Chapter
Eight
Stock Valuation
© 2003 The McGraw-Hill Companies, Inc. All rights reserved.
8.1
Key Concepts and Skills
 Understand how stock prices depend on future dividends and
dividend growth
 Be able to compute stock prices using the dividend growth
model
 Understand how corporate directors are elected
 Understand how stock markets work
 Understand how stock prices are quoted
8.2
Chapter Outline




Common Stock Valuation
Common Stock Features
Preferred Stock Features
Stock Market Reporting
8.3
Cash Flows for Shareholders 8.1
 If you buy a share of stock, you can receive cash in two ways
 Dividends
 Selling your shares
 As with any asset, the market price of common stock is equal
to the present value of the expected future cash flows the stock
will generate
8.4
One Period Example
 Suppose you are thinking of purchasing the stock of Moore Oil, Inc. and
you expect it to pay a $2 dividend in one year and you believe that you
can sell the stock for $14 at that time. If you require a return of 20% on
investments of this risk, what is the maximum you would be willing to
pay?
 Compute the PV of the expected cash flows
Div 1  Sale Price
1  r 
2  14

1.20
 $13.33
PVStock 
Calculator Approach
16
FV
0
PMT
1
N
20
I
PV
$13.33
8.5
Two Period Example
 Now what if you decide to hold the stock for two years? In addition to
the $2 dividend in one year, you expect a dividend of $2.10 in two
years and a stock price of $14.70 at the end of year 2. Now how much
would you be willing to pay now?
Div 1 Div 2  Sale Price

1  r 
1  r 2
2
2.10  14.70


1.20
1.20 2
 $13.33
PVStock 
Calculator Approach
0
CFj
2
CFj
16.80
CFj
20
I
2nd NPV
$13.33
8.6
Three Period Example
 Finally, what if you decide to hold the stock for three periods? In
addition to the dividends at the end of years 1 and 2, you expect to
receive a dividend of $2.205 at the end of year 3 and a stock price of
$15.435. Now how much would you be willing to pay?
Div 3  Sale Pr ice
Div 1
Div 2


1  r  1  r 2
1  r 3
2
2.10 2.205  15.435



1.20 1.20 2
1.203
 $13.33
PVStock 
Calculator Approach
0
CFj
2
CFj
2.10
CFj
17.64
CFj
20
I
2nd NPV
$13.33
8.7
Developing The Model
 We could continue this process for many time periods
 In fact, the price of the stock is just the present value of all
expected future dividends
 So, how can we estimate all future dividend payments?
8.8
Estimating Dividends: Special Cases
 Constant dividend
 The firm will pay a constant dividend forever
 Market instrument – preferred stock
 Price is computed using the level perpetuity formula
 Constant dividend growth
 The firm will increase the dividend by a constant percent every
period
 Market instrument – common stock
 Price is computed using a growing perpetuity formula
 Supernormal growth
 Dividend growth is high initially, but later settles down to a
long-run constant growth rate
8.9
Zero Growth Rate
 The dividends on most preferred stocks are expressed as a constant
percentage of the share’s face value
 Suppose a preferred share is expected to pay a $0.50 dividend every
quarter and the required return is 10% with quarterly compounding.
 What is the price?
Div 1
r
0.50

 0.10 


 4 
 $20.00
PVPreferred 
Stock
8.10
Constant Growth Rate
 To value a common stock, we usually assume the dividend stream will
grow at some constant growth rate over time
P0 
Div 3
Div 1
Div 2
Div 



.
.
.

1  r  1  r 2 1  r 3
1  r 
Div 0 1  g  Div 0 1  g  Div 0 1  g 
Div 0 1  g 




.
.
.

1  r 
1  r 2
1  r 3
1  r 
2
 With a little algebra, this reduces to:
Div 0 (1  g) Div 1
P0 

r -g
r -g
3

8.11
Constant Growth: Example 1
 Suppose Big D, Inc. just paid a dividend of $.50. It is expected to
increase its dividend by 2% per year. If the market requires a return of
15% on assets of this risk, how much should the stock be selling for?
Div 0 (1  g)
r -g
0.50(1.02)
0.15 - 0.02
 $3.92
P0 
8.12
Constant Growth: Example 2
 Suppose TB Pirates, Inc. is expected to pay a $2 dividend in one year. If
the dividend is expected to grow at 5% per year and the required return is
20%, what is the price?
Div 1
r -g
2.00
0.20 - 0.05
 $13.33
P0 
Stock Price Sensitivity to Dividend Growth, g
250
Div1 = $2; r = 20%
200
Stock Price
8.13
150
100
50
0
0
0.05
0.1
Growth Rate
0.15
0.2
Stock Price Sensitivity to Required Return, r
250
Div1 = $2; g = 5%
200
Stock Price
8.14
150
100
50
0
0
0.05
0.1
0.15
Required Return
0.2
0.25
0.3
8.15
Gordon Growth Company – Example 1
 Gordon Growth Company is expected to pay a dividend of $4 next
period and dividends are expected to grow at 6% per year. The required
return is 16%.
 What is the current price?
Div 1
r -g
4.00
0.16 - 0.06
 $40.00
P0 
8.16
Gordon Growth Company – Example 2
 What is the price expected to be in year 4?
P4 
Div 5
r -g
Div 1 1  g 

r -g
4
4.001.06 
0.16 - 0.06
 $50.50
4
8.17
Gordon Growth Company - Continued
 What is the holding period return due to the capital gain over the four
year period?
HPR 
P1  P0
P0
50.50  40.00
40.00
 26.25%

