6
Chapter
Common Stock Valuation
Fundamentals
of Investments
Valuation & Management
second edition
Charles J. Corrado Bradford D.Jordan
McGraw Hill / Irwin
Slides by Yee-Tien (Ted) Fu
6-2
Common Stock Valuation
Goal
Our goal in this chapter is to examine
the methods commonly used by
financial analysts to assess the
economic value of common stocks.
 These methods are grouped into two
categories:
 dividend
discount models
 price ratio models
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Security Analysis: Be Careful Out There




Fundamental analysis
Examination of a firm’s accounting statements and other
financial and economic information to assess the economic
value of a company’s stock.
The basic idea is to identify “undervalued” stocks to buy and
“overvalued” stocks to sell.
In practice however, such stocks may in fact be correctly
priced for reasons not immediately apparent to the analyst.
Numbers such as a company’s earnings per share, cash flow,
book equity value, and sales are often called fundamentals
because they describe, on a basic level, a specific firm’s
operations and profits (or lack of profits).
Information, regarding such things as management quality,
products, and product markets is often examined as well.
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The Dividend Discount Model
 A fundamental principle of finance holds that the economic
value of a security is properly measured by the sum of its
future cash flows, where the cash flows are adjusted for risk
and the time value of money.
 For example, suppose a risky security will pay either $100 or
$200 with equal
 probability one year from today. The expected future payoff is
$150 = ($100 + $200) / 2, and the security's value today is the
$150 expected future value discounted for a one-year waiting
period.
 If the appropriate discount rate for this security is, say, 5
percent, then the present value of the expected future cash flow
is $150 / 1.05 = $142.86. If instead the appropriate discount
rate is 15 percent, then the present value is $150 / 1.15 =
$130.43.
 As this example illustrates, the choice of a discount rate can
have a substantial impact on an assessment of security value.
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The Dividend Discount Model
Dividend discount model (DDM)
Method of estimating the value of a share of
stock as the present value of all expected
future dividend payments.
D(1)
D(2)
D(3)
D(T )
V (0) 



2
3
T
1  k  1  k  1  k 
1  k 
where V(0) = the present value of the future dividend
stream
D(t) = the dividend to be paid t years from now
k = the appropriate risk-adjusted discount rate
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The Dividend Discount Model
 Example 6.1 Using the DDM. Suppose again
that a stock pays three annual dividends of
$100 per year and the discount rate is k = 15
percent. In this case, what is the present value
V(0) of the stock?
 With a 15 percent discount rate, we have V(0)
= $228.32.
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The Dividend Discount Model
 Example 6.2 More DDM. Suppose instead that
the stock pays three annual dividends of $10,
$20,and $30 in years 1, 2, and 3, respectively,
and the discount rate is k = 10 percent. What is
the present value V(0) of the stock?
 Check that the answer is V(0) = $48.16.
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Constant Dividend Growth Rate Model
 For many applications, the dividend discount
model is simplified substantially by assuming
that dividends will grow at a constant growth
rate. This is called a constant growth rate
model. Letting a constant growth rate be
denoted by g, then successive annual dividends
are stated as D(t+1) = D(t)(1+g).
 constant growth rate model A version of the
dividend discount model that assumes a
constant dividend growth rate.
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Constant Dividend Growth Rate Model
 Assuming that the dividends will grow at a
constant growth rate g,
Dt  1  Dt  1  g 
 Then
T

D0  1  g 
1 g  
V 0  
 
1  
kg
  1  k  
V 0   T  D0 
gk
gk
 This is the constant growth rate model.
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Constant Dividend Growth Rate Model
 Actually, when the growth rate is equal to the
discount rate, that is, k = g, the effects of
growth and discounting cancel exactly, and the
present value V(0) is simply the number of
payments T times the current dividend D(0):
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Constant Dividend Growth Rate Model
Example: Constant Growth Rate Model
 Suppose the dividend growth rate is 10%, the
discount rate is 8%, there are 20 years of dividends to
be paid, and the current dividend is $10. What is the
value of the stock based on the constant growth rate
model?
20

