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Securities Analysis, Section IV
Security Valuation
&
EIC Analysis
(Part 2)
Lecture Presentation Software
to accompany
Investment Analysis and
Portfolio Management
Sixth Edition
by
Frank K. Reilly & Keith C. Brown
Chapters 11,14,15, & 18
Top-Down Approach, Step Three
• Company and Stock Analysis
Copyright © 2000 by Harcourt, Inc. All rights reserved
Company Analysis and Stock Selection
• After analyzing the economy and stock markets
for several countries you have decided to invest
some portion of your portfolio in common stocks
• After analyzing various industries, you have
identified those industries that appear to offer
above-average risk-adjusted performance over
your investment horizon
• Which are the best companies?
• Are they overpriced?
Copyright © 2000 by Harcourt, Inc. All rights reserved
Company Analysis and Stock Selection
• Good companies are not necessarily good
investments
• Compare the intrinsic value of a stock to its
market value
• Stock of a great company may be overpriced
• Stock of a growth company may not be growth
stock
Copyright © 2000 by Harcourt, Inc. All rights reserved
Types of Companies and Stocks
•
•
•
•
Growth
Defensive
Cyclical
Speculative
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Growth Companies
• Growth companies have historically been
defined as companies that consistently
experience above-average increases in sales
and earnings
• Financial theorists define a growth company
as one with management and opportunities
that yield rates of return greater than the
firm’s required rate of return
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Growth Stocks
• Growth stocks are not necessarily shares in
growth companies
• A growth stock has a higher rate of return
than other stocks with similar risk
• Superior risk-adjusted rate of return occurs
because of market undervaluation compared
to other stocks
Copyright © 2000 by Harcourt, Inc. All rights reserved
Value versus Growth Investing
• Growth stocks will have positive
earnings surprises and above-average
risk adjusted rates of return because the
stocks are undervalued
• Value stocks appear to be undervalued
for reasons besides earnings growth
potential
• Value stocks usually have low P/E ratio
or low ratios of price to book value
Copyright © 2000 by Harcourt, Inc. All rights reserved
Value versus Growth Investing
• Buffett’s view:
– Growth is a key determinant of value for any
stock, so it is always a component of determining
whether or not a stock is undervalued
– Furthermore, so long as the market is undervaluing a stock, then he would categorize it as a
“value” stock
– Finally, he considers all investing to be “value”
investing
– Thus, he considers “value” vs. “growth” investing
to be a false dichotomy
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Defensive Companies and Stocks
• Defensive companies’ future earnings are
more likely to withstand an economic
downturn
• Low business risk
• Not excessive financial risk
• Stocks with low or negative systematic risk
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Cyclical Companies and Stocks
• Sales and earnings heavily influenced by
aggregate business activity
• Stocks with high betas
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Speculative Companies and Stocks
• Assets involve great risk
– e.g., biotechs, bankruptcies, etc.
• Can be viewed as a gamble
– Possible great gain
– Stock may be overpriced
Copyright © 2000 by Harcourt, Inc. All rights reserved
Economic, Industry, and Structural
Links to Company Analysis
• Company analysis is the final step in the topdown approach to investing
• Macroeconomic analysis identifies industries
expected to offer attractive returns in the
expected future environment
• Analysis of firms in selected industries
concentrates on a stock’s intrinsic value
based on growth and risk
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Economic and Industry Influences
• If trends are favorable for an industry, the
company analysis should focus on firms in that
industry that are positioned to benefit from the
economic trends
• Firms with sales or earnings particularly sensitive
to macroeconomic variables should also be
considered
• Research analysts need to be familiar with the
cash flow and risk of the firms
Copyright © 2000 by Harcourt, Inc. All rights reserved
Structural Influences
• Social trends, technology, political, and
regulatory influences can have significant
influence on firms
• Early stages in an industry’s life cycle see
changes in technology that followers may
imitate and benefit from
