Corporate Finance
Lecture Seven - Stock 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.
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.
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.
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.
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.
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.
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.
7.1 (F) Authorized, Issued, and
Outstanding Shares
Authorized shares: maximum number of shares that the
company may sell, as per charter.
Issued shares:
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).
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.
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.
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,
7.2 (A) Primary Markets
First issue market where issuing
firm is involved.
• Initial public offering (IPO):
• Prospectus:
• Due diligence:
• Firm commitment:
• Best efforts:
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
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.
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.
7.3 Stock Valuation (continued)
Table 7.1 Differences between Bonds and Stocks
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?
7.3 Stock Valuation (continued)
Example 1 Answer
Price =
1

 1
n
1


1

r

Future Price 

Dividend
Stream


r
1 r n


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
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
I/Y
12
PV PMT
?
4 40
-37.57
FV
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
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
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
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
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?
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:
Input:
Key:
Output
P/Y=1; C/Y = 1
N
I/Y
5
12
?
PV PMT
2
20
-18.56
FV
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
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)
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?
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.
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.
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
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  


Pricen
1 r n
Note: This formula would lead to the same price estimate as the Gordon model, if it is assumed that the
growth rate of dividends and the required rate of return of the next owner, (after n years) remain the
same.
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.
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
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
Price 
0
r  g
 1 