 What is the annually compounded rate of return due to the capital gain?
r  1  HPR 
 1.2625
 6%
1
4
1
n
Note that the price of the stock grows at the
same rate as the growth rate in the dividend
stream!
8.18
Non-constant Dividend Growth
 Suppose a firm is expected to increase dividends by 20% in
one year and by 15% in year 2. After that, dividends will
increase at a rate of 5% per year indefinitely. If the last
dividend that was just paid was $1 and the required return is
20%, what is the price of the stock?
 Remember that we have to find the PV of all expected future
dividends.
0
$1.00
20% 1
15%
2
5%
3
5%
4 5%
∞
8.19
Non-constant Dividend Growth - Continued
 Compute the dividends until growth levels off
0
$1.00
20% 1
$1.20
15%
2
5%
$1.38
3
5%
$1.45
 Find the present value of the expected future cash flows
P0 
Div 3  1 
Div 1
Div 2




2
2 
1  r  1  r  r  g  1  r  
1.20 1.38
1.45
 1 




1.20 1.20 2 0.20  0.06  1.20 2 
 $8.67

4 5%
∞
8.20
Quick Quiz – Part I
 What is the value of a stock that is expected to pay a constant
dividend of $2 per year if the required return is 15%?
 What if the company starts increasing dividends by 3% per
year, beginning with the next dividend? Assume that the
required return stays at 15%.
8.21
Calculating the Required Rate of Return
 Start with the constant dividend growth formula:
Div 0(1  g)
r-g
Div 1

r-g
P0 
rearrange and solve for r
r

Div 0(1  g)
g
P0
Div 1
g
P0
 The required rate of return on a common stock can always be
decomposed into:
 Dividend yield
 Capital gain or loss
8.22
Example – Finding the Required Return
 Suppose a firm’s stock is selling for $10.50. They just paid a $1 dividend
and dividends are expected to grow at 5% per year. What is the required
return?
r
Div 0(1  g)
g
P0
1.00(1.05)
 0.05
10.50
 15%

 What is the dividend yield?
Dividend Yield 
Div 0(1  g)
P0
1.00(1.05)

10.50
 10%
What is the capital gains yield?
Capital Gain  g
 0.05
 5%
8.23
Table 8.1 - Summary of Stock Valuation
8.24
Common Stock – Features
 Voting Rights
 Other Rights
 Share proportionally in declared dividends
 Share proportionally in remaining assets during liquidation
 Preemptive right – the right to purchase new stock to
maintain proportional ownership, if desired
 Classes of stock
 Dual class shares
 Voting & not-voting
 Allows founders to retain control while raising new equity
 Coattail provision
 Protects non-voting shareholders in the event of a take-over bid
8.25
Dividends
 Dividends are not a liability of the firm until a dividend has
been declared by the Board
 Consequently, a firm cannot go bankrupt for not declaring
dividends
 Dividends and Taxes
 Dividend payments are not considered a business expense and
are not tax deductible
 Dividends received by individual shareholders are partially
sheltered by the dividend tax credit
 Dividends received by corporate shareholders are not taxed, thus
preventing the double taxation of dividends
8.26
Preferred Stock - Characteristics
 Preferreds have priority to common stock upon liquidation
 Dividends
 Most preferreds have a stated dividend that must be paid
before common dividends can be paid
 Dividends are not a liability of the firm and preferred
dividends can be deferred indefinitely
 Most preferred dividends are cumulative – any missed
dividends on preferred stock have to be paid before a
dividend can be paid on common stock
 Preferred stock generally does not carry voting rights
8.27
Preferred Stock & Taxes
 Companies with a low tax rate cannot make use of the tax
shield available from interest
 Therefore, they have an incentive to issue preferred shares,
which typically pay a dividend lower than a comparable
interest rate. The dividend is non-taxable in the hands of the
recipient corporation.
 The loophole was partially closed in 1987 by forcing issuers
of preferreds to pay a tax of 40% of the preferred dividend.
 However, it may still be cheaper to use preferreds than debt
for the firm with a zero marginal tax rate
8.28
Example: Preferreds & Taxes
 Assume that there are two firms, Zero Tax and Full Tax. As the
name implies, Zero Tax pays no tax but needs to raise $1,000. It
can issue debt at 10% or preferreds at 6.7%. Full Tax is a fully
taxed firm which will either purchase the preferreds or extend a
loan to Zero Tax.
Issuer: Zero Tax
Dividend or interest
Dividend tax @ 40%
Tax deduction on int.
Total cost of financing
After-tax cost
Preferred
$67.00
$26.80
0.00
$93.80
9.38%
Debt
$100.00
0.00
0.00
$100.00
10%
Buyer: Full Tax
Before tax income
Tax
After-tax income
After-tax yield
Preferred
$67.00
0.00
$67.00
6.70%
Debt
$100.00
$45.00
$55.00
5.5%
8.29
Stock Market Reporting 8.4
 Stock market quotations are published in the newspapers and
are also available on-line (usually with 15-minute delays)
 In Canada, large cap stocks trade on the TSX
 Quotes and corporate information on stocks that trade on the
TSX can be found at the exchange’s website
 Click on the web surfer to go to the site
8.30
Figure 8.1 – Sample Stock Market Quotation
8.31
Work the Web Example
 Information on a large number of stocks in several different
markets can also be found at the Globe & Mail website
 Click on the web surfer to go to the site
 Publicly traded companies usually have an investor relations
section on their webpage
8.32
Quick Quiz – Part II
 You observe a stock price of $18.75. You expect a dividend
growth rate of 5% and the most recent dividend was $1.50.
What is the required return?
 What are some of the major characteristics of common stock?
 What are some of the major characteristics of preferred stock?
8.33
Summary 8.5
 You should know:
 The price of a stock is the present value of all future
expected dividends
 There are three approaches to valuing the stock price,
depending on the growth rate(s) of the dividends
 The rights of common and preferred shareholders
 How to read a stock market quotation from the newspaper