• Politics and regulatory events can create
opportunities even when economic
influences are weak
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Company Analysis
•
•
•
•
Industry competitive environment
SWOT analysis
Present value of cash flows
Relative valuation ratio techniques
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Firm Competitive Strategies
•
•
•
•
•
Current rivalry
Threat of new entrants
Potential substitutes
Bargaining power of suppliers
Bargaining power of buyers
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Firm Competitive Strategies
• Defensive or offensive
• Defensive strategy deflects competitive
forces in the industry
• Offensive competitive strategy affects
competitive force in the industry to
improve the firm’s relative position
• Porter suggests two major strategies: lowcost leadership and differentiation
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Low-Cost Strategy
• Seeks to be the low cost leader in its
industry
– Through economies of scale (in production or
marketing), better logistics, etc.
• Must still command prices near industry
average, so still must differentiate
• Discounting too much erodes superior
rates of return
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Differentiation Strategy
• Identify as unique in its industry in
an area that is important to buyers
• Above average rate of return only
comes if the price premium
exceeds the extra cost of being
unique
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Focusing a Strategy
• Select segments in the industry
• Tailor strategy to serve those specific
groups
• Determine which strategy a firm is
pursuing and its success
• Evaluate the firm’s competitive
strategy over time
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SWOT Analysis
• Examination of a firm’s:
– Strengths
– Weaknesses
– Opportunities
– Threats
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SWOT Analysis
• Examination of a firm’s:
– Strengths
– Weaknesses
– Opportunities
– Threats
INTERNAL ANALYSIS
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SWOT Analysis
• Examination of a firm’s:
– Strengths
– Weaknesses
– Opportunities
– Threats
EXTERNAL ANALYSIS
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Lynch’s Favorable Attributes
1. Firm’s product is not faddish
2. Company has competitive advantage over
rivals
3. Industry or product has potential for market
stability
4. Firm can benefit from cost reductions
5. Firm is buying back its own shares or
managers (insiders) are buying
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Lynch’s Categories of Companies
1. Slow growers
2. Stalwart
3. Fast growers
4. Cyclicals
5. Turnarounds
6. Asset plays
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Approaches to the
Valuation of Common Stock
Two general approaches have developed:
1. Discounted cash-flow valuation
•
Present value of some measure of cash flow, such
as dividends, operating cash flow, and free cash
flow
2. Relative valuation technique
•
Value estimated based on its price relative to
significant variables, such as earnings, cash flow,
book value, or sales
Copyright © 2000 by Harcourt, Inc. All rights reserved
Approaches to the
Valuation of Common Stock
These two approaches have some factors in
common
• Both are affected by:
–
–
–
–
Investor’s required rate of return
kV
Estimated growth rate of the variable used
gV
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Valuation Approaches
and Specific Techniques
Approaches to Equity Valuation
Discounted Cash Flow
Techniques
Relative Valuation
Techniques
• Present Value of Dividends (DDM)
• Price/Earnings Ratio (PE)
•Present Value of Operating Cash Flow
•Price/Cash flow ratio (P/CF)
•Present Value of Free Cash Flow
•Price/Book Value Ratio (P/BV)
•Price/Sales Ratio (P/S)
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Why and When to Use the Discounted
Cash Flow Valuation Approach
• The measure of cash flow used
– Dividends
• Cost of equity as the discount rate
– Operating cash flow
• Weighted Average Cost of Capital (WACC)
– Free cash flow to equity
• Cost of equity
• Dependent on growth rates and discount
rate
Copyright © 2000 by Harcourt, Inc. All rights reserved
Why and When to Use the
Relative Valuation Techniques
• Provides information about how the market is
currently valuing stocks
– aggregate market
– alternative industries
– individual stocks within industries
• No guidance as to whether valuations are
appropriate; best used when:
– have comparable entities
– aggregate market is not at a valuation extreme
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Discounted Cash-Flow
Valuation Techniques

