Chapter
6
McGraw-Hill/Irwin
Common Stock
Valuation
Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved.
Learning Objectives
Separate yourself from the commoners by having a good
Understanding of these security valuation methods:
1. The basic dividend discount model.
2. The two-stage dividend growth model.
3. The residual income model.
4. Price ratio analysis.
6-2
Common Stock Valuation
• 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 three categories:
– Dividend discount models
– Residual Income models
– Price ratio models
6-3
Security Analysis: Be Careful Out There
• Fundamental analysis is a term for studying a
company’s accounting statements and other financial and
economic information to estimate 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.
6-4
The Dividend Discount Model
• The Dividend Discount Model (DDM) is a method to estimate the
value of a share of stock by discounting all expected future dividend
payments. The basic DDM equation is:
D3
D1
D2
DT
P0 



2
3
1 k  1 k  1 k 
1 k T
• In the DDM equation:
– P0 = the present value of all future dividends
– Dt = the dividend to be paid t years from now
– k = the appropriate risk-adjusted discount rate
6-5
Example: The Dividend Discount Model
• Suppose that a stock will pay three annual dividends of
$200 per year, and the appropriate risk-adjusted discount
rate, k, is 8%.
• In this case, what is the value of the stock today?
P0 
D3
D1
D2


1  k  1  k 2 1  k 3
P0 
$200
$200
$200


 $515.42
2
3
1  0.08  1  0.08  1  0.08 
6-6
The Dividend Discount Model:
the Constant Growth Rate Model
• Assume that the dividends will grow at a constant growth rate g. The
dividend next period (t + 1) is:
D t 1  D t  1  g
So, D 2  D1  (1  g)  D 0  (1  g)  (1  g)
• For constant dividend growth for “T” years, the DDM formula
becomes:
T
D1 (1  g)   1  g  
P0 
 
1  
k  g   1  k  
if k  g
P0  T  D 0
if k  g
6-7
Example: The Constant Growth Rate Model
• Suppose the current dividend is $10, the dividend growth rate is
10%, there will be 20 yearly dividends, and the appropriate discount
rate is 8%.
• What is the value of the stock, based on the constant growth rate
model?
T
D 0 (1  g)   1  g  
P0 
 
1  
k  g   1  k  
20
$10  1.10    1.10  
P0 
   $243.86
1  
.08  .10   1.08  
6-8
The Dividend Discount Model:
the Constant Perpetual Growth Model.
• Assuming that the dividends will grow forever at a
constant growth rate g.
• For constant perpetual dividend growth, the DDM formula
becomes:
P0 
D 0  1  g
D
 1
kg
kg
(Important : g  k)
6-9
Example: Constant Perpetual Growth Model
• Think about the electric utility industry.
• In 2007, the dividend paid by the utility company, DTE Energy Co.
(DTE), was $2.12.
• Using D0 =$2.12, k = 6.7%, and g = 2%, calculate an estimated value
for DTE.
P0 
$2.12  1.02 
 $46.01
.067  .02
Note: the actual mid-2007 stock price of DTE was $47.81.
What are the possible explanations for the difference?
6-10
The Dividend Discount Model:
Estimating the 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.
6-11
The Historical Average Growth Rate
•
Suppose the Broadway Joe Company paid the following dividends:
– 2002: $1.50
– 2003: $1.70
– 2004: $1.75
•
2005: $1.80
2006: $2.00
2007: $2.20
The spreadsheet below shows how to estimate historical average
growth rates, using arithmetic and geometric averages.
Year:
2007
2006
2005
2004
2003
2002
Dividend:
$2.20
$2.00
$1.80
$1.75
$1.70
$1.50
Pct. Chg:
10.00%
11.11%
2.86%
2.94%
13.33%
Arithmetic Average:
8.05%
Geometric Average:
7.96%
Year:
2002
2003
2004
2005
2006
2007
Grown at
7.96%:
$1.50
$1.62
$1.75
$1.89
$2.04
$2.20
6-12
The Sustainable Growth Rate
Sustainabl e Growth Rate  ROE  Retention Ratio
 ROE  (1 - Payout Ratio)
• Return on Equity (ROE) = Net Income / Equity
• Payout Ratio = Proportion of earnings paid out as dividends
• Retention Ratio = Proportion of earnings retained for investment
6-13
Example: Calculating and Using the
Sustainable Growth Rate
• In 2007, American Electric Power (AEP) had an ROE of 10.17%,
projected earnings per share of $2.25, and a per-share dividend of
$1.56. What was AEP’s:
– Retention rate?
– Sustainable growth rate?
• Payout ratio = $1.56 / $2.25 = .693
• So, retention ratio = 1 – .693 = .307 or 30.7%
• Therefore, AEP’s sustainable growth rate = .1017  .307 = .03122, or
3.122%
6-14
Example: Calculating and Using the
Sustainable Growth Rate, Cont.
• What is the value of AEP stock, using the perpetual growth model,
and a discount rate of 6.7%?
P0 
$1.56  1.03122 
 $44.96
.067  .03122
• The actual mid-2007 stock price of AEP was $45.41.
• In this case, using the sustainable growth rate to value the stock
gives a reasonably accurate estimate.
• What can we say about g and k in this example?
6-15
The Two-Stage Dividend Growth Model
• The 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.
• The Two-Stage Dividend Growth Model formula is:
T
T
D 0 (1  g1 )   1  g1    1  g1  D 0 (1  g2 )
P0 
 

