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
CLICK MOUSE OR HIT
SPACEBAR TO ADVANCE
Irwin/McGraw-Hill
copyright © 2002 McGraw-Hill Ryerson, Ltd.
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
Irwin/McGraw-Hill
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 2
T8.2 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
Irwin/McGraw-Hill
+
+
D2
(1 + R)2
D2
(1 + R)2
+
+
P2
(1 + R)2
D3
(1 + R)3
. Continuing to substitute, we obtain
+
D4
(1 + R)4
+ …
copyright © 2002 McGraw-Hill Ryerson, Ltd
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
Irwin/McGraw-Hill
copyright © 2002 McGraw-Hill Ryerson, Ltd
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
Irwin/McGraw-Hill
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 5
T8.3 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.
 Question:
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?
 Answer:
P0 = $1/.10 = $10.
 Question:
Given no change in the variables, what will the stock
be worth in one year?
Irwin/McGraw-Hill
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 6
T8.3 Common Stock Valuation: The Zero Growth Case (concluded)
 Answer:
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 no-growth stock will
never change.
Put another way, there is no reason to expect capital gains income from
this stock.
Irwin/McGraw-Hill
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 7
T8.4 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?
Irwin/McGraw-Hill
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 8
T8.4 Common Stock Valuation: The Constant Growth Case (concluded)
 Answer:
The equilibrium value of this constant-growth stock is
D1
$1.00
=
R-g
 Question:
= $20
.10 - .05
What would the value of the stock be if the growth rate
were only 3%?
 Answer:
D1
$1.00
=
= $14.29.
R-g
.10 - .03
Why does a lower growth rate result in a lower value?
Irwin/McGraw-Hill
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 9
T8.5 Stock Price Sensitivity to Dividend Growth, g
Stock price ($)
50
45
D1 = $1
Required return, R, = 12%
40
35
30
25
20
15
10
5
0
Irwin/McGraw-Hill
2%
4%
6%
8%
10%
Dividend growth
rate, g
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 10
T8.6 Stock Price Sensitivity to Required Return, r
Stock price ($)
100
90
80
D1 = $1
Dividend growth rate, g, = 5%
70
60
50
40
30
20
10
Required return, R
6%
Irwin/McGraw-Hill
8%
10%
12%
14%
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 11
T8.7 Common Stock Valuation - The Nonconstant 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?
 Answer: We return to the fundamental theory of value - the value today
equals the present value of all future cash flows.
 Put another way, the nonconstant growth model suggests that
P0 = present value of dividends in the nonconstant growth period(s)
+ present value of dividends in the “steady state” period.
Irwin/McGraw-Hill
copyright © 2002 McGraw-Hill Ryerson, Ltd
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?
Irwin/McGraw-Hill
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 13
ABC Company - answer
 1st calculate the value of the stock at p3 using the constant
growth formula

D/r-g = $5.00/(.08-.04) = $125
 Next discount this value back to p0
 P3/(1+r)3 = $125/1.25971 = $99.22
Irwin/McGraw-Hill
copyright © 2002 McGraw-Hill Ryerson, Ltd
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!!
Irwin/McGraw-Hill
copyright © 2002 McGraw-Hill Ryerson, Ltd
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  ( ____ )/( ____ -____ )
= $5.25/.04
= $_____ per share

What will the price be in a year?
Pt
= Dt+1/(R - g)
P1 = D___ /(R - g) = ($____  1.05)/(.09 - .05) = $137.8125
 By what percentage does P1 exceed P0? Why?
Irwin/McGraw-Hill
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 16
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.
Irwin/McGraw-Hill
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 17
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
Irwin/McGraw-Hill
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 18
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 (_____) + capital gains yield (_____)
=
____
Irwin/McGraw-Hill
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 19
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%
Irwin/McGraw-Hill
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 20
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
$ ____
(10% growth)
2
$ ____
(10% growth)
3
$6.534
( __% growth)
4
$6.926
( __% growth)
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 21
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)
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 22
Valuation Example cont’d
 At time 3, the value of the stock will be:
P3
=
D4/(R - g) = $_____ /(.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 + $115.434/1.12
=
$96.55
Irwin/McGraw-Hill
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 23
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
Irwin/McGraw-Hill
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 24
Solution to Problem 8.1
 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.
Irwin/McGraw-Hill
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 25
Solution to Problem 8.10
 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
0
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 26
Solution to Problem 8.10 (concluded)
 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.
Irwin/McGraw-Hill
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 27
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.
Irwin/McGraw-Hill
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 28
T8.10 Summary of Stock Valuation (Table 8.1) (concluded)
III. 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
P0 =
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).
Irwin/McGraw-Hill
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 29
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
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)
Irwin/McGraw-Hill
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 30
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
Irwin/McGraw-Hill
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 31
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
Irwin/McGraw-Hill
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 32
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
Irwin/McGraw-Hill
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 33
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)
Irwin/McGraw-Hill
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 34
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?
Irwin/McGraw-Hill
copyright © 2002 McGraw-Hill Ryerson, Ltd
Slide 35