Common stock.ppt

Chapter
McGraw-Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved.
6 Common Stock
Valuation

6-2
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.

6-3
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

6-4
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.

6-5
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:
• 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
       T
T
3
3
2
2
1
0
k
1
D
k
1
D
k
1
D
k
1
D
P







 

6-6
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?
     
     
$515.42
0.08
1
$200
0.08
1
$200
0.08
1
$200
P
k
1
D
k
1
D
k
1
D
P
3
2
0
3
3
2
2
1
0














6-7
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:
• For constant dividend growth for “T” years, the DDM formula
becomes:
g
k
if
D
T
P
g
k
if
k
1
g
1
1
g
k
g)
(1
D
P
0
0
T
1
0
























 
g)
(1
g)
(1
D
g)
(1
D
D
So,
g
1
D
D
0
1
2
t
1
t













6-8
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?
  $243.86
1.08
1.10
1
.10
.08
1.10
$10
P
k
1
g
1
1
g
k
g)
(1
D
P
20
0
T
0
0








































6-9
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:
 
k)
g
:
(Important
g
k
D
g
k
g
1
D
P 1
0
0 







6-10
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.
Note: the actual mid-2007 stock price of DTE was $47.81.
What are the possible explanations for the difference?
  $46.01
.02
.067
1.02
$2.12
P0 




6-11
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.

6-12
The Historical Average Growth Rate
• Suppose the Broadway Joe Company paid the following dividends:
– 2002: $1.50 2005: $1.80
– 2003: $1.70 2006: $2.00
– 2004: $1.75 2007: $2.20
• The spreadsheet below shows how to estimate historical average
growth rates, using arithmetic and geometric averages.
Year: Dividend: Pct. Chg:
2007 $2.20 10.00%
2006 $2.00 11.11%
2005 $1.80 2.86% Grown at
2004 $1.75 2.94% Year: 7.96%:
2003 $1.70 13.33% 2002 $1.50
2002 $1.50 2003 $1.62
2004 $1.75
8.05% 2005 $1.89
2006 $2.04
7.96% 2007 $2.20
Arithmetic Average:
Geometric Average:

6-13
The Sustainable Growth Rate
• Return on Equity (ROE) = Net Income / Equity
• Payout Ratio = Proportion of earnings paid out as dividends
• Retention Ratio = Proportion of earnings retained for investment
Ratio)
Payout
-
(1
ROE
Ratio
Retention
ROE
Rate
Growth
e
Sustainabl





6-14
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%

6-15
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%?
• 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?
  $44.96
.03122
.067
1.03122
$1.56
P 



0

6-16
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:
2
2
0
T
1
T
1
1
1
0
g
k
)
g
(1
D
k
1
g
1
k
1
g
1
1
g
k
)
g
(1
D
P































0

6-17
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?

6-18
Using the Two-Stage
Dividend Growth Model, II.
• 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.
$46.03.
$31.78
$14.25
0.04
0.10
0.04)
$5.00(1
0.10
1
0.90
0.10
1
0.90
1
0.10)
(
0.10
)
$5.00(0.90
P
g
k
)
g
(1
D
k
1
g
1
k
1
g
1
1
g
k
)
g
(1
D
P
5
5
2
2
0
T
1
T
1
1
1
0































































0
0

6-19
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.?

6-20
Experiencing “Supernormal” Growth, II.
• First, calculate the total dividends over the “supernormal” growth
period:
• 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
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

6-21
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:
       
       
million.
$87.58
$69.93
$6.36
$5.87
$5.42
0.20
1
$120.835
0.20
1
$10.985
0.20
1
$8.45
0.20
1
$6.50
P
k
1
P
k
1
D
k
1
D
k
1
D
P
3
3
2
3
3
3
3
2
2
1





















0
0

6-22
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

6-23
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.

6-24
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.

6-25
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.

6-26
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:
g
k
g
B
EPS
P
or
g
k
k
B
g)
(1
EPS
B
P
0
1
0
0
0
0
0










BTW, it turns out that the
RIM is mathematically the
same as the constant
perpetual growth model.

6-27
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? $19.46.
.04
$.7652
$1.308
$5.886
P
.09
.13
.13
$5.886
.09)
(1
$1.20
$5.886
P
g
k
k
B
g)
(1
EPS
B
P
0
0
0
0
0
0



















6-28
DEEP Growth
• Using the information from the previous slide, what growth rate
results in a DEEP price of $10.94?
3.55%.
or
.0355
g
6.254g
.2222
.4348
1.20g
5.054g
$.6570
.7652
1.20g
1.20
g)
(.13
$5.054
g
.13
.13
$5.886
g)
(1
$1.20
$5.886
$10.94
g
k
k
B
g)
(1
EPS
B
P 0
0
0
0

























6-29
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.

6-30
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.

6-31
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.

6-32
Price/Earnings Analysis, Intel Corp.
Intel Corp (INTC) - Earnings (P/E) Analysis
5-year average P/E ratio 27.30
Current EPS $.86
EPS growth rate 8.5%
Expected stock price = historical P/E ratio  projected EPS
$25.47 = 27.30  ($.86  1.085)
Mid-2007 stock price = $24.27

6-33
Price/Cash Flow Analysis, Intel Corp.
Intel Corp (INTC) - Cash Flow (P/CF) Analysis
5-year average P/CF ratio 14.04
Current CFPS $1.68
CFPS growth rate 7.5%
Expected stock price = historical P/CF ratio  projected CFPS
$25.36 = 14.04  ($1.68  1.075)

6-34
Price/Sales Analysis, Intel Corp.
Intel Corp (INTC) - Sales (P/S) Analysis
5-year average P/S ratio 4.51
Current SPS $6.14
SPS growth rate 7%
Expected stock price = historical P/S ratio  projected SPS
$29.63 = 4.51  ($6.14  1.07)

6-35
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.

6-36
The McGraw-Hill Company Analysis, I.

6-37
The McGraw-Hill Company Analysis, II.

6-38
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)

6-39
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) 2008 (CSR)
Beginning BV per share 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
1.075
3.05 1.075
6.50
6.50)
-
(6.9875
-
3.2788
Plug"
" 

6-40
The McGraw-Hill Company Analysis
(Using the Residual Income Model, II)
• Using the CSR assumption:
• 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)
$54.73.
P
.075
.126
.126
$6.50
.075)
(1
$3.05
$6.50
P
g
k
k
B
g)
(1
EPS
B
P
0
0
0
0
0
0















$20.23
P
.075
.126
6.50)
-
($9.25
$3.45
$6.50
P
g
k
k
B
g)
(1
EPS
B
P
0
0
0
0
0
0












Stock price at the time = $57.27.
What can we say?

6-41
The McGraw-Hill Company Analysis, IV.

6-42
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

6-43
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

6-44
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

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