Chapter 14
Stock Valuation and the EMH
Investments
© K. Cuthbertson and D. Nitzsche
Explosive Growth Problem
 A company’s growth is estimated at 14% for the next
3 years, 12% for year 4&5; 7% in year six and then
4% forever. Last dividend was 1.05 and required
return is estimated at 9%. What is the value of this
company stock?

First calculate dividends year one to seven:
© K. Cuthbertson and D. Nitzsche
Explosive Growth Problem
 Dividend 1-6 are future cash flows (returns) that
have to be discounted at the required rate of return
to their PV (part of the price):
 The sum of these PV’s =7.20 (keep this in memory)
© K. Cuthbertson and D. Nitzsche
Explosive Growth problem
 Another component of the stock price is the PV of
the stock price in year 6 ( constant growth model):


P6 = D7/(r-g)= 2.17/(.09-.04)=43.42
PV = 25.89 (P6 discounted for 6 years at 9%)
 The price of this stock is the sum of 7.20 and 25.89
 P=33.09
© K. Cuthbertson and D. Nitzsche
Learning Objectives
 To estimate the fair value of a stock using PV
techniques and discounted cash flows.
 Dividend Discount model
 Use of ‘relative valuation’ and comparable
 Discuss the EMH and stock picking strategies
© K. Cuthbertson and D. Nitzsche
Fair Value and EMH
 Discounted Future Cash Flow approach
 Investors price stock on the basis of anticipated
inflows
 Since dividends are the only cash reward for
investing, a popular valuation model is the dividend
discount model
© K. Cuthbertson and D. Nitzsche
Present Value of
Free Cash Flow to Equity
• The Constant Growth Formula
FCFE1
Value 
r  g FCFE
where:
FCFE = the expected free cash flow in period 1
r = the required rate of return on equity for the firm
gFCFE = the expected constant growth rate of free cash flow
to equity for the firm
• A multi-stage model similar to DDM can also
be applied
Present Value of
Operating Free Cash Flow
 Discount the firm’s operating free cash flow to the
firm (FCFF) at the firm’s weighted average cost of
capital (WACC).
FCFF =EBIT (1-Tax Rate)
+ Depreciation Expense
- Capital Spending
-  in Working Capital
-  in other assets
Figure 1 : Equity – cash flow
V
D4
D2
D1
0
1
D3
2
3
V = fair value
D1, D2, D3, … = expected dividends
© K. Cuthbertson and D. Nitzsche
4
Time
Figure 2 : Dividend discount model
P
D1
0
© K. Cuthbertson and D. Nitzsche
1
D1(1+g)2
D1(1+g)
2
3
4
Time
Present Value of Dividends
 Simplifying assumptions help in estimating present
value of future dividends
 Constant Growth DDM
Value of equity or price:
P= D1/(R-g) and D1= D0(1+g)
 Growth Rate Estimates
– Average Dividend Growth Rate
Dn
n
g
1
D0
–
Sustainable Growth Rate
g = RR X ROE
Internal Rate of Return
 As we examined the feasibility of a physical
investment project we used IRR (y)
 Similarly the IRR can be calculated using the
observed market price P
P= D1/(y-g)
y=D1/P +g
Buy if >R
© K. Cuthbertson and D. Nitzsche
(D1/P is div. yield)
Calculating the Discount Rate (R)
 Using CAPM and the security market line
 Beta of stock measures the market(systematic) risk
in a stock and is estimated as:
© K. Cuthbertson and D. Nitzsche
SML
 Estimate expected market risk premium (slope)
 Determine the risk-free rate (intercept)
 Calculate beta of a stock
 Calculate the expected return on the stock (as a
reward for the market risk in the stock).
© K. Cuthbertson and D. Nitzsche
Figure 3 : Security market line
Average return
M
9%
SML
Ri = 5 + 8bi
Q
r = 5%
bi = 0.5
© K. Cuthbertson and D. Nitzsche
1
Beta, bi
Company Data
 Market Timing
 Performance measures
 Value Line report
© K. Cuthbertson and D. Nitzsche
Additional Measures of Relative Value
 Price/Book Value (PB/V) Ratio
Book value is a reasonable measure of value for firms that
have consistent accounting practice
 It can been applied to firms with negative earnings or
cash flows
 Should not attempt to use this ratio to compare firms
with different levels of hard assets—for example, a heavy
industrial firm and a service firm

Additional Measures of Relative Value
 Price/Cash Flow (P/CF) Ratio
The price/cash flow ratio has grown in prominence and
use because many observers contend that a firm’s cash
flow is less subject to manipulation
 See Exhibit 9.9

 Price/Sales (P/S) Ratio
 Sales growth drives the growth of all subsequent earnings
and cash flow and sales is one of the purest numbers
available
 See Exhibit 9.9
Analysis of Growth Companies
 Generating rates of return greater than the firm’s
cost of capital is considered to be temporary
 Earnings higher the required rate of return are
pure profits
 How long can they earn these excess profits?
Value of No-Growth Firms
 A No-Growth Firm
E = r x Assets
 E = r x Assets = Dividends (Firms has retention ratio, b, of
0)

