Transcript Chapter 1

Chapter 7
Stocks and
Stock Valuation
Learning Objectives
1. Explain the basic characteristics of common
stock.
2. Define the primary market and the secondary
market.
3. Calculate the value of a stock given a history of
dividend payments.
4. Explain the shortcomings of the dividend pricing
models.
5. Calculate the price of preferred stock.
6. Understand the concept of efficient markets.
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7.1 Characteristics of Common
Stock
• Major financing vehicle for corporations
• Provides holders with an opportunity to
share in the future cash flows of the issuer.
• Holders have ownership in the company.
• Unlike bonds, no maturity date and
variable periodic income.
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7.1 (A) Ownership
• Share in the residual profits of the company.
• Claim to all its assets and cash flow once
the creditors, employees, suppliers, and
taxes are paid off.
• Voting rights
– participate in the management of the company
– elect the board of directors which selects the
management team that runs the company’s dayto-day operations.
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7.1 (B) Claim on Assets and
Cash Flow (Residual Claim)
• In case of liquidation…
Shareholders have a claim on the residual assets
and cash flow of the company.
Known as “residual” rights.
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7.1 (C) Vote (Voice in
Management)
• Standard voting rights: Typically, one vote
per share provided to shareholders to vote
in board elections and other key changes to
the charter and bylaws.
• Can be altered by issuing several classes of
stock.
– Non-voting stock, which is usually for a
temporary period of time,
– Super voting rights, which provide the holders
with multiple votes per share, increasing their
influence and control over the company.
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7.1 (D) No Maturity Date
• Considered to be permanent financing
• Infinite life, i.e. no maturity date
• No promised date when investment is
returned.
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7.1 (E) Dividends and Their Tax
Effect
• Companies pay cash dividends periodically (usually every
quarter) to their shareholders out of net income.
• Unlike coupon interest paid on bonds, dividends cannot be
treated as a tax-deductible expense by the company.
• For the recipient, however, dividends are considered to be
taxable income.
• More material on dividends and dividend policy is covered in
Chapter 17.
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7.1 (F) Authorized, Issued, and
Outstanding Shares
Authorized shares: maximum number of shares
that the company may sell,
as per charter.
Issued shares:
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the number of shares that
has already been sold by the
company and are either
currently available for public
trading (outstanding shares)
or held by the company for
future uses such as
rewarding employees
(treasury stock).
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7.1 (G) Treasury Stock
• Non-dividend paying, non-voting shares
being held by the issuing firm right from the
time they were first issued
OR
• Shares that have been later repurchased by
the issuing firm in the market.
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7.1 (H) Preemptive Rights
• Privileges that allow current shareholders to
buy a fixed percentage of all future issues
before they are offered to the general
public.
• Enables current common stockholders to
maintain their proportional ownership in the
company.
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7.2 Stock Markets
Stocks are traded in two types of markets;
1. the primary or “first sale” market, and the
2. secondary or “after-sale” market,
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7.2 (A) Primary Markets
First issue market where issuing
firm is involved.
• Initial public offering (IPO):
• Prospectus:
• Due diligence:
• Firm commitment:
• Best efforts:
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7.2 (B) Secondary Markets:
How Stocks Trade
• Forum where common stock can be traded among
investors themselves.
• Provides liquidity and variety.
• In the United States, 3 well-known secondary stock
markets:
• NYSE
• AMEX
• NASDAQ
Specialist
Ask price
Bid price
Bid-ask spread
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7.2 (C) Bull Markets and Bear
Markets
• A Bull market: prolonged rising stock
market, coined on the analogy that a bull
attacks with his horns from the bottom up.
• A Bear market: prolonged declining market,
based on the analogy that a bear swipes
with his paws from the top down.
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7.3 Stock Valuation
• Value of a share of stock the present
value of its expected future cash flow…
– Cash dividends paid (if any).
– Future selling price of the stock.
– The discount rate i.e. risk-appropriate rate of
return to be earned on the investment.
• No guaranteed cash flow information.
• No maturity date.
• Valuation is more of an “art” than a science.
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7.3 Stock Valuation (continued)
Table 7.1 Differences between Bonds and
Stocks
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7.3 Stock Valuation (continued)
Example 1: Stock price with known
dividends and sale price.
Agnes wants to purchase common stock of New
Frontier Inc. and hold it for 3 years. The
directors of the company just announced that
they expect to pay an annual cash dividend of
$4.00 per share for the next 5 years. Agnes
believes that she will be able to sell the stock
for $40 at the end of three years. In order to
earn 12% on this investment, how much should
Agnes pay for this stock?
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7.3 Stock Valuation (continued)
Example 1 Answer
Price =
1

