# Chapter 7

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```					Chapter 7

Equities
Intrinsic Value

• Present value of expected net cash
flows that accrues to the owner of a
security
Dividend Discount Model

• Process of evaluating stocks on basis of
present value of their expected stream
of dividends
Intrinsic Value of Common Stock

d1        d2       d3                 dH                 PH
Vo                                                  
1  r  1  r  1  r 
2         3
1  r 
H
1  r 
H

dt =    dividend during period t
r =     required rate of return
H =     holding period
PH =    price of the stock at the end of the holding
period
Required Rate of Return
• Rate of return on an investment
required by market to justify degree of
risk incurred
• Risk-free rate plus the risk premium
(e.g., the Capital Asset Pricing Model)
• In equilibrium (quantity supplied equals
quantity demanded), required rate of
return equal to expected rate of return.
Holding Period Model Is
• Problem with defining price of stock in
terms of dividends and selling price is
that this is circular argument, as it begs
the question of what determines selling
price.
• Selling price is present value of
dividends to be paid forever thereafter.
Dividend Discount Model

d1           d2     d3             d
Vo                                
1  r  1  r  1  r 
2      3
1  r 



dt

t  1 1  r 
t

• Because model runs to infinity, it can’t
be implemented without making
future dividends.
Value Cannot Be Based on
Earnings
• Double counting
– Earnings retained (i.e., reinvested) in firm
should lead to higher earnings in future
– Higher earnings are NOT additional value
to investor, but simply a return on value of
earnings previously invested
Valuation of Stocks
That Don’t Pay Dividends
• If they will never, ever pay a dividend:
– Truly worthless
• If they will start paying a dividend in the
future:
– Value today based on when they are
expected to start paying dividends, and
amount of payment at that time
Gordon (Constant) Growth Model

• Form of dividend discount model
• Used to evaluate the intrinsic value of an
asset based on assumptions of constant
growth rate g of cash flow or dividends and a
known discount rate r, where r > g.
(continued)
Gordon (Constant) Growth Model
(continued)

Vo = d1/(r – g) = d0 x (1 + g)/(r – g)

where V0   = intrinsic value,
d1   = next year’s dividend,
g    = growth rate of dividends, and
r    = required rate of return.

dn = dn – 1(1+g)   or     dn = d0(1 + g)n
Implications of Growth Model

• Decrease in required rate of return (that is,
discount rate), will cause value of stock to be
higher
• Increase in expected growth rate of dividends
(g), will cause value of stock to be higher
• Increase in next year’s expected dividend (d1)
will cause value of stock to be higher
Alternative Meaning of “g”

• Can solve constant growth rate model for r:
r = d1/Vo + g
= dividend yield plus growth rate
• Expected Return equals expected dividend
yield plus expected percentage price change
• If discount rate = Expected Return, then
expected dividend growth rate =
expected percentage price change
Zero Growth Model

• Assume dividends will never change (i.e., no
growth)
V=d/r

where V = intrinsic value of a stock whose
dividends are expected to form a
perpetuity
d = the constant, annual dividend
r = discount rate
Food for Thought

• Suppose someone offered you a perpetuity of
\$10 per year (starting next year), and you
believed the appropriate discount rate was
10%, what is the perpetuity worth?
• Suppose you were walking down the street
and found \$100 on the sidewalk (and no one
was around). Are you wealthier picking this
up or accepting the perpetuity?
Selection of Discount Rate

• Sufficient to compensate investor for the
riskiness of dividend stream
• Frequently use CAPM:
ri = r f +  (r M – r f)
Application of CAPM

Risk-free rate
• interest rate on riskless investment,
such as Treasury bill

Market portfolio
• portfolio of all assets, but good
surrogate is S&P 500
Market Price Based Ratios

• Used to judge relative appropriateness
of current stock price
– Price-earnings ratio
– Price-cash flow ratio
• Price-free cash flow ratio
– Price-sales ratio
– Price-earnings/growth rate ratio
Earnings Per Share (EPS)

