Chapter 7
Common Stock
Valuation
CHAPTER OUTLINE
• Security analysis
• The dividend discount model
• The two-stage dividend growth model
• The residual Income Model
• Price ratio analysis
• An analysis of McGraw-Hill Company
© 2009 McGraw-Hill Ryerson
Limited
7-1

 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.
© 2009 McGraw-Hill Ryerson
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7-2

 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 DDM equation is:

V(0)


D(1)
1
 k
 
1
D(2)
 k
 
1
D(3)
 k

3
 

1
D(T)
 k

T
In the DDM equation:
 V (0) = the present value of all future dividends


D (t) = the dividend to be paid t years from now k = the appropriate risk-adjusted discount rate
© 2009 McGraw-Hill Ryerson
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7-3

 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?
V(0)


D(1)
1
 k
 
1
D(2)
 k
 
1
D(3)
 k

3
V(0)


1
$200

0.08
 
1

$200
0.08
 
1

$200
0.08

3

$515.42
© 2009 McGraw-Hill Ryerson
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7-4

 Assume that the dividends will grow at a constant growth rate g.
 Then, the dividend next period (t + 1) is:
D
 t

1


D
 


1
 g

 In this case, the DDM formula becomes:
V(0)

D(0)(1
 k
 g g)




1

1

1
 g k
T



 if k
 g
V(0)

T

D(0) if k
 g
© 2009 McGraw-Hill Ryerson
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7-5

 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?
V(0)

D(0)(1
 k
 g g)




1

1

1
 g k
T



 if k
 g
V

$10
.08



1.10
.10





1

1.10
1.08
20 



$243.86
© 2009 McGraw-Hill Ryerson
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7-6

 Assuming that the dividends will grow forever at a constant growth rate g.
 In this case, the DDM formula becomes:
V

D
   k

1 g
 g

 k
D

  g g
 k
© 2009 McGraw-Hill Ryerson
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7-7

 Think about the electric utility industry.
 In mid-year, the dividend paid by the utility company,
American Electric Power (AEP), was $1.40.
 Using D(0)=$1.40, k = 7.3%, and g = 1.5%, calculate an estimated value for AEP.
V

$1.40
.073



1.015

.015

$24.50
 Note: the actual mid-year stock price of AEP was
$38.80.
What are the possible explanations for the difference?
© 2009 McGraw-Hill Ryerson
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7-8


g

Using the company’s historical average growth rate.
 Using an industry median or average growth rate.
 Using the sustainable growth rate .
© 2009 McGraw-Hill Ryerson
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7-9

 Suppose the Broadway Joe Company paid the following dividends:



2005: $1.50
2006: $1.70
2008: $1.80
2009: $2.00

2007: $1.75
2010: $2.20
The spreadsheet below shows how to estimate historical average growth rates, using arithmetic and geometric averages.
Year:
2010
2009
2008
2007
2006
2005
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:
Geometric Average:
8.05%
7.96%
Year:
2005
2006
2007
2008
2009
2010
Grown at
7.96%:
$1.50
$1.62
$1.75
$1.89
$2.04
$2.20
10

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
© 2009 McGraw-Hill Ryerson
Limited
7-11



In 2011, American Electric Power (AEP) had an ROE of 14.59%, projected earnings per share of $2.94, and a per-share dividend of $1.40. What was AEP’s:


Retention rate?
Sustainable growth rate?
Payout ratio = $1.40 / $2.94 = .476
So, retention ratio = 1 – .476 = .524 or 52.4%

Therefore, AEP’s sustainable growth rate = .1459 
52.4% = 7.645%
© 2009 McGraw-Hill Ryerson
Limited
7-12



What is the value of AEP stock, using the perpetual growth model, and a discount rate of 8.3%?
The actual stock price of AEP was $38.80.
V

$1.40
.083



1.07645
.07645


$ 230

$38.80


In this case, using the sustainable growth rate to value the stock gives a reasonably poor estimate.
What can we say about g and k in this example?
© 2009 McGraw-Hill Ryerson
Limited
7-13




To estimate a sustainable growth rate, you need the (relatively stable) dividend payout ratio and ROE.
Changes in sustainable growth rate likely stem from changes in ROE.
The DuPont formula separates ROE into three parts ( profit margin , asset turnover, equity multiplier )
Net Income
Equity

ROE

Net Income
Sales

Sales
Assets

Assets
Equity
 Managers can increase the sustainable growth rate by:
 Decreasing the dividend payout ratio

Increasing profitability ( Net Income / Sales )


Increasing asset efficiency ( Sales / Assets )
Increasing debt ( Assets / Equity )
14



The two-stage dividend growth model assumes that a firm will initially grow at a rate g
1 g
2 for T years, and thereafter grow at a rate
< k during a perpetual second stage of growth.
The Two-Stage Dividend Growth Model formula is:
V ( 0 )