 1
n
1

1 r 

Future Price 
n  Dividend Stream 
r
1 r 


Price =
1

1


4
1


1 0.12
$40.00 
 $4.00  
4
0.12
1 0.12
















Price = $40.00 x 0.635518 + $4.00 x 3.03734
Price = $25.42 + $12.149 = $37.57
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7.3 Stock Valuation (continued)
Example 1 Answer (continued)
Method 2. Using a financial calculator
Mode:
P/Y=1; C/Y = 1
Input: N
Key:
4
Output
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I/Y
12
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PV
PMT
?
4
-37.57
FV
40
7.3 Stock Valuation (continued)
4 variations of a dividend pricing model have
been used to value common stock
1. The constant dividend model with an infinite
horizon
2. The constant dividend model with a finite
horizon
3. The constant growth dividend model with a
finite horizon
4. The constant growth dividend model with an
infinite horizon
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7.3 (A) The Constant Dividend
Model with an Infinite Horizon
Assumes that the firm is paying the same dividend
amount in perpetuity.
i.e. Div1 = Div2 = Div3 = Div4 = Div5 = Div∞
For perpetuities,
PV = PMT/r
where r the required rate and PMT is the cash flow.
Thus, for a stock that is expected to pay the same
dividend forever,
Price = Dividend/Required rate of return
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7.3 (A) The Constant Dividend Model
with an Infinite Horizon (continued)
Example 2. Quarterly dividends forever
Let’s say that the Peak Growth Company is paying a
quarterly dividend of $0.50 and has decided to pay the
same amount forever. If Joe wants to earn an annual
rate of return of 12% on this investment, how much
should he offer to buy the stock at?
Answer
Quarterly dividend = $0.50
Quarterly rate of return = Annual rate/4= 12%/4 = 3%
PV = Quarterly dividend/Quarterly rate of return
Price = 0.50/.03 = $16.67
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7.3 (B) The Constant Dividend
Model with a Finite Horizon
• Assumes that the stock is held for a finite period of time
and then sold to another investor.
• Constant dividends received over the investment
horizon.
• Price estimated as the sum of the present value of an
annuity (constant dividend) and that of a single sum
(the selling price).
• Similar to a typical non-zero coupon, corporate bond.
• Have to estimate the future selling price, since that is
not a given value, unlike the par value of a bond
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7.3 (B) The Constant Dividend Model
with a Finite Horizon (continued)
Example 3. Constant dividends with finite
holding period.
Let’s say that the Peak Growth Company is
paying an annual dividend of $2.00 and has
decided to pay the same amount forever.
Joe wants to earn an annual rate of return of
12% on this investment, and plans to hold the
stock for 5 years, with the expectation of selling
it for $20 at the end of 5 years.
How much should he offer to buy the stock at?
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7.3 (B) The Constant Dividend Model
with a Finite Horizon (continued)
Example 3 Answer
Annual dividend = $2.00 = PMT
Selling Price = $20 = FV
Annual rate of return = 12%
PV = PV of dividend stream over 5 years + PV of Year 5
price
Mode: P/Y=1; C/Y = 1
Input:
N
I/Y
PV PMT
Key:
5
12
?
2
Output
-18.56
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FV
20
7.3 (C) The Constant Growth Dividend
Model with an Infinite Horizon
Known as the Gordon model (after its
developer, Myron Gordon).
Estimate is based on the discounted value of
an infinite stream of future dividends that
grow at a constant rate, g.
1
2
3

