Valuing Common Stocks
Fundamentals of Corporate Finance
Chapter 7 BMM
Finansiell ekonomi LiU
2012
Keep in mind
• Present value concepts can be applied to the
valuation of common stocks
• the relationship between stock price, earnings
per share EPS and growth rate g
• learn the process of estimating the cost of
equity
Learning objectives
1. Market Values, Book Values, and Liquidation
Values
2. How to value Common Stocks
3. Simplifying the Dividend Discount Model (the
discounted cash flow model)
4. Growth Stocks and Income Stocks
5. There Are No Free Lunches on Wall Street
Concepts and definitions
Primary Market - Market for the sale of new securities
by corporations.
Secondary Market - Market in which previously issued
securities are traded among investors.
Common Stock - Ownership shares in a publicly held
corporation.
Some concepts
Book Value: Net worth of the firm according to the balance
sheet.
Dividend: Periodic cash distribution from the firm to the
shareholders.
P/E Ratio: Price per share divided by earnings per share.
Earnings per share: EPS = Earnings/ number of shares
ROE:
return on equity= Earnings /Book value of equity
Note, earnings =net income= årsresultat= vinst
Going concern value
• The difference between a firm’s actual market
value and its’ liquidation value is the so called
“going concern value.”
Market value-Liquidation Value = Going
concern value
Liquidation Value
Net proceeds that could be realized by selling
the firm’s assets and paying off its creditors.
Valuation of common stocks
Single period investment case
• The (present) value of a common stock equals
the present value of dividends expected
during the period plus the present value of
the expected end-of-period price.
Div1  P1
Price  P0 
1 r
The present value of future cash flows from a stock is also called
the Intrinsic value of the stock.
The DCF model: discounted cash flow
method (Dividend Discount Model)
The value of any stock is the present value of its
future cash flows.
Dividends represent the future cash flows of the
firm.
PV(stock)  PV(expecte d future dividends)
How Common Stocks Are Valued
Expected Return r
The percentage yield that an investor forecasts from a
specific investment over a set period of time.
Div1  P1  P0
Expected Return  r 
P0
Valuing Common Stocks
For a stock with no growth, and assuming the stock
will exist indefinitely, we can value the stock as a
PERPETUITY.
Div1 EPS1
Perpetuity  P0 

r
r
No growth means all earnings are paid to shareholders.
How Common Stocks Are Valued
Example: If Blue Sky 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 
 0.15
100
How Common Stocks Are Valued
The price of any share of stock can be
thought of as the present value of the
futures cash flows. For a stock the future
cash flows are dividends and the
ultimate sales price of the stock.
Div1  P1
Price  P0 
1 r
Present value of one period return
How Common Stocks Are Valued
Example - continued: Blue Sky price can be thought
of as follows.
5  110
Price  P0 
 100
1.15
Valuing Common Stocks
Constant Growth DDM - A version of the
dividend growth model in which dividends
grow at a constant rate (Gordon Growth
Model).
Div1
P0 
rg
Given any combination of variables in the
equation, you can solve for the unknown
variable.
Example: valuing stocks
What is the value of the stock that expects to pay a
$3.00 dividend next year, and then increase the
dividend at a rate of 8% per year, indefinitely?
Assume a 12% expected return. (note: suppose that
Blue Sky invested 40% back to the company, the
dividend becomes 5*60%=3.)
Div1
$3.00
P0 

 $75.00
r  g 0.12  0.08
Estimating the Cost of Equity Capital
Dividend Growth Rate can also 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
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.
How Common Stocks Are Valued
Formula
Div1
Div2
Div H  PH
P0 

...
1
2
(1  r ) (1  r )
(1  r ) H
H
Div t
PH
P0  

t
H
(
1

r
)
(
1

r
)
t 1
How Common Stocks Are Valued
Example
Blue Sky is forecasted to pay a $5.00 dividend at the end of year one and a
$5.50 dividend at the end of year two. At the end of the second year the
stock will be sold for $121. If the discount rate is 15%, what is the price of
the stock?
5.00
5.50  121
PV 

1
2
(1  0.15) (1  0.15)
PV  $100.00
How Common Stocks Are Valued
Example
Current forecasts are for Blue Sky 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?
How Common Stocks Are Valued
Example
Current forecasts are for Blue Sky 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
3.50  94.48
PV 


1
2
3
(1  0.12) (1  0.12)
(1  0.12)
PV  $75.00
How Common Stocks Are Valued
Estimating the Cost of Equity Capital
Example – A stock was selling for $42.45 per
share at the start of 2012. Dividend payments
for the next year were expected to be $1.68 a
share. What is the dividend yield?
1.68
Dividend Yield 
42.45
 0.04
Estimating the Cost of Equity Capital
Example - continued - Northwest Natural Gas stock was selling
for $42.45 per share at the start of 2009. Dividend payments
for the next year were expected to be $1.68 a share. What is
the expected return, assuming a growth rate of 6.1%?
1.68
r
 0.061
42.45
r  0.101
Estimating the Cost of Equity Capital
Required Return Measurements
Div 1
Dividend Yield 
P0
Restated
Div1
rg
Div1
r 
g
P0
P0 
Estimating the Cost of Equity Capital
• Valuing Non-Constant Growth
Div1
Div 2
Div H
PH
PV 

 ... 