1  
k  g1   1  k    1  k 
k  g2
6-16
Using the Two-Stage
Dividend Growth Model, I.
• Although the formula looks complicated, think of it as two
parts:
– Part 1 is the present value of the first T dividends (it is the same
formula we used for the constant growth model).
– Part 2 is the present value of all subsequent dividends.
• So, suppose MissMolly.com has a current dividend of
D0 = $5, which is expected to shrink at the rate, g1 = 10%
for 5 years, but grow at the rate, g2 = 4% forever.
• With a discount rate of k = 10%, what is the present value
of the stock?
6-17
Using the Two-Stage
Dividend Growth Model, II.
T
T
D 0 (1  g1 )   1  g1    1  g1  D 0 (1  g 2 )
P0 
 

1  
k  g1   1  k    1  k 
k  g2
5
5
$5.00(0.90 )   0.90    0.90  $5.00(1  0.04)
P0 
 

1  
0.10  ( 0.10)   1  0.10    1  0.10 
0.10  0.04
 $14.25  $31.78
 $46.03.
• The total 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.
6-18
Example: Using the DDM to Value a Firm
Experiencing “Supernormal” Growth, I.
• Chain Reaction, Inc., has been growing at a phenomenal rate of 30%
per year.
• You believe that this rate will last for only three more years.
• Then, you think the rate will drop to 10% per year.
• Total dividends just paid were $5 million.
• The required rate of return is 20%.
• What is the total value of Chain Reaction, Inc.?
6-19
Example: Using the DDM to Value a Firm
Experiencing “Supernormal” Growth, II.
• First, calculate the total dividends over the “supernormal” growth
period:
Year
Total Dividend: (in $millions)
1
$5.00 x 1.30 = $6.50
2
$6.50 x 1.30 = $8.45
3
$8.45 x 1.30 = $10.985
• Using the long run growth rate, g, the value of all the shares at Time
3 can be calculated as:
P3 = [D3 x (1 + g)] / (k – g)
P3 = [$10.985 x 1.10] / (0.20 – 0.10) = $120.835
6-20
Example: Using the DDM to Value a Firm
Experiencing “Supernormal” Growth, III.
• Therefore, to determine the present value of the firm today, we need
the present value of $120.835 and the present value of the dividends
paid in the first 3 years:
P0 
D3
P3
D1
D2