CFt
Vj  
t
t 1 (1  k )
Where:
Vj = value of stock j
n = life of the asset
CFt = cash flow in period t
k = the discount rate that is equal to the investor’s required rate
of return for asset j, which is determined by the uncertainty
(risk) of the stock’s cash flows
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The Dividend Discount Model
(DDM)
The value of a share of common stock is the
present value of all future dividends
D3
D1
D2
D
Vj 


 ... 
2
3
(1  k ) (1  k ) (1  k )
(1  k ) 

Dt

t
(
1

k
)
t 1
Where:
Vj = value of common stock j
Dt = dividend during time period t
k = required rate of return on stock j
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The Dividend Discount Model
(DDM)
If the stock is not held for an infinite period, a
sale at the end of year 2 would imply:
SPj 2
D1
D2
Vj 


2
(1  k ) (1  k )
(1  k ) 2
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The Dividend Discount Model
(DDM)
If the stock is not held for an infinite period, a
sale at the end of year 2 would imply:
SPj 2
D1
D2
Vj 


2
(1  k ) (1  k )
(1  k ) 2
Selling price at the end of year two is the
value of all remaining dividend payments,
which is simply an extension of the original
equation
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The Dividend Discount Model
(DDM)
Stocks with no dividends are expected to start
paying dividends at some point else they
would not have any value!
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The Dividend Discount Model
(DDM)
Stocks with no dividends are expected to start
paying dividends at some point, say year
three...
D3
D1
D2
D
Vj 


 ... 
2
3
(1  k ) (1  k )
(1  k )
(1  k ) 
Where:
D1 = 0
D2 = 0
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The Dividend Discount Model
(DDM)
Infinite period model assumes a constant
growth rate for estimating future dividends
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The Dividend Discount Model
(DDM)
Infinite period model assumes a constant
growth rate for estimating future dividends
D0 (1  g ) D0 (1  g )
D0 (1  g )
Vj 

 ... 
2
n
(
1

k
)
(
1

k
)
(
1

k
)
Where:
2
Vj = value of stock j
D0 = dividend payment in the current period
g = the constant growth rate of dividends
k = required rate of return on stock j
n = the number of periods, which we assume to be infinite
Copyright © 2000 by Harcourt, Inc. All rights reserved
n
The Dividend Discount Model
(DDM)
Infinite period model assumes a constant
growth rate for estimating future dividends
D0 (1  g ) D0 (1  g )
D0 (1  g )
Vj 

 ... 
2
(1  k )
(1  k )
(1  k ) n
D1
Vj 
This can be reduced to:
kg
2
1. Estimate the required rate of return (k)
2. Estimate the dividend growth rate (g)
Copyright © 2000 by Harcourt, Inc. All rights reserved
n
Infinite Period DDM
and Growth Companies
Assumptions of DDM:
1. Dividends grow at a constant rate
2. The constant growth rate will continue for
an infinite period
3. The required rate of return (k) is greater
than the infinite growth rate (g)
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Infinite Period DDM
and Growth Companies
Growth companies have opportunities to earn
return on investments greater than their required
rates of return
To exploit these opportunities, these firms
generally retain a high percentage of earnings for
reinvestment, and their earnings grow faster than
those of a typical firm
This is inconsistent with the infinite period DDM
assumptions
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Infinite Period DDM
and Growth Companies
The infinite period DDM assumes constant
growth for an infinite period, but
abnormally high growth usually cannot be
maintained indefinitely
Risk and growth are not necessarily related
Temporary conditions of high growth cannot
be valued using the CGR-DDM
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Valuation with Temporary
Supernormal Growth
Combine the models to evaluate the years of
supernormal growth and then use DDM to
compute the remaining years at a
sustainable rate
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Valuation with Temporary
Supernormal Growth
Combine the models to evaluate the years of
supernormal growth and then use DDM to
compute the remaining years at a
sustainable rate
For example:
With a 14 percent required rate of return, a
most recently paid dividend of $2.00 per
share, and dividend growth of:
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Valuation with Temporary
Supernormal Growth
Year
1-3:
4-6:
7-9:
10 on:
Dividend
Growth Rate
25%
20%
15%
9%
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Valuation with Temporary
Supernormal Growth
The value equation becomes
2.00(1.25) 2.00(1.25) 2 2.00(1.25) 3
Vi 


