
Pmt Date
0
9,000
9,000
2,000
1,000
$11
Post Pmt
1,000 (91 sh @ $11)
9,000
10,000
2,000
1,091
$11
NEW SHARES ARE ISSUED
Dividend Policy is Irrelevant
Example - continued - Shareholder Value
Stock
Cash
Record
12,000
0
Total Value
12,000
Stock = 1,000 sh @ $12 = 12,000
Dividend Policy is Irrelevant
Example - continued - Shareholder Value
Stock
Cash
Record
12,000
0
Pmt
11,000
1,000
Total Value
12,000
12,000
Stock = 1,000sh @ $11 = 11,000
Dividend Policy is Irrelevant
Example - continued - Shareholder Value
Stock
Cash
Record
12,000
0
Pmt
11,000
1,000
Post
12,000
0
Total Value
12,000
12,000
12,000
Stock = 1,091sh @ $115 = 12,000
 Assume stockholders purchase the new issue with the cash
dividend proceeds.
Dividends Increase Value
Market Imperfections and Clientele Effect
There are natural clients for high-payout stocks,
but it does not follow that any particular firm can
benefit by increasing its dividends. The high
dividend clientele already have plenty of high
dividend stock to choose from.
These clients increase the price of the stock
through their demand for a dividend paying stock.
Dividends Increase Value
Dividends as Signals
Dividend increases send good news about cash
flows and earnings. Dividend cuts send bad news.
Because a high dividend payout policy will be
costly to firms that do not have the cash flow to
support it, dividend increases signal a company’s
good fortune and its manager’s confidence in
future cash flows.
Dividends Decrease Value
Tax Consequences
Companies can convert dividends into capital
gains by shifting their dividend policies. If
dividends are taxed more heavily than capital
gains, taxpaying investors should welcome such a
move and value the firm more favorably.
In such a tax environment, the total cash flow
retained by the firm and/or held by shareholders
will be higher than if dividends are paid.
Dividends Decrease Value
Firm A
Firm B
Next years price
$112.50
$102.50
Dividend
Total pretax payoff
$0
$112.50
$10.00
$112.50
Todays stock price
Capital gain
$100
$12.50
$97.78
$4.72
Pretax rate of return (%)
12.5
100
= 12.5%
Tax on dividend @ 40%
$0
Tax on capital gain @ 20% .20 x $12.50 = $2.50
Total after tax income
(0 + 12.50) - 2.50
(dividend plus capital
= $10.00
gains less taxes)
10
Aftertax rate of return (%)
100 =.10 = 10%
14.72
97.78
= 15.05%
.40 x $10 = $4.00
.20 x $4.72 = $.94
(10.00 + 4.72)
- (4.00-.94)
= $9.78
9.78
97.78 =.10 = 10%