$10  1.10
1.10  

 V 0 
   $243.86
1  
.08  .10   1.08  

Thus the price of the stock should be $243.86.
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Constant Perpetual Growth
 Assuming that the dividends will grow forever
at a constant growth rate g,
D0 1  g  D1
V 0 

kg
kg
gk
 This is the constant perpetual growth model which is
:A version of the dividend discount model in which
dividends grow forever at a constant rate, and the
growth rate is strictly less than the discount rate
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Constant Perpetual Growth
 The reason is that a perpetual dividend growth
rate greater than a discount rate implies an
infinite value because the present value of the
dividends keeps getting bigger and bigger.
Since no security can have infinite value, the
requirement that g < k simply makes good
economic sense.
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Constant Perpetual Growth
Example: Constant Perpetual Growth Model
 Consider the electric utility industry. In late 2000, the
utility company Detroit Edison (DTE) paid a $2.06
dividend. Using D(0)=$2.06, k =8%, and g=2%,
calculate a present value estimate for DTE. Compare
this with the late-2000 DTE stock price of $36.13.
$2.06  1.02 
 V 0  
 $35.02
.08  .02
 Our estimated price is a little lower than the $36.13
stock price.
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Applications of the Constant Perpetual
Growth Model
 A standard example of an industry for which the
constant perpetual growth model can often be
usefully applied is the electric utility industry.
Consider the first company in the Dow Jones
Utilities, American Electric Power, which is traded
on the New York Stock Exchange under the ticker
symbol AEP. At midyear 1997, AEP's annual
dividend was $1.40; thus we set D(0) = $1.40, k=
6.5% , g=1.5 % ,
$1.40  1.015
V 0  
 $28.42
.065  .015
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Sustainable Growth Rate
 The growth rate in dividends (g) can be
estimated in a number of ways.
 Using
the company’s historical average growth
rate.
 Using an industry median or average growth rate.
 Using the sustainable growth rate, Which
involves using a company’s earnings to estimate g.
 sustainable growth rate A dividend growth rate
that can be sustained by a company's earnings.)
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Sustainable Growth Rate
 As we have discussed, a limitation of the constant
perpetual growth model is that it should be applied only
to companies with stable dividend and earnings growth.
Essentially, a company's earnings can be paid out as
dividends to its stockholders or kept as retained
earnings within the firm to finance future growth.
 (retained earnings Earnings retained within the firm to
finance growth.)
 (payout ratio Proportion of earnings paid out as dividends.)
 (retention ratio Proportion of earnings retained for
reinvestment.)
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Sustainable Growth Rate
Sustainable = ROE  Retention ratio
growth rate
Return on equity (ROE) = Net income / Equity
Retention ratio = 1 – Payout ratio
Payout ratio = dividends \net income
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Sustainable Growth Rate
Example: The Sustainable Growth Rate
 DTE has a ROE of 12.5%, earnings per share (EPS)
of $3.34, and a per share dividend (D(0)) of $2.06.
Assuming k = 8%, what is the value of DTE’s stock?
 Payout ratio = $2.06/$3.34 = .617
So, retention ratio = 1 – .617 = .383 or 38.3%
 Sustainable growth rate = 12.5%  .383 = 4.79%
$2.06  1.0479 
 V 0  
 $67.25  $36.13
.08  .0479
 DTE’s stock is perhaps undervalued, or more likely,
its growth rate has been overestimated.
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The Two-Stage Dividend Growth Model
 In the previous section, we examined dividend discount
models based on a single growth rate. You may have
already thought that a single growth rate is often
unrealistic, since companies often experience
temporary periods of unusually high or low growth,
with growth eventually converging to an industry
average or an economy-wide average.
 In such cases as these, financial analysts frequently use
a two-stage dividend growth model.
 (two-stage dividend growth model Dividend model
that assumes a firm will temporarily grow at a rate
different from its long-term growth rate.)
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The Two-Stage Dividend Growth Model
 A two-stage dividend growth model assumes
that a firm will initially grow at a rate g1 for T
years, and thereafter grow at a rate g2 < k
during a perpetual second stage of growth.
T
T