 1 r 
 + Pricen

n

1 r


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
Price 0 
 1 
 +

.14  .1072   1.14   1.147
 = $42.195 *0.184829 + 34.40 = $42.19
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
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.
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%
7.3 (E) Non-constant Growth
Dividends (continued)
Example 7 Answer
Step 1. Calculate the annual dividends expected
using the appropriate growth rates.
in Years 1-4,
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
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
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.
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.
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
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.
Operational efficiency and
Informational efficiency.
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.
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).
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:
– 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.
• Strong-form efficient markets:
– 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!
Additional Problems with Answers
Problem 1
Pricing constant growth stock, with finite horizon: The
Crescent Corporation just paid a dividend of $2.00 per share
and is expected to continue paying the same amount each
year for the next 4 years.
If you have a required rate of return of 13%, plan to hold the
stock for 4 years, and are confident that it will sell for $30 at
the end of 4 years,
How much should you offer to buy it at today?
Additional Problems with Answers
Problem 1 (Answer)
In this case, we have an annuity of $2 for 4 periods, followed
by a lump sum of $30, to be discounted at 13% for the
respective number of years.
Using a financial calculator
Mode:
P/Y=1; C/Y = 1
Input:
Key: 4
Output
N
13
I/Y
?
PV
PMT
2
30
-24.35
FV
Additional Problems with Answers
Problem 2
Constant growth rate, infinite horizon (with
growth rate estimated from past history:
Using the historical dividend information
provided below to calculate the constant
growth rate, and a required rate of return of
18%, estimate the price of Nigel Enterprises’
common
stock.
1999 2000 2001 2002 2003 2004 2005 2006 2007 2008
$0.35 $0.45 $0.51 $0.65 $0.75 $0.88 $0.99 $1.10 $1.13 $1.30
Additional Problems with Answers
Problem 2 (Answer)
First, estimate the historical average growth
rate of dividends by using the following
equation:
g = [(FV/PV)1/n – 1]
Where FV = Div2008 = $1.30
PV = Div1999 = $0.35
n = number of years in between =9
g = [(1.30/0.35)1/9 – 1]
 15.7%
Additional Problems with Answers
Problem 2 (Answer) (continued)
Next, use the constant growth, infinite horizon model to
calculate price:
i.e. Price0 = Div0(1+g)/(r-g)
Div0 = Div2008= $1.30;
Div1= Div0*(1+g) =$1.30*(1.157)$1.504;
r = 18%; g = 15.7% (as calculated above)
Price0 = $1.504/(.18-.157)
Price0 = $65.40
Additional Problems with Answers
Problem 3
Pricing common stock with multiple dividend patterns: The
Wonder Products Company is expanding fast and therefore will
not pay any dividends for the next 3 years.
After that, starting at the end of year 4, it will pay a dividend of
$0.75 per share to its common shareholders and increase it by
12% each year until it pays $1.50 at the end of year 10.
After that it will pay $1.50 per year forever. If an investor wants
to earn 15% per year on this investment, how much should he
pay for the stock?
Additional Problems with Answers
Problem 3 (Answer)
First lay out the dividends on a time line.
Expected Dividend Stream of The Wonder Products Co.
T0
T1
T2
T3
T4
T5
T6
T7
T8
T9
T10
…
T∞
--- $0.00 $0.00 $0.00 $0.75 $0.84 $0.94 $1.05 $1.18 $1.32 $1.50 …$1.50
Note: There are 3 distinct dividend payment
patterns Years 1-3, no dividends; Years 4-10,
dividends grow at 12%; Years 11 onwards, zerogrowth in dividends.
Additional Problems with Answers
Problem 3 (Answer) (continued)
Next, Calculate the price at the end of Year 10, i.e. when
the dividend growth rate is zero.
Price10 = Div11/r = 1.50/.15 = $10;
Using the NPV function and the annual cash flows
calculate the price;
NPV(15,0,{0.00,0.00,0.00,0.75,0.84,0.94,1.05,1.18,1.32,1
.50+10.00} $5.25
Price = $5.25
Additional Problems with Answers Problem 4
Pricing non-constant growth common stock: The WedLink
Corporation just paid a dividend of $1.25 to its common
shareholders.
It announced that it expects the dividends to grow by 25% per year
for the next 3 years.
Then drop to a growth rate of 16% for an additional 2 years.
Finally the dividends will converge to the industry median growth
rate of 8% per year.
If investors are expecting 12% per year on WedLink’s stock,
calculate the current stock price.
Additional Problems with Answers
Problem 4 (Answer)
Determine the dividend per share in Years 1-5 using the
stated annual growth rates:
D1=$1.25*(1.25)=$1.56;
D2=$1.56*(1.25)=$1.95;
D3=1.95*(1.25)=$2.44;
D4=$2.44*(1.16)=$2.83;
D5=$2.83*(1.16)=3.28
Next, Calculate the price at the end of Year 5; using the
Gordon Model.
Additional Problems with Answers
Problem 4 (Answer) (continued)
Using r = 12% and g = 8% (constant growth
phase)
i.e. P5 = D5(1+g)/(r – g)
P5 = $3.28*(1.08)/(.12-.08)
3.54/.04=$88.56
Finally calculate the present value of all the
dividends in Years 1-5 and the price in Year 5, by
using the NPV function….(TI-83 keystrokes
shown here)
NPV(12,0,{1.56, 1.95, 2.44, 2.83, 3.28+88.56} =
$58.60
Additional Problems with Answers
Problem 5 (A)
Pricing common stock with constant growth and
finite life versus infinite life.
The ANZAC Corporation plans to be in business
for 30 years.
They announce that they will pay a dividend of
$3.00 per share at the end of one year, and
continue increasing the annual dividend by 4%
per year until they liquidate the company at the
end of 30 years.
If you want to earn a rate of return of 12% by
investing in their stock, how much should you pay
for the stock?
Additional Problems with Answers
Problem 5 (A) (Answer)
Div1 = $3.00; r = 12%; g = 4%; n = 30
Using the formula for a growing annuity we can solve for the
current price.
Div   1 g 30 
1  1 


Price 

0 r  g   1 r  


  1.04 30 
$3.00

Price0 
 1 

.12  .04    1.12  
Price0 = $37.5*0.89174 = $33.44
Additional Problems with Answers
Problem 5 (B)
If the company was to announce that it would
continue increasing the dividend at 4% per
year forever, how much more would you be
willing to pay for its stock, assuming your
required rate of return is still 12%?
Additional Problems with Answers
Problem 5 (B) (Answer)
If the growth rate is 4% forever, the price of
the stock can be figured out by using the
Gordon Model;
Div
D1=$3.00; r=12%
1
Price 
0 r  g
 $3.00/(.12 - .04) $37.50
Table 7.2 Coca-Cola Annual
Dividends
Table 7.3 Annual Dividend Growth for Coca- Cola
Table 7.4 Recent Dividend History
of Five Firms
Table 7.5 Ranking of Stock Risk Levels
Based on Expected Returns
Table 7.6 Recent Annual Dividends
of Five Other Firms