2
1.14
1.14
1.14 3
2.00(1.25) 3 (1.20) 2.00(1.25) 3 (1.20) 2


4
1.14
1.14 5
2.00(1.25) 3 (1.20) 3 2.00(1.25) 3 (1.20) 3 (1.15)


6
1.14
1.14 7
2.00(1.25) 3 (1.20) 3 (1.15) 2 2.00(1.25) 3 (1.20) 3 (1.15) 3


8
1.14
1.14 9
2.00(1.25) 3 (1.20) 3 (1.15) 3 (1.09)
(.14  .09)

(1.14) 9
Copyright © 2000 by Harcourt, Inc. All rights reserved
Computation of Value for Stock of Company
with Temporary Supernormal Growth
Year
Dividend
1
2
3
4
5
6
7
8
9
10
$
2.50
3.13
3.91
4.69
5.63
6.76
7.77
8.94
10.28
11.21
$ 224.20
Discount
Present
Growth
Factor
Value
Rate
0.8772
0.7695
0.6750
0.5921
0.5194
0.4556
0.3996
0.3506
0.3075
a
0.3075
$
$
$
$
$
$
$
$
$
b
2.193
2.408
2.639
2.777
2.924
3.080
3.105
3.134
3.161
25%
25%
25%
20%
20%
20%
15%
15%
15%
9%
$ 68.943
$ 94.365
a
Value of dividend stream for year 10 and all future dividends, that is
$11.21/(0.14 - 0.09) = $224.20
b
The discount factor is the ninth-year factor because the valuation of the
remaining stream is made at the end of Year 9 to reflect the dividend in
Year 10 and all future dividends.
Copyright © 2000 by Harcourt, Inc. All rights reserved
Present Value of
Operating Cash Flows
• 2nd DCF method
Derive the value of the total firm by
discounting the total operating cash flows
prior to the payment of interest to the debtholders
Then subtract the value of debt to arrive at an
estimate of the value of the equity
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Present Value of
Operating Cash Flows
n
OCFt
Vj  
t
t 1 (1  WACC j )
Where:
Vj = value of firm j
n = number of periods; assumed to be infinite
OCFt = the firms operating cash flow in period t
WACC = firm j’s weighted average cost of capital
(OCF and WACC to be discussed in Chapter 20)
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Present Value of
Operating Cash Flows
Similar to DDM, this model can be used to
estimate an infinite period
Where growth has matured to a stable rate, the
adaptation is
Where:
OCF1
Vj 
WACC j  gOCF
OCF1=operating cash flow in period 1
gOCF = long-term constant growth of operating cash flow
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Present Value of
Operating Cash Flows
• Assuming several different rates of growth
for OCF, these estimates can be divided into
stages as with the supernormal dividend
growth model
• Estimate the rate of growth and the duration
of growth for each period
• This will be demonstrated later
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Present Value of
Free Cash Flows to Equity
• 3rd DCF method
• “Free” cash flows to equity are derived after
operating cash flows have been adjusted for
debt payments (interest and principle)
• The discount rate used is the firm’s cost of
equity (k) rather than WACC
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Follow the Cash
Free cash flow to equity defined
• Volume
• Pricing
• Expenses
• Leases
• Tax Provision
• Deferred Taxes
• Tax Shield
Sales
Operating
Margin
Cash
Earnings
Cash
Taxes
minus
• A/R
• Inventories
• A/P
• Net PP&E
•Operating
Leases
DWorking
Capital
Capital
Expenditures
Acquisitions/
Divestitures
Free Cash Flow
Cash available
for distribution to
all claimholders
Investment
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Present Value of
Free Cash Flows to Equity

FCFt
Vj  
t
(
1

k
)
t

1
j
Where:
Vj = Value of the stock of firm j
n = number of periods assumed to be infinite
FCFt = the firm’s free cash flow in period t
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Relative Valuation Techniques
• Value can be determined by comparing to similar
stocks based on relative ratios
• Relevant variables include earnings, cash flow,
book value, and sales
• Multiply this variable by some “capitalization
factor”
• The most popular relative valuation technique is
based on price to earnings (the P/E approach)
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Earnings Multiplier Model
• This values the stock based on expected
annual earnings
• The price earnings (P/E) ratio, or
Earnings Multiplier
Current Market Price

