T8.1 Chapter Outline
Chapter 8
Stock Valuation
Chapter Organization
 8.1 Common Stock Valuation
 8.2 Common Stock Features
 8.3 Preferred Stock Features
 8.3 Stock Market Reporting
 8.4 Summary and Conclusions
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2005
Common Stock Valuation - the theory
 Investment theorists argue that the best measure of going
- concern value for a common stock is the present value of
expected future dividends
 The basic approach is to :
 estimate the future earnings of the company
 make a judgment on the proportion of earnings that would be
paid out as dividends
 discount the future dividend stream at the appropriate
discount rate
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2005
Slide 2
Common Stock Cash Flows and the Fundamental Theory of Valuation
 In 1938, John Burr Williams postulated what has become the fundamental
theory of valuation:
The value today of any financial asset equals the present value of all of its
future cash flows.
 For common stocks, this implies the following:
P0 =
D1
+
(1 + R)1
P1
and
(1 + R)1
P1 =
D2
(1 + R)1
+
P2
(1 + R)1
substituting for P1 gives
P0 =
P0 =
D1
(1 + R)1
D1
(1 + R)1
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+
+
D2
(1 + R)2
D2
(1 + R)2
+
+
2005
P2
(1 + R)2
D3
(1 + R)3
. Continuing to substitute, we obtain
+
D4
(1 + R)4
Slide 3
+ …
Common Stock Valuation - the theory
 We ultimately lose the future value of the stock price in the
equation given that it is assumed to be in the distant future
and the present value of this distant price is essentially
zero
 this allows us to focus solely on the future dividend stream
as the driver of the stock’s value
 What happens if the firm does not pay dividends - does
this mean the stock does not have any value?


The issue here is one of expectations of future dividends or
some form of liquidating dividend
according to the theory - rational investors would never place
a value on a stock that was never going to pay a dividend
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2005
Slide 4
Common Stock Valuation - the theory
 3 situations where the model can be applied
 Zero Growth Case - no growth assumed for the dividends over
time  Constant Growth - steady growth in dividends is assumed constant or even
 Non-constant Growth - after a certain period of time
dividends are assumed to grow at a constant pace - but at
some point in the future
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2005
Slide 5
Common Stock Valuation: The Zero Growth Case
 According to the fundamental theory of value, the value of a
financial asset at any point in time equals the present value of all
future dividends.
 If all future dividends are the same, the present value of the
dividend stream constitutes a perpetuity.
 The present value of a perpetuity is equal to
C/r or, in this case, D1/R.
 example:
Cooper, Inc. common stock currently pays a $1.00
dividend, which is expected to remain
constant
forever. If the required return on
Cooper stock is
10%, what should the stock
sell for today?
P0 = $1/.10 = $10.
Given no change in the variables, what will the stock
be worth in one year?
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2005
Slide 6
Common Stock Valuation: The Zero Growth Case (concluded)
One year from now, the value of the stock, P1, must
be equal to the present value of all remaining future
dividends.
Since the dividend is constant, D2 = D1 , and
P1 = D2/R = $1/.10 = $10.
In other words, in the absence of any changes in expected cash
flows (and given a constant discount rate), the price of a nogrowth stock will never change.
Put another way, there is no reason to expect capital gains income
from this stock.
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2005
Slide 7
Common Stock Valuation: The Constant Growth Case
 In reality, investors generally expect the firm (and the dividends it
pays) to grow over time. How do we value a stock when each dividend
differs from the one preceding it?
 As long as the rate of change from one period to the next, g, is
constant, we can apply the growing perpetuity model:
P0 =
P0 =
D1
D2
+
+
(1 + R)1 (1 + R)2
D0(1 + g)
R-g
=
D1
R- g
D3
+ …=
(1 + R)3
D0(1+g)1
+
(1 + R)1
D0(1+g)2
(1 + R)2
D0(1+g)3
+
+ ...
(1 + R)3
.
 Now assume that D1 = $1.00, r = 10%, but dividends are expected to
increase by 5% annually. What should the stock sell for today?
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2005
Slide 8
Common Stock Valuation: The Constant Growth Case (concluded)
The equilibrium value of this constant-growth stock is
D1
$1.00
=
R-g
= $20
.10 - .05
What would the value of the stock be if the growth rate were only 3%?
D1
$1.00
=
= $14.29.
R-g
.10 - .03
Why does a lower growth rate result in a lower value?
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Slide 9
Stock Price Sensitivity to Dividend Growth, - ‘g’
Stock price ($)
50
45
D1 = $1
Required return, R, = 12%
40
35
30
25
20
15
10
5
0
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2%
4%
2005
6%
8%
Slide 10
10%
Dividend growth
rate, g
Stock Price Sensitivity to Required Return, - ’r’
Stock price ($)
100
90
80
D1 = $1
Dividend growth rate, g, = 5%
70
60
50
40
30
20
10
Required return, R
6%
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8%
2005
10%
12%
14%
Slide 11
Common Stock Valuation - The Non-constant Growth Case
 For many firms (especially those in new or high-tech industries),
dividends are low or non existent but are expected to be paid at some
point in the future. As product markets mature, the dividend growth
rate is then expected to evolve to a “steady state” rate. How should
stocks such as these be valued?
: We return to the fundamental theory of value - the value today equals
the present value of all future cash flows.
 Put another way, the non-constant growth model suggests that
P0 = present value of dividends in the non-constant growth period(s)
+ present value of dividends in the “steady state” period.
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2005
Slide 12
Common Stock Valuation - Non Constant Growth Case
 Example
Assume:
 company ABC pays a C/S dividend of $5.00 per share today
 no growth is assumed for 3 years followed by constant growth
of 4%
 using a discount rate of 8% what is the value of the stock?
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Slide 13
ABC Company -
 1st calculate the value of the stock at p3 using the
constant growth formula