 Firm Value
V 
E
R

(1  b )E
R
E
R
V
Stock as a Present Value
21
 Investors price stock on the basis of anticipated
inflows
 Since dividends are the only cash reward for
investing, a popular valuation model is the dividend
discount model
Valuation of Apple Computer
22
Example
Microsoft pays a $0.50 dividend. This is expected to
grow at a rate of 7%. The required rate of return is
10%.
Based on the dividend discount model, what is the
value of Microsoft’s common stock?
Valuation of Apple Computer
(con’d)
23
Example
Stock price =
Next dividend / Required return in Excess of
anticipated dividend growth rate
Stock price = $0.50 (1.07) / [0.10 – 0.07]
= $0.535 / 0.03
= $18
Valuation of Apple Computer
(con’d)
24
Example
Small errors in estimation result in huge changes in
estimated stock price value!
Increase dividend growth rate by ten percent (to
7.7%)
Stock price = $0.50 (1.077) / [0.10 – 0.077]
= $0.5385 / 0.023
= $23.41
That is a 30% increase!
Accounting Versus Finance
Perspectives
25

Account looks at past and present to determine:



Where firm is (balance sheet)
How it got there (income statement)
Finance looks at the future
Present Value of Growth
Opportunities
26
 Present value equals
 Valuation of current earnings


Assuming earnings and required return stay constant
Present value of growth opportunities (PVGO)
 This technique essentially identifies PVGO
 PVGO is estimated and less certain
 Hence, investors tend to prefer stocks with lower
PVGO values
Present Value of Growth
Opportunities
27
Example
Abell Machines is priced at $34, had earning of $1.45
over the past year, and a required return of 9.5
percent.
Bell Retailers is priced at $45, had earnings of $2.20
over the past year, and a required return of 12.3
percent.
Which company has the lower PVGO value?
Present Value of Growth
Opportunities
(con’d)
28
PV = E/K + PVGO
Hence, PV – E/K = PVGO
PVGO of Abell Machines:
$34 - $1.45 / 0.095 = $34 - $15.26 = $18.74
PVGO of Bell Retail:
$45 - $2.2/0.123 = $45 – 17.89 = $27.11
Since PVGO is uncertain, most investors would prefer Abell
Machines, despite its lower level of earnings
EBITDA
29
 Earnings Before Interest, Taxes, Depreciation and
Amortization
 Tool: Stock price / EBITDA
 Seek firms with lower stock price/EBITDA ratios
 Not as popular as others because firms may claim
expenses as investments in assets, reducing EBITDA
Cash Flows
30
 Changes in cash arising from business operations
 Tool: Stock Price/Operating cash flow
 Generally seek firms with lower ratios
 Modification:
 Use Free Cash Flow
 Operating cash flow less required investment in plant and
equipment
 Excess is money available to investors
PEG Ratios
31
 Price/earnings ratio dividend by dividend growth
rate
 Investors seek PEG ratios less than 1.0
 Problems:


Identifying earnings (Past? Forecast?)
Identifying growth rate (1-year forecast?, 5-year forecast?)
Additional Measures of Relative Value
 P/BV
 P/CF
 P/S
The Required Return
33
 Real Portion:
 Return for saving instead of spending money
 Relatively stable in the 3-4 percent range
 Inflation Adjustment:
 Reflects changes in general price level
 Relatively stable in the 3 percent range
 Risk Premium:Depends on


Firm conditions
Overall economic conditions
 Note: Small changes in any of these can result in large
changes in firm valuation
Changes in Stock Price
34
 Primary Long-Term Driver of Change
 Earnings – or lack thereof
 Primary Short-term Driver of Price Change
 Changes in investor sentiment
 Relatively stable in the 3 percent range
 Note: Both are difficult to predict
Equity Risk Premium
35
 Extra return on equity
 8.4% higher than Treasury bills
 6.7% higher than Treasury bonds
 In any year stocks could be lower

After all, this is an equity “risk” premium
 Note: Beta is multiplied by the equity risk premium
in the capital asset pricing model
Anticipated Equity
Risk Premium Changes
36
 Forecasts suggest a diminishing equity risk
premium

One reason is the anticipated higher costs for raw
materials
 Note: The market sets these, not individual
investors
Though investors could sell shares not providing
sufficient returns
 The sale increases supply, reducing price, and increasing
returns to the buyer!

Greenspan Model
37
 General indicator of whether the stock market is
over- or undervalued
 Mentioned in 1997 Federal Reserve Board
publication
 Alan Greenspan was Chairman of the Federal
Reserve Board at that time
 Model: YieldU.S. Treasury note less P/ES&P 500
 Positive Result: Stock market overvalued
 Negative Result: Stock market undervalued
Changing PE Multiples
38
 The amount individuals are willing to pay for a dollar of





earnings varies
Long-run average is 16
Varies over time
Returns will come from higher earnings and higher
price/earnings ratios
A companies earnings cannot be manipulated by investors
However, investors can buy firms with lower P/E ratios


Yet, such firms are not expected to have as high a rate of earnings
growth
Hence, the lower price/earning ratio
Company Analysis & Stock Valuation
 Which are the best companies?
 Are they overpriced?
 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
Growth Companies
 Growth companies have historically been defined as
companies that consistently experience aboveaverage 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
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
Defensive Companies and Stocks
 Defensive Companies
 The firms whose future earnings are more likely to withstand
an economic downturn
 Low business risk
 No excessive financial risk
 Typical examples are public utilities or grocery chains—firms
that supply basic consumer necessities
Defensive Companies and Stocks
 Defense Stocks
 The rate of return is not expected to decline or decline less
than the overall market decline
 Stocks with low or negative systematic risk