Expected Twelve - Month Earnings
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Earnings Multiplier Model
The infinite-period dividend discount model
indicates the variables that should determine
the value of the P/E ratio
D1
Pi 
kg
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Earnings Multiplier Model
The infinite-period dividend discount model
indicates the variables that should determine
the value of the P/E ratio
D1
Pi 
kg
Dividing both sides by expected earnings
during the next 12 months (E1)
Pi
D1 / E1

E1
kg
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Earnings Multiplier Model
Thus, the P/E ratio is determined by
– 1. Expected dividend payout ratio
– 2. Required rate of return on the stock (k)
– 3. Expected growth rate of dividends (g)
Pi
D1 / E1

E1
kg
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Earnings Multiplier Model
As an example, assume:
–
–
–
–
Dividend payout = 50%
Required return = 12%
Expected growth = 8%
D/E = .50; k = .12; g=.08
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Earnings Multiplier Model
As an example, assume:
–
–
–
–
Dividend payout = 50%
Required return = 12%
Expected growth = 8%
D/E = .50; k = .12; g=.08
.50
P/E 
.12 - .08
 .50/.04
 12.5
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Earnings Multiplier Model
A small change in either or both k or g can
have a large impact on the multiplier
Pi
D1 / E1

E1
kg
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Earnings Multiplier Model
A small change in either or both k or g can
have a large impact on the multiplier
D/E = .50; k=.13; g=.08
Pi
D1 / E1

E1
kg
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Earnings Multiplier Model
A small change in either or both k or g can
have a large impact on the multiplier
D/E = .50; k=.13; g=.08
P/E = .50/(.13-/.08) = .50/.05 = 10
Pi
D1 / E1

E1
kg
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Earnings Multiplier Model
A small change in either or both k or g can
have a large impact on the multiplier
D/E = .50; k=.13; g=.08
P/E = 10
Pi
D1 / E1

E1
kg
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Earnings Multiplier Model
A small change in either or both k or g can
have a large impact on the multiplier
D/E = .50; k=.13; g=.08
P/E = 10
D/E = .50; k=.12; g=.09
P/E = 16.7
D/E = .50; k=.11; g=.09
P/E = 25
Pi
D1 / E1

E1
kg
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Earnings Multiplier Model
small change in either or both k or g can
have a large impact on the multiplier
D/E = .50; k=.12; g=.09
P/E = 16.7
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Valuation Using the
Earnings Multiplier Model
Given current earnings of $2.00 and growth of
9%
You would expect E1 to be $2.18
D/E = .50; k=.12; g=.09
P/E = 16.7
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Valuation Using the
Earnings Multiplier Model
Given current earnings of $2.00 and growth of
9%
You would expect E1 to be $2.18
D/E = .50; k=.12; g=.09
P/E = 16.7
V = 16.7 x $2.18 = $36.41
Compare this estimated value to market price
to decide if you should invest in it
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The Price-Cash Flow Ratio
•
•
•
•
2nd relative valuation approach
Companies can manipulate earnings
Cash-flow is less prone to manipulation
Cash-flow is important for fundamental
valuation and in credit analysis
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The Price-Cash Flow Ratio
• Companies can manipulate earnings
• Cash-flow is less prone to manipulation
• Cash-flow is important for fundamental
valuation and in credit analysis
Pt
P / CFi 
CFt 1
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The Price-Cash Flow Ratio
• Companies can manipulate earnings
• Cash-flow is less prone to manipulation
• Cash-flow is important for fundamental
valuation and in credit analysis
Pt
P / CFi 
CFt 1
Where:
P/CFj = the price/cash flow ratio for firm j
Pt = the price of the stock in period t
CFt+1 = expected cash low per share for firm j
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The Price-Book Value Ratio
• 3rd relative valuation approach
Widely used to measure bank values (most
bank assets are liquid (bonds and
commercial loans)
Fama and French study indicated inverse
relationship between P/BV ratios and excess
return for a cross section of stocks
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The Price-Book Value Ratio
Pt
P / BV j 
BVt 1
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The Price-Book Value Ratio
Pt
P / BV j 
BVt 1
Where:
P/BVj = the price/book value for firm j
Pt = the end of year stock price for firm j
BVt+1 = the estimated end of year book value
per share for firm j
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The Price-Book Value Ratio
• Be sure to match the price with either a
recent book value number, or estimate the
book value for the subsequent year
• Can derive an estimate based upon
historical growth rate for the series or use
the growth rate implied by the (ROE) X
(Ret. Rate) analysis
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The Price-Sales Ratio
• 4th relative valuation approach
• Strong, consistent growth rate is a
requirement of a growth company
• Sales is less subject to manipulation than
other financial data
• Popularized by Ken Fisher
Copyright © 2000 by Harcourt, Inc. All rights reserved
The Price-Sales Ratio
Pt
P