Div  1 g Div 1 g
Div 1 g
Div 1 g
0
0
0
0
Price 




0
1
2
3


1

r
1 r 
1 r 
1 r 
where r is the required rate of return
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7.3 (C) The Constant Growth Dividend
Model with an Infinite Horizon (cont’d)
• With some algebra, this can be simplified
to….
Div  1 g
0
Price 
r  g
0
• And since Div0 x (1+g) = Div1
Div
1
Price 
0 r  g
• Or more generally Pn = Divn+1/(r-g)
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7.3 (C) The Constant Growth Dividend
Model with an Infinite Horizon (cont’d)
Example 4: Constant growth rate, infinite
horizon (with growth rate given).
Let’s say that the Peak Growth Company just paid
its shareholders an annual dividend of $2.00 and
has announced that the dividends would grow at an
annual rate of 8% forever. If investors expect to
earn an annual rate of return of 12% on this
investment how much would they offer to buy the
stock for?
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7.3 (C) The Constant Growth Dividend
Model with an Infinite Horizon (cont’d)
Example 4 Answer
Div0 = $2.00; g=8%; r=12%
Div1=Div0*(1+g)
Div1=$2.00*(1.08)Div1=$2.16
P0 = Div1/(r-g)$2.16/(.12 - .08)$54
Price0 = $54
Note: r and g must be in decimals.
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7.3 (C) The Constant Growth Dividend
Model with an Infinite Horizon (cont’d)
EXAMPLE 5: Constant growth rate, infinite
horizon (with growth rate estimated from past
history).
Let’s say that you are considering an investment in
the common stock of QuickFix Enterprises and are
convinced that its last paid dividend of $1.25 will
grow at its historical average growth rate from here
on. Using the past 10 years of dividend history and
a required rate of return of 14%, calculate the price
of QuickFix’s common stock.
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7.3 (C) The Constant Growth Dividend
Model with an Infinite Horizon (cont’d)
QuickFix Enterprises’ Annual Dividends
1999 2000 2001 2002 2003 2004 2005 2006 2007 2008
$0.50 $0.55 $0.61 $0.67 $0.73 $0.81 $0.89 $0.98 $1.08 $1.25
Required rate of return = 14%
Compound growth rate “g” = (FV/PV)1/n -1
Where FV = $1.25; PV = 0.50; n = 9
g = (1.25/0.50)1/9 – 1 10.72%
Div1 = Div0(1+g)$1.25*(1.1072)$1.384
P0 = Div1/(r-g)  $1.384/(.14-.1072)$42.19
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7.3 (D) The Constant Growth
Dividend Model with a Finite Horizon
Investor expects to hold a stock for a limited number of years,
Company’s dividends are growing at a constant rate.
Following formula is used to value the stock…
Div  1 g   1 g n 
0
 +
Price 
 1 

r  g
0

 1 r  
Price n
1 r n

 as the Gordon model, if it is
Note: This formula would lead to the same
price estimate
assumed that the growth rate of dividends and the required rate of return of the next owner,
(after n years) remain the same.
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7.3 (D) The Constant Growth Dividend
Model with a Finite Horizon (continued)
Example 6:Constant growth, finite horizon.
The QuickFix Company just paid a dividend of
$1.25 and analysts expect the dividend to grow at
its compound average growth rate of 10.72%
forever.
If you plan on holding the stock for just 7 years,
and you have an expected rate of return of 14%,
how much would you pay for the stock?
Assume that the next owner also expects to earn
14% on his or her investment.
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7.3 (D) The Constant Growth Dividend
Model with a Finite Horizon (continued)
Example 6 Answer
We can solve this in 2 ways.
Method 1: Use the constant growth, finite
horizon formula
Method 2: Use the Gordon Model since g is
constant forever, and both investors have
the same required rates of return
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7.3 (D) The Constant Growth Dividend
Model with a Finite Horizon (continued)
Example 6 Answer (continued)
Method 1 Use the following equation:
Div  1 g   1 g n 
0
  + Pricen
Price 
 1 

0
r  g
1

r


 

 1 r n
Price in year 7 = Div8/(r-g)
Div0 = $1.25; g =10.72%; r=14%;  Div8 = D0(1+g)8
Div81.25*(1.1072)8 = 2.25844
P7=2.25844/(.14-.1072)$86.07
7
1.25  1.1072   1.1072  86.07
Price0 
 1 
 +