P3 = D4/r-g = $5.20/(.08-.04) = $130
 Next discount this value back to p0
 P3/(1+r)3 = $130/1.25971 = $103.20
 Add PV of dividends for first 3 years
 $4.63 + 4.29 + 3.97 + 103.20 = $116.09
……suggest drawing a dividend time line to visualize the cash
flows
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2005
Slide 14
Common Stock Valuation - other theories
 Burton Malkiel in his book ‘ A Random Walk Down Wall
Street’ gives his four ‘fundamental’ rules of stock prices:




investors pay a higher price the larger the dividend growth
rate
investors pay a higher price the larger the proportion of
earnings paid out in dividends
investors pay a higher price per share the less risky the
company’s stock is
investors pay a higher price per share the lower the level of
interest rates
.....there are other theories!!
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2005
Slide 15
Examples
 Suppose a stock has just paid a $5 per share dividend. The dividend is
projected to grow at 5% per year indefinitely. If the required return is 9%,
then the price today is _____ ?
P0 = D1/(R - g)
= $5  ( 1.05 )/( .09 - .05 )
= $5.25/.04
= $131.25 per share

What will the price be in a year?
Pt
= Dt+1/(R - g)
P1 = D 2 /(R - g) = ($5.25  1.05)/(.09 - .05) = $137.8125
 By what percentage does P1 exceed P0? Why?
P1 exceeds P0 by 5% -- the capital gains yield.
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2005
Slide 16
Components of the Required Rate of Return
We know that P0 = D1/(r-g)
Then r = D1/P0 + g
 D1/P0 is the dividend yield
 The dividend growth rate – g is also the rate the stock
price is expected to grow (consistent with the theory that
future cash flows drive the value of the security)