S St 1
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The Price-Sales Ratio
Where:
Pj
Sj
Pt
P

S St 1
 price to sales ratio for firm j
Pt  end of year stock price for firm j
St 1  annual sales per share for firm j during Year t
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The Price-Sales Ratio
Match the stock price with recent annual
sales, or future sales per share
This ratio varies dramatically by industry
Profit margins also vary by industry
Relative comparisons using P/S ratio should
be between firms in similar industries
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Estimating the Inputs: The Required Rate of
Return and The Expected Growth Rate of
Valuation Variables
Valuation procedure is the same for securities
around the world, but the required rate of
return (k) and expected growth rate of
earnings and other valuation variables (g)
such as book value, cash flow, and dividends
differ among countries
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Required Rate of Return (k)
• Required rate of return on equity (ke) affects
valuation, regardless of approach:
– kV , and vice versa
• This required rate of return will be used as the
discount rate and also affects relative-valuation
• Although ke is not directly used in the present
value of operating cash flow approach, it is
nonetheless a component of WACC
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Required Rate of Return (k)
• But, what is the proper approach for
deriving ke?
– CAPM?
– APT?
– Haugen’s ad hoc expected return factor model?
• Still an open question
– CAPM most widely used in practice
– Even then, questions can remain in terms of
how to apply the model
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Estimating Growth Rates
Three general approaches:
1. Reinvestment-rate approaches
–
Sustainable Growth Rate = RR X ROE
2. Historical estimates
–
–
Point estimates of growth rates
Regression-based estimates of growth rates
3. Back out growth rates from estimated size of
future market
–
Compare company to industry (Ch. 20) and industry
to economy as a whole (Ch. 19)
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Expected Growth Rate of Dividends
• Determined by
– the growth of earnings
– the proportion of earnings paid in dividends
• In the short run, dividends can grow at a different
rate than earnings due to changes in the payout
ratio
• Earnings growth is also affected by compounding
of earnings retention
g = (Retention Rate) x (Return on Equity)
= RR x ROE
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DuPont Breakdown of ROE
ROE 
Net Income
Sales
Total Assets