.14  .1072   1.14   1.147
 = $42.195 *0.184829 + 34.40 = $42.19
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7.3 (D) The Constant Growth Dividend
Model with a Finite Horizon (continued)
Example 6 Answer (continued)
Method 2: Use the Gordon Model
P0 = D0(1+g)/(r-g)
P0 = $1.25*(1.1072)/(.14-.1072)
P0 = $42.19
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7.3 (E) Non-constant Growth
Dividends
• The above 4 models work if a firm is either
expected to pay a constant dividend amount
indefinitely, or is expected to have its dividends
grow at a constant rate for long periods of time.
• For most firms, the dividend growth patterns of
most firms tend to be variable, making the
valuation process complicated.
• However, if we can assume that at some point in
the future, the dividend growth rate will become
constant, we can use a combination of the Gordon
Model and present value equations to calculate the
price of the stock.
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7.3 (E) Non-constant Growth
Dividends (continued)
Example 7: Non-constant dividend pattern
The Rapid Growth Company is expected to pay a
dividend of $1.00 at the end of this year.
Thereafter, the dividends are expected to grow at
the rate of 25% per year for 2 years, and then drop
to 18% for 1 year, before settling at the industry
average growth rate of 10% indefinitely.
If you require a return of 16% to invest in a stock
of this risk level, how much would you be justified
in paying for this stock?
D1=$1.00; g1=25%; n1=2; g2=18%; n2=1; gc=10%;
r=16%
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7.3 (E) Non-constant Growth
Dividends (continued)
Example 7 Answer
Step 1. Calculate the annual dividends expected
in Years 1-4, using the appropriate growth rates.
D1=$1.00; D2=$1.00*(1.25)=$1.25;
D3=$1.25*(1.25) = $1.56; D4=$1.56*(1.18) = $1.84;
Step 2. Calculate the price at the start of the constant
growth phase using the Gordon model.
P4 = D4*(1+g)/(r-g) = $1.84*(1.10)/(.16-.10)
= $2.02/.06 = $33.73
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7.3 (E) Non-constant Growth
Dividends (continued)
Example 7 Answer (continued)
Step 3. Discount the annual dividends in Years 1-4 and the Price
at the end of Year 4, back to Year 0 using the required rate of
return as the discount rate, and add them up to solve for the
current price.
P0 = $1.00/(1.16) +
1.25/(1.16)2+$1.56/(1.16)3+$1.84/(1.16)4+$33.73/(1.16)4
P0 = $$0.862+0.928+$.999+$1.016+$18.63 = $22.44
Note: This uneven cash flow stream can also be discounted by
using the NPV function of the financial calculator….
CF0=0;CF1=1.00;CF2=1.25;CF3=1.56;CF4=1.84+33.73;I=16%;
NPV=$22.44
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7.4 Dividend Model
Shortcomings
• Need future cash flow estimates and a required rate of return,
therefore difficult to apply universally.
– Erratic dividend patterns,
– Long periods of no dividends,
– Declining dividend trends
• Need a pricing model that is more inclusive than the dividend
model, one that can estimate expected returns for stocks
without the need for a stable dividend history.
• The capital asset pricing model (CAPM), or the security market
line (SML), which will be covered in Chapter 8, is one option.
• SML can be used to estimate expected returns for companies
based on their risk, the premium for taking on risk, and the
reward for waiting and not on their historical dividend
patterns.
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7.5 Preferred Stock
Pays constant dividend as long as the stock is outstanding.
Typically has infinite maturity, but some are convertible into
common stock at some pre-determined ratio.
Have “preferred status” over common stockholders in the case
of dividend payments and liquidation payouts.
Dividends can be cumulative or non-cumulative
To calculate the price of preferred stock, we use the PV of a
perpetuity equation, i.e. Price0 = PMT/r
PMT = Annual dividend (dividend rate * par value); and
r = investor’s required rate of return.
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7.5 Preferred Stock (continued)
Example 8: Pricing preferred stock.
The Mid-American Utility Company’s preferred
stock pays an annual dividend of 8% per year
on its par value of $60. If you want to earn
10% on your investment how much should you
offer for this preferred stock?
Answer
Annual dividend = .08*$60 = $4.80
Price = $4.80/0.10 = $48
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7.6 Efficient Markets
Market in which security prices are current
and fair to all traders.
Transactions costs are minimal.
There are two forms of efficiency:
1.
2.
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Operational efficiency and
Informational efficiency.
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7.6 (A) Operational Efficiency
• Speed and accuracy with which trades are
processed.
• Ease with which the investing public can
access the best available prices.
– The NYSE’s SuperDOT computer system,
– NASDAQ’s SOES
• Match buyers and sellers very efficiently and
at the best available price.
• Therefore definitely very operationally
efficient markets.
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7.6 (B) Informational Efficiency
• Speed and accuracy with which information is
reflected in the available prices for trading.
• Securities would always trade at their fair or
equilibrium value.
– Diverse information -- financial economists have
come up with three versions of efficient markets from
an information perspective:
– weak form,
– semi-strong form,
– strong form.
• These three forms make up what is known as
the efficient market hypothesis (EMH).
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7.6 (B) Informational Efficiency
(continued)
• Weak-form efficient markets :
– Current prices reflect past prices and trading volume.
– Technical analysis – not useful
•
Semi-strong-form efficient markets:
•
Strong-form efficient markets:
– Current prices reflect price and volume information and all
available relevant public information as well.
– Publicly available news or financial statement information not
very useful.
– Current prices reflect price and volume history of the stock,
all publicly available information, and even all private
information.
– All information is already embedded in the price--no
advantage to using insider information to routinely
outperform the market.
• Jury is still out, evidence is not conclusive!
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