Chapter 7
Stocks
and Stock
Valuation
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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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7-2
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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7-3
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 day-today operations.
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7-4
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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7-6
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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7-7
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, dividends are considered to be taxable
income.
• More material on dividends and dividend policy is covered in
Chapter 17.
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7-8
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).
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7-9
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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7-10
7.1 (H) Preemptive Right
• A privilege that allows 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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7-11
7.2 Stock Markets
Stocks are traded in two types of markets:
1. the primary or “first sale” market
2. secondary or “after-sale” market,
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7-12
7.2 (A) Primary Markets
First-issue market where issuing firm is involved.
• Initial public offering (IPO): first public equity issue of a
firm.
• Prospectus: document providing information about the
issuing form and its securities.
• Due diligence: all relevant information must be
disclosed prior to the sale.
• Firm commitment: Investment banker buys the entire
issue from the firm and then tries to sell at a higher
price.
• Best efforts: Investment banker pledges to do his or
her best in selling the shares in exchange for small
commission.
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7-13
7.2 (B) Secondary Markets
• Forum where common stock can be traded
among investors themselves.
• Provides liquidity and variety.
• In the United States, three well-known secondary
stock markets:
• NYSE
• AMEX
• NASDAQ
Specialist
Ask price
Bid price
Bid-ask spread
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7-14
7.2 (C) Bull Markets and Bear
Markets
• A Bull market is a prolonged rising stock
market, coined on the analogy that a bull
attacks with his horns from the bottom up.
• A Bear market is a prolonged declining
market, based on the analogy that a bear
swipes with his paws from the top down.
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7-15
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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7-16
Table 7.1 Differences between Bonds
and Stocks
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7-17
7.3 Stock Valuation (continued)
Example 1: Stock Price with Known Dividends
and Sale Price
PROBLEM:
Client wants to purchase common stock of New
Frontier Inc. and hold it for four years. The
directors of the company just announced that they
expect to pay an annual cash dividend of $4.00 per
share for at least the next 4 years. Client believes
that he will be able to sell the stock for $40 at the
end of four years. In order to earn 12% on this
investment, how much should Client pay for this
stock?
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7-18
7.3 Stock Valuation (continued)
Solution
Method 1. Using an equation
Price = $40.00 x 0.635518 + $4.00 x 3.03734
Price = $25.42 + $12.149 = $37.57
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7-19
7.3 Stock Valuation (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
-37.57
Copyright © 2010 Pearson Prentice Hall. All rights reserved.
FV
40
7-20
7.3 Stock Valuation (continued)
Four variations of a dividend pricing model have been used
to value common stock:
1.
2.
3.
4.
The
The
The
The
constant
constant
constant
constant
dividend model with an infinite horizon
dividend model with a finite horizon
growth dividend model with an infinite horizon
growth dividend model with a finite horizon
These models make different assumptions about
1. The dividend stream--is it constant or growing?
2. The maturity of the stock--is it held forever or up to a point
at which it is needed?
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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:
Div1 = Div2 = Div3 = Div4 = Div5 = Div∞
For perpetuities,
PV = PMT/r
where r is the required rate of return 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
Problem
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?
Solution
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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7-23
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.
• Assumes that constant dividends are received over
the investment horizon.
• Price is estimated as the sum of the present value
of an annuity stream (constant dividend) and that
of a single sum (the selling price).
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7-24
7.3 (B) The Constant Dividend
Model with a Finite Horizon
(continued)
Example 3. Constant Dividends with a
Finite Holding Period
Problem
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 for the stock?
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7-25
7.3 (B) The Constant Dividend
Model with a Finite Horizon
(continued)
Solution
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
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PV PMT
?
2
-18.56
FV
20
7-26
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 