This growth rate is interpreted as the capital gains yield
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2005
Slide 17
The Required Rate of Return
 Find the required return:
Suppose a stock has just paid a $5 per share dividend.
The dividend is projected to grow at 5% per year indefinitely.
If the stock sells today for $65 5/8, what is the required return?
P0
=
D1/(R - g)
(R - g) =
D1/P0
R
=
D1/P0 + g
=
$5.25/$65.625 + .05
=
dividend yield ( .08 ) + capital gains yield ( .05 )
=
.13 = 13%
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2005
Slide 18
What Discount Rate or Rate of Return to Use?
 Concept of risk vs return
 The higher the risk the higher the return is needed to
compensate for this risk
 Time horizon
 Short term rates for long term
Long Government of Canada Bonds - 5 % range
Historical rates of return – table 12.4 page 349 in text
Canadian equities – 10. 29% average return over past 50 years
Long term Bonds - 9.01%
,,,many financial planners today are suggesting 8-10% as a
realistic average rate of return to expect on a diversified
portfolio
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2005
Slide 19
Valuation Example
 Suppose a stock has just paid a $5 per share dividend. The
dividend is projected to grow at 10% for the next two years, the
8% for one year, and then 6% indefinitely. The required return
is 12%. What is the stock’s value?
Irwin/McGraw-Hill
Time
Dividend
0
$ 5.00
1
$ 5.50
(10% growth)
2
$ 6.05
(10% growth)
3
$6.534
( 8% growth)
4
$6.926
( 6% growth)
2005
Slide 20
Valuation Example cont’d
 At time 3, the value of the stock will be:
P3
=
D4/(R - g) = $6.926/(.12 - .06) = $115.434
 The value today of the stock is thus:
P0
=
D1/(1 + R) + D2/(1 + R)2 + D3/(1 + R)3 + P3/(1 + R)3
=
$5.5/1.12 + $6.05/1.122 + $6.534/1.123 + $115.434/1.123
=
$96.55
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2005
Slide 21
Examples
 Green Mountain, Inc. just paid a dividend of $2.00 per
share on its stock. The dividends are expected to grow at a
constant 5 percent per year indefinitely. If investors require
a 12 percent return on Favre stock, what is the current
price? What will the price be in 3 years? In 15 years?
 According to the constant growth model,
P0 = D1/(R - g) = $2.00(1.05)/(.12 - .05) = $30.00
 If the constant growth model holds, the price of the stock
will grow at g percent per year, so
P3 = P0  (1 + g)3 = $30.00  (1.05)3 = $34.73, and
P15 = P0  (1 + g)15 = $30.00  (1.05)15 = $62.37.
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2005
Slide 22
Examples
 Metallica Bearings, Inc. is a young start-up company. No
dividends will be paid on the stock over the next 5 years.
The company will pay a $6 per share dividend in six years
and will increase the dividend by 5% per year thereafter. If
the required return on this stock is 21%, what is the
current share price?
 The current market price of any financial asset is the
present value of its future cash flows, discounted at the
appropriate required return. In this case, we know that:
D1 = D2 = D3 = D4 = D5 =
D6 = $6.00
D7 = $6.00(1.05) = $6.30
.
.
.
Irwin/McGraw-Hill
2005
0
Slide 23
Examples
 This share of stock represents a stream of cash flows with
two important features:
First, because they are expected to grow at a constant rate
(once they begin), they are a growing perpetuity;
Second, since the first cash flow is at time 6, the
perpetuity is a deferred cash flow stream.
 Therefore, the answer requires two steps:
1.
By the constant-growth model, D6/(r - g) = P5;
i.e., P5 = $6.00/(.21 - .05) = $37.50.
2.
And, P0 = P5 1/(1 + .21)5 = $37.50  .3855 = $14.46.
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2005
Slide 24
Summary of Stock Valuation (Table 8.1)
I. The General Case
In general, the price today of a share of stock, P0, is the present value of all of its future
dividends, D1, D2, D3, . . .
P0 =
D1
+
(1 + R)1
D2
(1 + R)2
D3
+
(1 + R)3
+ …
where r is the required return.
II. Constant Growth Case
If the dividend grows at a steady rate, g, then the price can be written as:
P0 = D1/(R - g)
This result is the dividend growth model.
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2005
Slide 25
T8.10 Summary of Stock Valuation (Table 8.1) (concluded)
III.Non Constant or Supernormal Growth
If the dividend grows steadily after t periods, then the price can be written as:
P0 =
D1
+
(1 + R)1
D2
(1 + R)2
+...+
Dt
+
(1 + R)t
Pt
(1 + R)t
where
Pt =
Dt+1  (1 + g)
(R - g)
IV. The Required Return
The required return, r, can be written as the sum of two things:
R = D1/P0 + g
where D1/P0 is the dividend yield and g is the capital gains yield (which is the same thing
as the growth rate in dividends for the steady growth case).
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Slide 26
T8.11 Features of Common Stock
 Features of Common Stock
The right to vote - including major events like takeovers
The right to share proportionally in dividends paid
The right to share proportionally in assets remaining after
liabilities have been paid, in event of a liquidation
The preemptive right
 Dividends…are paid from earnings
Not a liability until declared by the Board of Directors
Unlike interest on debt, dividends are not tax deductible to the
firm
However, shareholder receipt of dividends does have preferential
tax treatment (See Chapter 2)
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Slide 27
T8.11 Features of Common Stock
 Classes of Stock
Dual Class shares are becoming more commonplace
Usually classes divide into voting and non-voting shares
“Coattail” provisionally invoked at the time of a takeover
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2005
Slide 28
T8.12 Features of Preferred Stock
 Features of Preferred Stock
Preferences over common stock - dividends, liquidation
Dividend arrearages
Cumulative and non-cumulative
Stated/liquidating value
Typically non - voting
 Is preferred stock really debt?
Preferred stock and taxes
Tax treatment differs from debt
Differential tax treatment suggests a preferred stock clientele
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Slide 29
Preferred Stock - why it looks like debt
 Pref. Shareholders receive a stated dividend much like the
stated coupon on a bond
 Pref. Shares often carry credit ratings much like a bond
issues
 Pref. Stock is often callable by the issuer
 Some pref. Share issues even have sinking funds
 Floating rate pref. Shares are similar in concept to floating
rate bond issues
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2005
Slide 30
Other Valuation Theories and Growth
 If a firm pays virtually all of its earnings out in the form of
dividends – the value of the share = EPS/r or Dividends/r
 Where some cash is reinvested into growing the business
then the share value = EPS/r + NPV of growth opportunities
(GO)
 Application of the P/E ratio
 Price per share/EPS = 1/r + NPVGO/EPS
…..firm with higher growth opportunities should sell for higher
valuations (prices)
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2005
Slide 31
Other Valuation Theories With Price Earnings and PEG Ratios
 The P/E ratio is partially impacted by the net present value
of growth opportunities

for a given level of earnings, two stocks can trade at much
different P/E ratios - one reason being investors are willing to
pay more (a higher multiple of earnings) for the firm that has
the greater growth opportunities.
 PEG ratio is the P/E ratio / earnings growth rate
 useful when comparing stocks which have high P/E ratios - to
help differentiate e.g
-two stocks may both be trading at high P/E’s of say 50
-one may be growing earnings at 25 times per year and the
other at 10 times....the two firms have PEG’s of 2.5 and 5.
-all other things being equal - which one would be the better
investment?
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2005
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