D01  g1   1  g1 
 1  g1  D01  g 2 
V 0 
 

1  
k  g1   1  k    1  k 
k  g2
The first term on the right-hand side measures the present value of
the first T dividends and is the same expression we used earlier
for the constant growth model. The second term then measures
the present value of all subsequent dividends.
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The Two-Stage Dividend Growth Model
 Example 6.9 Using the Two-Stage Model Suppose a firm has a
current dividend of D(0) = $5, which is expected to “shrink” at the
rate g1 = -10 percent for T = 5 years, and thereafter grow at the rate
g2 = 4 percent. With a discount rate of k = 10 percent, what is the
value of the stock?
 Using the two-stage model, present value, V(0), is calculated as:
 The total present value of $46.03 is the sum of a $14.25 present
value of the first five dividends plus a $31.78 present value of all
subsequent dividends.
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Discount Rates for Dividend Discount Models
 The discount rate for a stock can be estimated using
the capital asset pricing model (CAPM ).
 Discount = time value + risk
rate
of money premium
= T-bill + ( stock  stock market )
rate
beta risk premium
T-bill rate = return on 90-day U.S. T-bills
stock beta = risk relative to an average stock
stock market = risk premium for an average stock
risk premium
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Discount Rates for Dividend Discount Models
 A stock’s beta is a measure of a single stock’s risk
relative to an average stock, and we discuss beta at
length in a later chapter. For now, it suffices to know
that the market average beta is 1.0.
 A beta of 1.5 indicates that a stock has 50 percent
more risk than average, so its risk premium is 50
percent higher.
 A beta of .50 indicates that a stock is 50 percent less
sensitive than average to market volatility, and has a
smaller risk premium
 (beta Measure of a stock’s risk relative to the stock
market average.)
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Discount Rates for Dividend Discount Models
 Example 6.13 Stride-Rite’s Beta Look back at
Example 6.12. What beta did we use to determine the
appropriate discount rate for Stride-Rite? How do you
interpret this beta?
 Again assuming a T-bill rate of 5 percent and stock
market risk premium of 8.6 percent, we have
 13.9% = 5% + Stock beta × 8.6%
 Thus Stock beta = (13.9% - 5%) / 8.6% = 1.035
 Since Stride-Rite’s beta is greater than 1.0, it had
greater risk than an average stock — specifically, 3.5
percent more.
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Observations on Dividend Discount Models
Constant Perpetual Growth Model
 Simple to compute.
 Not usable for firms that do not pay dividends.
 Not usable when g > k.
 Is sensitive to the choice of g and k.
 k and g may be difficult to estimate accurately.
 Constant perpetual growth is often an
unrealistic assumption.
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Observations on Dividend Discount Models
Two-Stage Dividend Growth Model
 More realistic in that it accounts for two stages
of growth. ( it accounts for low, high, or zero
growth in the first stage, followed by constant
long-term)
 Usable when g > k in the first stage.
 Not usable for firms that do not pay dividends.
 Is sensitive to the choice of g and k.
 k and g may be difficult to estimate accurately.
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Price Ratio Analysis
 Price-earnings ratio (P/E ratio)
The most popular price ratio used to assess the value of
common stock
 Current stock price divided by annual earnings per share
(EPS).

 Earnings yield
Inverse of the P/E ratio: earnings divided by price (E/P).
 annual earnings per share can be calculated either as the
most recent quarterly earnings per share times four or the
sum of the last four quarterly earnings per share figures.
 High-P/E stocks are often referred to as growth stocks, while
low-P/E stocks are often referred to as value stocks.

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Price Ratio Analysis
 Price-cash flow ratio (P/CF ratio)
Current stock price divided by current cash flow
per share.
 In this context, cash flow is usually taken to be net
income plus depreciation.