Sales
Total Assets Common Equity
=
Profit
Margin
Total Asset
x Turnover
Financial
x Leverage
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Estimating Growth Based on History
•
•
•
Alternative to reinvestment rate approach
Historical growth rates of sales, earnings, cash
flow, and dividends
Two general techniques
1. arithmetic or geometric average of annual
percentage changes (point estimates)
2. linear or log-linear regression models
•
Both use time-series plot of data
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Checking Your Figures:
Three Alternative Measures of Value
(cf., Value Investing)
1. Value of Company’s Assets
–
–
–
Graham & Dodd net-net approach
Book Value of Assets – P/BV for valuation
Market value / replacement value of assets
2. Earnings Power Value
–
–
–
Value company’s current earnings, adjusted for seasonality /
cyclicality – DCF value assuming growth = 0 or = long-run
growth in economy
Greater than value of company’s underlying assets iff
company holds competitive advantage or benefits from
barriers to entry
Understanding value requires knowledge of industry
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Checking Your Figures:
Three Alternative Measures of Value
(cf., Value Investing)
3. What is Growth Worth?
–
Adds value only if growth occurs “within the franchise”
•
•
•
•
Potential problem - firm retains earnings, but reinvestment returns
are below the firm’s cost of capital (i.e., project NPV is negative)
Taking on more projects means that sales and earnings will grow,
but not by enough to cover additional costs of capital, so growth
will actually destroy value held by current shareholders
Key lesson = not all growth is “value-adding”
Only projects with positive NPV’s will create value, and projects
will only have positive NPV if they exploit or occur within the
firm’s realm of competitive advantage, i.e., within the firm’s
franchise
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Analysis of Growth Companies
• Generating rates of return greater than the firm’s
cost of capital is considered to be temporary
• Earnings higher than the required rate of return are
pure profits
• How long can they earn these excess profits?
• How long are they likely to earn these excess
profits?
• How long does the market expect them to earn
these excess profits?
• Is the stock properly valued?
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Measures of Value-Added
• The Franchise Factor
– Breaks P/E into two components
• P/E based on ongoing business (base P/E)
• Franchise P/E the market assigns to the expected value of
new and profitable business opportunities
Franchise P/E = Observed P/E - Base P/E
Incremental Franchise P/E = Franchise Factor X Growth Factor
Rk

G
rk
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Growth Duration
• Evaluate the high P/E ratio by relating P/E ratio to
the firm’s rate and duration of growth
• P/E is function of
– expected rate of growth of earnings per share
– stock’s required rate of return
– firm’s dividend-payout ratio
• Use the ratio of P/E’s, related to growth and
dividend rates, to infer the market’s implied
growth duration:
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Intra-Industry Analysis
• Directly compare two firms in the same industry
• An alternative use of T to determine a reasonable
P/E ratio
• Factors to consider
– A major difference in the risk involved
– Inaccurate growth estimates
– Stock with a low P/E relative to its growth rate
is undervalued
– Stock with high P/E and a low growth rate is
overvalued
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Growth Duration
T

(1  G g  D g ) 
 Pg (0)/E g (0) 


  
 (1  G  D ) T 


P
0
/
E
(0)
B
B
B
 B
 

 Pg (0)/E g (0) 
 1  G g  Dg 
  T ln 

ln 
 PB 0 / E B (0) 
 1  G B  DB 
 P/E g 

ln 
P/E B 

T
 1  G g  Dg 

ln 
 1  G B  DB 
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Growth Duration
Alternatively, the equation can be rearranged to determine a
justified P/E ratio for a firm, given its expected dividend yield and
growth rate and the expected length of time over which the firm will
continue to experience above-average growth, relative to its
benchmark (B).
 1  G g  Dg 

P/E g  P/E B 
 1  G B  DB 
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T
Extensions on Growth Duration
• For more information and additional
extensions and applications in using marketbased information to infer the market’s
assumptions about the various factors that
drive a stock’s valuation, see:
– www.expectationsinvesting.com
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When to Sell
• Knowing when to sell is an even harder decision
than knowing when to buy
– Holding a stock too long may lead to lower returns than
expected
– If stocks decline right after purchase, is that a further
buying opportunity or an indication of incorrect analysis?
– Continuously monitor key assumptions
– Evaluate closely when market value approaches estimated
intrinsic value
– Know why you bought it and watch for that to change
– Always need a “sell discipline”
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Efficient Markets
• Opportunities are mostly among less well-known
companies
• To outperform the market you must find disparities
between stock values and market prices - and you must
be correct
• Concentrate on identifying what is wrong with the
market consensus and what earning surprises may exist
– Again, useful to examine the expectations that underlie the
current market price
– Are these realistic/optimistic/pessimistic?
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Next Up:
Final Topics
• Bond Portfolio Management
• Are the Markets Rational?
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Copyright © 2000 by Harcourt, Inc. All rights reserved