1
2
H
(1  r ) (1  r )
(1  r )
(1  r ) H
The H period has
a share value PH
it is evaluated as a
growing
perpetuity
Div H 1
PH 
rg
Estimating the Cost of Equity Capital
Example – Phoenix produces dividends in three consecutive
years of 0, 0.31, and 0.65, respectively. The dividend in year
four is estimated to be .67 and should grow in perpetuity at
4%. Given a discount rate of 10%, what is the price of the
stock?


0
0.31
0.65
1
0.67
PV 





1
2
3
3
(1  0.1) (1  0.1) (1  0.1)  (1  0.1) (0.10  0.04) 
 9.13
Note here the
discount factor is
1/(1+0,1)3
Stock Price and Earnings Per Share
• If a firm chooses 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
The payout ratio= 1-Plowback ratio
Stock Price and Earnings Per Share
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 retain
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 earnings distribution
decision?
Example
• Pay a $8.33 dividend next year, which represents 100% of its
earnings. a 15% expected return.
•
plowback 40% of the earnings at the firm’s current return
on equity of 25%.
the value of the stock with and without growth:
No Growth
8.33
P0 
 $55.56
0.15
With growth of the equity, the price of the share
worth more than before! 100-55,56=44,44
With Growth
g  0.25  0.40  0.10
P0 
5.00
 $100.00
0.15  0.10
Stock Price and Earnings Per Share
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
Remain critical! The growth rate of dividend 10% would
amount to huge payment after 10 year! Especially when it is
close to the discount rate. (r-g should be larger than 0). The
stock price will explode!
Stock Price and Earnings Per Share
Present Value of Growth Opportunities (PVGO):
Net present value of a firm’s future
investments.
div1
div1
PVGO 

rg
r
Sustainable Growth Rate is the steady rate at
which a firm can grow:
g = 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.
FCF1
FCF2
FCFH
PVH
PV 

 ... 

1
2
H
(1  r ) (1  r )
(1  r )
(1  r ) H
Valuing a Business
Valuing a Business or Project
FCF1
FCF2
FCFH
PVH
PV 

 ... 

1
2
H
H
(1  r ) (1  r )
(1  r )
(1  r )
PV (free cash flows)
PV (horizon value)
Sustainable growth
• Long-term growth rate in dividends is a function
of Plowback ratio and return on equity.
• Growth rate of equity=g
• ROE= Earning/equity= (1+g)Earnings/(1+g)equity
The second year will have (1+g) Earnings to
distribute to shareholders. Keep the payout ratio
constant, we will have an dividend growth (1+g).
No Free Lunches
Technical Analysts
Investors
who attempt to identify undervalued
stocks by searching for patterns in past stock
prices.
Forecast stock prices based on the watching the
fluctuations in historical prices (thus “wiggle
watchers”)
No Free Lunches
Scatter Plot of NYSE Composite Index over two successive weeks.
Where’s the pattern?
Random Walk Theory
• Security prices change randomly, with no
predictable trends or patterns.
• Statistically speaking, the movement of stock
prices is random (skewed positive over the long term).
Random Walk Theory
Coin Toss Game
Heads
Heads
$106.09
$103.00
Tails
$100.43
$100.00
Heads
Tails
$100.43
$97.50
Tails
$95.06
Random Walk Theory
S&P 500 Five Year Trend?
or
5 yrs of the Coin Toss Game?
Level
180
130
80
Month
Random Walk Theory
Level
230
S&P 500 Five Year Trend?
or
5 yrs of the Coin Toss Game?
180
130
80
Month
Random Walk Theory
Market
Index
1,300
1,200
1,100
Cycles
disappear
once
identified
Last
Month
This
Month
Next
Month
Another Tool
Fundamental Analysts
Investors
who attempt to find mispriced
securities by analyzing fundamental information,
such as accounting data and business prospects.
Research the value of stocks using NPV and other
measurements of cash flow
Efficient Market Theory
Efficient Market - Market in which prices reflect all
available information.
• Weak Form Efficiency
– Market prices reflect all historical information
• Semi-Strong Form Efficiency
– Market prices reflect all publicly available information
• Strong Form Efficiency
– Market prices reflect all information, both public and
private
Efficient Market Theory
Cumulative Abnormal Return
(%)
Announcement Date
39
34
29
24
19
14
9
4
-1
-6
-11
-16
Days Relative to annoncement date
Market Anomalies
Existing Anomalies
•The Earnings Announcement Puzzle
•The New-Issue Puzzle
Old Anomalies
•The Small Firm Effect
•The January Effect
•The PE Effect
•The Neglected Firm Effect
•The Value Line Effect
Behavioral Finance
• Attitudes towards risk
• Beliefs about probabilities
Thank you!
Problems?
yinghong.chen@liu.se