 Most analysts agree that in examining a
company’s financial performance, cash flow
can be more informative than net income.
 Earnings and cash flows that are far from each
other may be a signal of poor quality earnings.
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Price Ratio Analysis
 Most analysts agree that cash flow can be more
informative than net income in examining a
company's financial performance. To see why,
consider the hypothetical example ?
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Price Ratio Analysis
 Twiddle-Dee Co. chooses straight-line depreciation
and Twiddle-Dum Co. chooses accelerated
depreciation. These two depreciation schedules are
tabulated below:
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Price Ratio Analysis
 Now, let's look at the resulting annual cash flows and
net income figures for the two companies, recalling
that in each year, Cash flow = Net income +
Depreciation:
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Price Ratio Analysis
 Price-sales ratio (P/S ratio)
Current stock price divided by annual sales per share.
 A high P/S ratio suggests high sales growth, while a low
P/S ratio suggests sluggish sales growth.

 Price-book ratio (P/B ratio)
Market value of a company’s common stock divided by its
book (accounting) value of equity.
 A ratio bigger than 1.0 indicates that the firm is creating
value for its stockholders.
 A ratio smaller than 1.0 indicates that the company is
actually worth less than it cost.
 because of varied and changing accounting standards, book
values are difficult to interpret

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Price Ratio Analysis
Intel Corp (INTC) - Earnings (P/E) Analysis
Current EPS
$1.35
5-year average P/E ratio
30.4
EPS growth rate
16.5%
expected = historical  projected EPS
stock price
P/E ratio
= 30.4
 ($1.351.165)
= $47.81
* Late-2000 stock price = $89.88
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Price Ratio Analysis
Intel Corp (INTC) - Cash Flow (P/CF) Analysis
Current CFPS
$1.97
5-year average P/CF ratio 21.6
CFPS growth rate
15.3%
expected = historical  projected CFPS
stock price
P/CF ratio
= 21.6
 ($1.971.153)
= $49.06
* Late-2000 stock price = $89.88
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6 - 36
Price Ratio Analysis
Intel Corp (INTC) - Sales (P/S) Analysis
Current SPS
$4.56
5-year average P/S ratio
6.7
SPS growth rate
13.3%
expected = historical  projected SPS
stock price
P/S ratio
=
6.7
 ($4.561.133)
= $34.62
* Late-2000 stock price = $89.88
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An Analysis of the
McGraw-Hill Company
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An Analysis of the McGraw-Hill Company
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An Analysis of the McGraw-Hill Company
Getting the Most from the Value Line Page
6 - 40
An Analysis of the McGraw-Hill Company
@2002 by the McGraw- Hill Companies Inc.All rights reserved.
6 - 41
Getting the Most from the Value Line Page
An Analysis of the McGraw-Hill Company
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An Analysis of the McGraw-Hill Company
 Based on the CAPM,
k = 6% + (.85  9%) = 13.65%
 Retention ratio = 1 – $1.02/$2.75 = 62.9%
sustainable g = .629  25.5% = 16.04%
 Since g > k, the constant growth rate model
cannot be used.
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An Analysis of the McGraw-Hill Company
Quick calculations used: P/CF = P/E  EPS/CFPS
P/S = P/E  EPS/SPS
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An Analysis of the McGraw-Hill Company
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Chapter Review
 Security Analysis: Be Careful Out There
 The Dividend Discount Model
Constant Dividend Growth Rate Model
 Constant Perpetual Growth
 Applications of the Constant Perpetual Growth
Model
 The Sustainable Growth Rate

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Chapter Review
 The Two-Stage Dividend Growth Model
Discount Rates for Dividend Discount Models
 Observations on Dividend Discount Models

 Price Ratio Analysis
Price-Earnings Ratios
 Price-Cash Flow Ratios
 Price-Sales Ratios
 Price-Book Ratios
 Applications of Price Ratio Analysis

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Chapter Review
 An Analysis of the McGraw-Hill Company
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