• Net income of company, minus any preferred
dividend requirements, divided by the number
of outstanding common shares
• Provides investor or potential investor with
information on stability of dividends and
capital gains potential
• Considered one of most important indications
of value of common stock
Price-Earnings (P/E) Ratio

• Price divided by actual or anticipated earnings per
share
– For trailing earnings, stock price relative to most
recent 12-month earnings per share
• Factual
– For ex ante earnings, stock price relative to
expected next 12-month earnings.
• Fantasy
• Analyst should at least use someone else’s estimate of
earnings
Dividend Payout Ratio

• Dividends on common stock paid out as
percentage of net income (after
preferred dividends)
Growth Model & P/E Ratio

V0 = E0 x m x (1 + g) / (r – g)

Where E0 = last year’s earnings
m = the payout ratio
(continued)
Growth Model & P/E Ratio (continued)

Dividing through by last year’s earnings
produces the price-to-past earnings ratio:

V0 / E0 = m x (1 + g) / (r – g)
Growth Model & P/E Ratio (continued)

Dividing prior equation by (1 + g)
produces the price-to-future earnings
ratio:
V0 / [E0 x (1+ g)] = m / (r – g)

V0 / E1 = m / (r – g)
Characteristics of Companies with
High P/E Ratios
• Lower discount rate (less risky)
• Higher expected growth rate of earnings
• Small spread between the discount rate
and growth rate
Growth Stocks vs. Value Stocks

• Growth stocks synonymous with above
average PE ratios
• Value stocks synonymous with below
average PE ratios
• Neither category consistently outperforms the
other over long time periods
P/Es Combined With Other
Factors
• Firm Size
– Many low P/E firms are also small
companies
• Analyst neglect
– Neglected firm effect
• Low price effect
• Takeover candidates
Forecasting with P/E Ratio

• Individual stock:
– Forecast earnings per share
– Forecast P/E ratio
– Multiply the two together
• Market:
– Forecast earnings for index
– Forecast P/E for that index
– Multiply the two together
Impact of Inflation
• Tax impact
– Corporate taxes based on historical costs of plants, equipment,
and inventories (i.e., depreciation charge understates
replacement)
– Investors pushed into high tax brackets.
– Individual taxes applied to nominal dividend and interest income.
• Cost impact
– Greater capital needed for new plant, equipment, and inventories.
– Higher interest costs incurred on borrowings.
• Price impact
– Resistance to price increases.
– Competition from substitutes may increase.
– International competition may increase.
Inflation and Stock Prices

• Cohn and Modigliani found evidence
that:
– Investors have capitalized earnings
incorrectly by comparing current cash
earnings with nominal rather than real
bond returns (i.e., too high of a discount
rate for stock)
– Investors failed to recognize that inflation
devalues corporate debt
Other Equity Instruments

• Preferred Stock (Straight)
• Rights
• Warrants
Preferred Stock
• Dividends not legal obligation, and must
be declared each time by the Board
• Almost always cumulative
• Usually callable
• Promised fixed divided payment
• Most owned by corporations (taxes)
• If miss too many dividends, can take
control of the Board
Rights

• Mandatory in some states, optional
in rest
• Allow an investor to maintain pro
rata ownership of company
• Should ALWAYS be exercised or
sold
Typical Rights Calendar
Rights Valuation Formula

Value = (Price of Stock – Subscription Price) /
# of rights required to buy one new
share
Warrants

• Usually given out in conjunction
with debt financing (bank loan
or bond issue) for purpose of
lower interest rate today & sale
of stock by corporation later at a
higher price
Mechanics of Dividends

•   Declaration date (Board)
•   Ex-dividend date (Exchange)
•   Record date (Board)
•   Payment date (Board)
Dividend Patterns

• Many companies boast of number of
years of consecutive dividend payments
• Dividends paid on same date of each
quarter
• Dividend increases usually same
quarter of each year

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