D ( 0 k
)( 1

 g
1 g
1
)




1

1

1
 g
1 k
T




1

1
 g
1 k
T
D ( 0 k
)( 1

 g
2 g
2
)
 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.
© 2009 McGraw-Hill Ryerson
Limited
7-15

So, suppose Molly.com has D(0) = $5, which is expected to “shrink” at the rate g
1
= -10% for 5 years, but grow at the rate g
2
= 4% forever.
With a discount rate of k = 10%, what is the present value of the stock?
V(0)

D(0)(1 k

 g
1 g
1
)

 1


1

1
 g
1 k
T



V(0)

$5.00(0.90
0.10

(

)
0.10)

 1


1
0.90

0.10

$14.25

$31.78

$46.03

1

1

5



 g
1 k
T
D(0)(1 k
0.90
1

0.10

5
 g
2 g
2
)
$5.00(1
0.10


0.04)
0.04
 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 .
7-16




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.?
First, calculate the total dividends over the “supernormal” growth period:
Year
1
2
3
Total Dividend: (in $millions)
$5.00 x 1.30 = $6.50
$6.50 x 1.30 = $8.45
$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:
V(3) = [D(3) x (1 + g)] / (k – g)
V(3) = [$10.985 x 1.10] / (0.20 – 0.10) = $120.835
7-17

 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:
V(0)


D(1)
1
 k
 
D(2)
1
 k

2


1
D(3)
 k

3


1
V(3)
 k

3
V(0)


1
$6.50

0.20
 
1
$8.45

0.20

2


1
$10.985

0.20

3


$120.835
1

0.20

3

$5.42

$5.87

$6.36

$69.93

$87.58
million.
7-18



 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 the following formula:
 Discount rate = time value of money + risk premium
= T-bill rate + (stock beta x stock market risk premium)
T-bill rate: return on 90-day T-bills
Stock Beta: Risk relative to an average stock
Stock Market Risk Premium: Risk premium for an average stock
© 2009 McGraw-Hill Ryerson
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7-19

•
•
•
•
•
•
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.
© 2009 McGraw-Hill Ryerson
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7-20

•
•
•
•
•
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.
© 2009 McGraw-Hill Ryerson
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7-21

 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.
© 2009 McGraw-Hill Ryerson
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7-22

 Inputs needed:



Earnings per share at time 0, EPS
0
Book value per share at time 0, B
0
Earnings growth rate, g
 Discount rate, k
 There are two equivalent formulas for the Residual
Income Model:
P
0

B
0

EPS
0
(1
 k g)
 g

B
0
 k or
BTW, it turns out that the
RIM is mathematically the same as the constant perpetual growth model.
P
0

EPS
1 k

B
0
 g
 g
© 2009 McGraw-Hill Ryerson
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7-23

 National Beverage Corporation (FIZ)
 It is July 1, 2005—shares are selling in the market for $7.98.
 Using the RIM:


EPS
0
=$0.47
DIV = 0


B
0
=$4.271
g = 0.09

K = .103
What can we say about the market price of FIZ?
P
0

B
0

EPS
0

(1 k

 g)

B
0 g
 k
P
0

$4.271

$.47

(1

.09)

$4.271

.103
.103

.09
P
0

$4.271

$5.57

$9.84.
© 2009 McGraw-Hill Ryerson
Limited
7-24

 Using the information from the previous slide, what growth rate results in a FIZ price of $7.98?
P
0

B
0
$7.98
$3.709



EPS
$4.271
(.103
0


(1
 k
 g) g
 g)

.47


B
0

.47g
k
$.47

(1
 g)

.103
$4.271

.103
 g

.4399
$.3820
.3519


3.709g
4.179g
g

.47g

.0842
or 8.42%.

.0301
7-25


We can value companies that do not pay dividends using the residual income model.

Note: We assume positive earnings when we use the residual income model.

But, there are companies that do not pay dividends and have negative earnings.

Negative earnings = little value?

We calculate earnings based on accounting rules and tax codes.

It is possible that a company has:
 negative earnings
 positive cash flows
 a positive value.
26


Depreciation—the key to understand how a company can have negative earnings and positive cash flows

Depreciation reduces earnings because it is counted as an expense (more expenses = lower taxes paid).

Most stock analysts, however, use a relatively simple formula to calculate
Free Cash Flow, FCF:
FCF = Net Income + Depreciation – Capital Spending
 We can see that it is possible for: Net Income < 0 and FCF > 0

Depreciation and Capital Spending matter in FCF.
27


The DDMs calculate a value of the equity only.



DDMs use dividends, a cash flow only to equity holders
DDMs use the CAPM to estimate required return
DDMs use an equity beta to account for risk

Using the FCF model, we calculate a value for the firm.