1  k  1  k 2 1  k 3 1  k 3
$6.50
$8.45
$10.985
$120.835
P0 



1  0.20  1  0.20 2 1  0.20 3 1  0.20 3
 $5.42  $5.87  $6.36  $69.93
 $87.58 million.
6-21
Discount Rates for
Dividend Discount Models
• The discount rate for a stock can be estimated using the capital
asset pricing model (CAPM ).
• We will discuss the CAPM in a later chapter.
• However, we can estimate the discount rate for a stock using this
formula:
Discount rate = time value of money + risk premium
= U.S. T-bill Rate + (Stock Beta x Stock Market 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: risk premium for an average stock
6-22
Observations on Dividend
Discount Models, I.
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.
6-23
Observations on Dividend
Discount Models, II.
Two-Stage Dividend Growth Model:
•
•
•
•
•
More realistic in that it accounts for two stages of growth
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.
6-24
Residual Income Model (RIM), I.
• We have valued only companies that pay dividends.
– But, there are many companies that do not pay dividends.
– What about them?
– It turns out that there is an elegant way to value these
companies, too.
• The model is called the Residual Income Model (RIM).
• Major Assumption (known as the Clean Surplus Relationship, or
CSR): The change in book value per share is equal to earnings per
share minus dividends.
6-25
Residual Income Model (RIM), II.
• Inputs needed:
–
–
–
–
Earnings per share at time 0, EPS0
Book value per share at time 0, B0
Earnings growth rate, g
Discount rate, k
• There are two equivalent formulas for the Residual Income Model:
P0  B 0 
EPS0 (1  g)  B 0  k
kg
or
P0 
BTW, it turns out that the
RIM is mathematically the
same as the constant
perpetual growth model.
EPS1  B 0  g
kg
6-26
Using the Residual Income Model.
• Superior Offshore International, Inc. (DEEP)
• It is July 1, 2007—shares are selling in the market for $10.94.
• Using the RIM:
–
–
–
–
–
EPS0 = $1.20
DIV = 0
B0 = $5.886
g = 0.09
k = .13
• What can we say
about the market
price of DEEP?
P0  B 0 
EPS0  (1  g)  B 0  k
kg
P0  $5.886 
$1.20  (1  .09)  $5.886  .13
.13  .09
P0  $5.886 
$1.308  $.7652
 $19.46.
.04
6-27
DEEP Growth
• Using the information from the previous slide, what growth rate
results in a DEEP price of $10.94?
P0  B 0 
EPS 0  (1  g)  B 0  k
kg
$10.94  $5.886 
$1.20  (1  g)  $5.886  .13
.13  g
$5.054  (.13  g)  1.20  1.20g  .7652
$.6570  5.054g  1.20g  .4348
.2222  6.254g
g  .0355 or 3.55%.
6-28
Price Ratio Analysis, I.
• Price-earnings ratio (P/E ratio)
– Current stock price divided by annual earnings per share (EPS)
• Earnings yield
– Inverse of the P/E ratio: earnings divided by price (E/P)
• High-P/E stocks are often referred to as growth stocks,
while low-P/E stocks are often referred to as value
stocks.
6-29
Price Ratio Analysis, II.
• 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.
6-30
Price Ratio Analysis, III.
• 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.
6-31
Price/Earnings Analysis, Intel Corp.
Intel Corp (INTC) - Earnings (P/E) Analysis
5-year average P/E ratio
Current EPS
EPS growth rate
27.30
$.86
8.5%
Expected stock price = historical P/E ratio  projected EPS
$25.47 = 27.30  ($.86  1.085)
Mid-2007 stock price = $24.27
6-32
Price/Cash Flow Analysis, Intel Corp.
Intel Corp (INTC) - Cash Flow (P/CF) Analysis
5-year average P/CF ratio
Current CFPS
CFPS growth rate
14.04
$1.68
7.5%
Expected stock price = historical P/CF ratio  projected CFPS
$25.36 = 14.04  ($1.68  1.075)
Mid-2007 stock price = $24.27
6-33
Price/Sales Analysis, Intel Corp.
Intel Corp (INTC) - Sales (P/S) Analysis
5-year average P/S ratio
Current SPS
SPS growth rate
4.51
$6.14
7%
Expected stock price = historical P/S ratio  projected SPS
$29.63 = 4.51  ($6.14  1.07)
Mid-2007 stock price = $24.27
6-34
An Analysis of the
McGraw-Hill Company
The next few slides contain a financial
analysis of the McGraw-Hill Company, using
data from the Value Line Investment Survey.
6-35
The McGraw-Hill Company Analysis, I.
6-36
The McGraw-Hill Company Analysis, II.
6-37
The McGraw-Hill Company Analysis, III.
• Based on the CAPM, k = 3.1% + (.80  9%) = 10.3%
• Retention ratio = 1 – $.66/$2.65 = .751
• Sustainable g = .751  23% = 17.27%
• Because g > k, the constant growth rate model cannot be
used. (We would get a value of -$11.10 per share)
6-38
The McGraw-Hill Company Analysis
(Using the Residual Income Model, I)
•
Let’s assume that “today” is January 1, 2008, g = 7.5%, and k = 12.6%.
•
Using the Value Line Investment Survey (VL), we can fill in column two
(VL) of the table below.
•
We use column one and our growth assumption for column three (CSR) of
the table below.
End of 2007
2008 (VL)
NA
$6.50
$6.50
EPS
$3.05
$3.45
$3.2788
DIV
$.82
$.82
$2.7913
Ending BV per share
$6.50
$9.25
$6.9875
Beginning BV per share
2008 (CSR)
3.05  1.075 6.50 1.075
" Plug"  3.2788 - (6.9875 - 6.50)
6-39
The McGraw-Hill Company Analysis
(Using the Residual Income Model, II)
•
Using the CSR assumption:
P0  B 0 
EPS 0  (1  g)  B 0  k
kg
P0  $6.50 
Stock price at the time = $57.27.
What can we say?
•
Using Value Line numbers for
EPS1=$3.45, B1=$9.25
B0=$6.50; and using the actual
change in book value instead of an
estimate of the new book value,
(i.e., B1-B0 is = B0 x k)
$3.05  (1  .075)  $6.50  .126
.126  .075
P0  $54.73.
P0  B 0 
EPS0  (1  g)  B 0  k
kg
P0  $6.50 
$3.45  ($9.25 - 6.50)
.126  .075
P0  $20.23
6-40
The McGraw-Hill Company Analysis, IV.
6-41
Useful Internet Sites
•
•
•
•
•
www.nyssa.org (the New York Society of Security Analysts)
www.aaii.com (the American Association of Individual
Investors)
www.eva.com (Economic Value Added)
www.valueline.com (the home of the Value Line Investment
Survey)
Websites for some companies analyzed in this chapter:
• www.aep.com
• www.americanexpress.com
• www.pepsico.com
• www.intel.com
• www.corporate.disney.go.com
• www.mcgraw-hill.com
6-42
Chapter Review, I.
• 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
6-43
Chapter Review, II.
• The Two-Stage Dividend Growth Model
– Discount Rates for Dividend Discount Models
– Observations on Dividend Discount Models
• Residual Income Model (RIM)
• Price Ratio Analysis
–
–
–
–
–
Price-Earnings Ratios
Price-Cash Flow Ratios
Price-Sales Ratios
Price-Book Ratios
Applications of Price Ratio Analysis
• An Analysis of the McGraw-Hill Company
6-44