L

0
1
2
3
1
r


1 r 
1 r 
1 r 
where r is the required rate of return.
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7-27
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 
0
r  g
• And since Div0 x (1+g) = Div1
Div
1
Price 
0 r  g
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7-28
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).
Problem
Let’s say that Gekko Company just paid its
shareholders an annual dividend of $2.00 and has
announced that the dividends will 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 will they offer for the
stock?
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7-29
7.3 (C) The Constant Growth
Dividend Model with an Infinite
Horizon (cont’d)
Example 4 (Answer)
Solution
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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7-30
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)
Problem
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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7-31
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
Solution
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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7-32
7.3 (D) The Constant Growth
Dividend Model with a Finite
Horizon
In this model, the investor expects to hold a stock for a
limited number of years, Company’s dividends are growing
at a constant rate.
The following adjusted formula can be used to value the
stock:
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.
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7-33
7.3 (D) The Constant Growth
Dividend Model with a Finite Horizon
(continued)
Example 6: Constant Growth, Finite
Horizon
Problem
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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7-34
7.3 (D) The Constant Growth
Dividend Model with a Finite Horizon
(continued)
We can solve this in 2 ways.
Solution
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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7-35
7.3 (D) The Constant Growth
Dividend Model with a Finite Horizon
(continued)
Method 1: Use the following equation:
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 = 2.82305
P7=2.82305/(.14-.1072)$86.07
 = $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)
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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7-37
7.3 (E) Nonconstant 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 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) Nonconstant Growth
Dividends (continued)
Example 7: Nonconstant Dividend Pattern
Problem
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?
Solution
D1=$1.00; g1=25%; n1=2; g2=18%; n2=1; gc=10%; r=16%
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7.3 (E) Nonconstant Growth
Dividends (continued)
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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7-40
7.3 (E) Nonconstant Growth
Dividends (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. Then 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
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7-41
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 rather than on historical dividend patterns.
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7-42
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 predetermined ratio.
• Has “preferred status” over common stockholders in the case of
dividend payments and liquidation payouts.
•
• Dividends can be cumulative or noncumulative
• 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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7-43
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?
Annual dividend = .08*$60 = $4.80
Price = $4.80/0.10 = $48
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7-44
7.6 Efficient Markets
An efficient market is one in which security
prices are current and fair to all traders, and
transaction costs are minimal.
There are two forms of efficiency:
1. Operational efficiency
2. 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.
• Definitely, very operationally efficient
markets.
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7-46
7.6 (B) Informational Efficiency
• Speed and accuracy with which information is
reflected in the available prices for trading.
• In this kind of market, securities would always trade
at their fair or equilibrium value.
– But information is diverse, so 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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7-47
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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7-48
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 today?
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7-49
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:
Output
N
4
I/Y
13
PV
PMT
?
2
-24.35
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FV
30
7-50
ADDITIONAL PROBLEMS WITH
ANSWERS
Problem 2
Constant Growth Rate, with 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
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7-51
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%
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ADDITIONAL PROBLEMS WITH
ANSWERS
Problem 2 (ANSWER continued)
Next, use the constant growth dividend model
with infinite horizon 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
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7-53
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?
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7-54
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%; Year 11 onwards,
zero-growth in dividends.
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7-55
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;
Discount each dividend and the Year 10 price back to time 0 at
15%:
0.75(1.15)4+0.84(1.15)5+0.94(1.15)6+1.05(1.15)7+1.1
8(1.15)8+1.32(1.15)9+1.50(1.15)10+10(1.15)10
Price=$5.25
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7-56
ADDITIONAL PROBLEMS WITH
ANSWERS
Problem 4
Pricing Nonconstant 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 dividends will 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.
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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.
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ADDITIONAL PROBLEMS WITH
ANSWERS
Problem 4 (ANSWER–continued)
Using r = 12% and g = 8% (constant growth
phase), we have
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
discounting them at 12% for the respective number
of years:
1.56/(1.12)+1.95/(1.12)2+2.44/(1.12)3+2.83
/(1.12)4+3.28/(1.12)5+88.56(1.12)5=$58.60
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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.
It announces that it 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
it liquidates the company at the end of 30 years.
If you want to earn a rate of return of 12% by
investing in ANZAC’s stock, how much should you
pay for the stock?
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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.

30 
Div


1
g

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
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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%?
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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;
D1=$3.00; r=12%
Div
1
Price 
0 r  g 
 $3.00/(.12 - .04) $37.50
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Table 7.2 Coca-Cola Annual Dividends
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Table 7.3 Annual Dividend Growth for
Coca-Cola
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Table 7.4 Recent Dividend History of
Five Firms
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Table 7.5 Ranking of Stock Risk Levels
Based on Expected Returns
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Table 7.6 Recent Annual Dividends of
Five Other Firms
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