Free cash flow can be paid to debt holders and to stockholders.


We can still calculate the value of equity using FCF

Calculate the value of the entire firm

Subtract out the value of debt
We need a beta for assets, not the equity, to account for risk
28




Asset betas measure the risk of the company’s industry.

Firms in an industry should have about the same asset betas.

Their equity betas, however, could be quite different.
 Investors can increase portfolio risk by using margin (i.e., borrowing money to buy stock).

A business can increase risk by using debt.
So, to value the company, we must “convert” reported equity betas into asset betas by adjusting for leverage.
The following conversion formula is widely used:
B
Equity

B
Asset

[1

Debt
Equity
(1
 t )]

What happens when a firm has no debt?
tax rate.
29


Inputs

An estimate of FCF:







Net Income
Depreciation

Capital Expenditures
The growth rate of FCF
The proper discount rate
Tax rate
Debt/Equity ratio
Equity beta

Calculate value using a “DDM” formula

“DDM” because we are using FCF, not dividends.
30


An estimate of FCF:





Net Income: $25 million
Depreciation: $10 million
Capital Expenditures: $3 million
Assume:
No dividends
Risk-free rate = 4%
Market risk premium = 7%
Growth rate of FCF: 3%
Tax rate: 35% Using Basic DDM :


Debt/Equity ratio: .40
Equity beta: 1.2
London Air Value

(25

10 3)

(1.03)
.1065
.03

$430.85
million

Asset Beta:
1.2 = B
Asset x [1+.4 x (1-.35)]
1.2 = B
Asset x 1.26
B
Asset
= 0.95
If London Air has $100 million in debt, the value of the equity is $330.85
million.
Value per share

$330.85
million / number of shares.
 The proper discount rate: k = 4.00 + (7.00 × 0.95) = 10.65%
31








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 .
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.
7-32

 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.
© 2009 McGraw-Hill Ryerson
Limited
7-33

Intel Corp (INTC) - Earnings (P/E) Analysis
P/E P/CF P/S
5-year average Price ratio 37.30
19.75
6.77
Current EPS, CFPS, SPS
Expected stock price = historical Price ratio
 projected EPS,CFPS,SPS
Mid-2005 stock price =
$1.16
$50.84
=37.30

($1.16

1.175)
$26.50
$1.94
Intel Corp (INTC) - Earnings (P/E) Analysis
EPS, CFPS, SPS growth rate 17.5% 13.50%
$5.47
10.50%
$43.49
= 19.75

($1.94

1.135)
$26.50
$40.92
= 6.77

($5.47

1.105)
$26.50
© 2009 McGraw-Hill Ryerson
Limited
7-34

Figure 7.2
The next few slides contain a financial analysis of the
McGraw-Hill
Company, using data from the
Value Line
Investment
Survey.
7-35

 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)
© 2009 McGraw-Hill Ryerson
Limited
7-36



Let’s assume that “today” is January 1, 2005, g = 7%, and k
= 10.3%.
Using the Value Line Investment Survey (VL), we can fill in column two (VL) of the table below.
Beginning BV per share
EPS
DIV
Ending BV per share
2005 (time 0)
NA
2006 (VL)
9.45
2006 (CSR)
9.45
2.25
0.66
9.45
2.65
0.66
11.50
2.4075
1.7460
10.1115
2.25

1.07
9.45

1.07
© 2009 McGraw-Hill Ryerson
Limited
" Plug"

2.4075
(10.1115
-
7-37
9.45)

 Using the CSR assumption:
Stock price at the time = $47.04.
What can we say?
P
0

B
0

EPS
0

(1 k

 g)

B
0 g
 k
P
0

$9.45

$2.25

(1

.07)

$9.45

.103
.103

.07
P
0

$52.91.

Using Value Line numbers for
EPS
1
B
0
=$2.65, B
1
=$11.50
=$9.45; and using the actual change in book value instead of an estimate of the new book value, (i.e., B
1
-B
0 is = B
0 x k)
P
0

B
0

EPS
0

(1
 g)

B
0 k
 g
 k
P
0

$9.45

$2.65

($11.50
.103

.07
9.45)
P
0

$27.63
7-38

Quick calculations used: P/CF = P/E

EPS/CFPS
P/S = P/E

EPS/SPS
Table 7.4
© 2009 McGraw-Hill Ryerson
Limited
7-39

•
• www.nyssa.org
(the New York Society of Security Analysts) www.valueline.com
(the home of the Value Line Investment Survey)
• Websites for the companies analyzed in this chapter:
•
• www.aep.com
www.americanexpress.com
•
•
• www.pepsico.com
www.starbucks.com
www.sears.com
•
•
• www.intel.com
www.disney.go.com
www.mcgraw-hill.com
© 2009 McGraw-Hill Ryerson
Limited
7-40