Chapter 7
Equity
Valuation
What determines the value
of stock? Old ideas are still
new.
Chapter 7 Outline
7.1 Equity Securities
•The basics of valuing
equity
•The required rate of
return
2
7.2 Discounted Cash Flow
Approaches to Valuing
Equity
•Valuing preferred stock
•Valuing common stock
•The basic dividend
discount model and its
limitations
•Estimating the required
rate of return
•Estimating the value of
growth opportunities
7.3 Using Multiples to
Value Equity
•The price-earnings ratio
and its limitations
•Additional multiples or
relative value ratios
7.1 Equity Securities

A corporation will issue an equity security, which is a financial
instrument that represents ownership in the corporation.


A unit of ownership is represented by a share or a share of stock,
and an owner of a share is a shareholder or stockholder.

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Because a corporation has a perpetual life, the owners of these securities own
a security that has no fixed maturity date.
Companies that issue equity securities may choose to pay a cash
dividend, which is paid from after-tax earnings.

3
We often refer to this financial instrument as the stock of the company.
Unlike interest payments on debt obligations, dividends are not a taxdeductible expense to the paying corporation.
Equity Securities

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A corporation, at a minimum, has common stock, but it may
also choose to issue preferred stock.
Preferred stock and common stock both represent
ownership interest, or equity, but preferred shareholders, as
the name implies, have a prior claim to income and assets of
the company relative to common shareholders.
Common shareholders are the residual claimants of the
corporation, which means that they are entitled to income
remaining only after all creditors and other, more senior
claimants, including preferred shareholders, have been paid.
Equity Securities

By far, the most common type of equity security is the
common share, which represents a certificate of ownership
in a corporation.


A publicly traded corporation may have millions or even
billions of common shares outstanding at a point in time.

5
A purchaser of 100 shares of common stock owns 100/n
percent of the corporation, where n is the total number of
shares of common stock outstanding.
For example, at the end of their June 30, 2013, fiscal year end,
Microsoft had 8.36 billion shares of stock outstanding.
Equity Securities

Preferred stock provides the owner with a claim to a fixed
amount of equity that is established when the shares are
first issued.
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Most preferred stockholders have preference over common
stockholders with respect to income and assets (in the event of
liquidation), but they rarely have any voting rights.
Traditionally, preferred stock has no maturity date, but over the
past 30 years preferred stock has been increasingly issued with
a fixed maturity date, similar to a bond.
Preferred Securities



The main difference between preferred stock and a bond is
that the board of directors declares the dividends and until
then, and unlike an interest payment, dividends are not a
legal obligation of the company.
Usually, no payments can be made to common shareholders
until preferred shareholders have been paid the dividends
they are due in entirety.
Dividends are not considered a cost of doing business, and
therefore they are not deductible for tax purposes by the
paying company.

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This is different than the interest paid by the company issuing
bonds; interest is a deductible expense for tax purposes.
The Basics of Valuing Equity


Valuing equity requires estimating future dividends.
In the case of preferred stock, the dividends are generally
fixed in terms of the payment frequency and the amount,
but these still are paid at the discretion of the company’s
board of directors.


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We refer to preferred stock with a fixed dividend, no maturity, and no
embedded option as straight preferred stock.
In the case of common stock, we possibly are dealing with
uneven cash flows, ad infinitum.
The Basics of Valuing Equity


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We generally value preferred stock using discounted cash
flow methods, discounting the expected dividends at a
discount rate that reflects the uncertainty associated with
the payment of these dividends.
Because common stock is the last in line in terms of the
pecking order of claims on a company and because some
companies simply reinvest earnings instead of paying them
out to shareholders, there are two common approaches to
valuing common stock:
 The discounted cash flow approach
 The method of multiples
Approaches to Valuing
Common Stock
The discounted cash flow
approaches require an
estimate of the required rate
of return, which is the
minimum return that
investors expect to earn on
the investment in the stock.
In the method of multiples,
we approach valuation at a
different angle: we estimate
values based on the market’s
assessment of comparable
companies.
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The Required Rate of Return

Key to the discount models used to value preferred and
common stock is the required rate of return, which becomes
a benchmark for valuation:
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If a company returns more than required, the value of the stock
rises; if a company returns less than required, the value of the
stock falls. The difficulty is that we cannot observe this required
rate of return directly.
We can back into this return by looking at how the market
values a company’s stock, given a projection of dividends,
but we cannot simply look up the required rate of return.
The Required Rate of Return

We generally think of the discount rate for equities as the sum
of the risk-free rate of return—that is, the compensation for
the time value of money—plus a premium for bearing risk:
re = rf + Risk premium

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where re is the required return on an equity security and rf is
the risk-free rate of return.
The risk-free rate comprises the real rate of return plus
expected inflation, and we often use the return on Treasury
bonds to represent this rate of return.
The risk premium is based on an estimate of the risk associated
with the security; the higher the risk, the higher the risk
premium because investors require a higher return as
compensation for bearing more risk.
7.2 Discounted Cash Flow
Approaches to Valuing
Equity
We estimate the expected future cash flows
associated with the security and then determine the
discounted present value of those future cash flows,
based on an appropriate discount rate (re).
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Valuing Preferred Stock
Traditional preferred stock has no maturity date and
pays dividends of a fixed amount at regular intervals
indefinitely (that is, to infinity, ∞), as we depict in
the figure below, where we represent the periodic
dividend payment as Dp.
The Cash Flow Pattern for a Straight Preferred Stock
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Valuing Preferred Stock


15
Because the payments are essentially fixed when the
preferred shares are issued, they are often referred to as
fixed-income investments.
We can estimate the value of preferred shares using the
equation that determines the present value of a perpetuity,
where Pp is the present value of the preferred stock, Dp is
the periodic dividend amounts (or payments), and rp is the
required rate of return on the preferred shares (or discount
rate):
Valuing Preferred Stock
Example
Problem: Suppose a preferred stock has a par value of $50 per
share and a dividend rate of 8%. If the required rate of return
for this preferred stock is 6%, what is the value of a share of
this stock?
Solution: The dividend is $50 × 0.08 = $4 per share, which we
discount at the rate of 6%:
The stock trades at a premium to its face value.
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Valuing Preferred Stock
Example
What if the required rate of return on the given stock is 10%,
instead of 6%?
In this case, the stock trades at a discount to its face value.
What if the required rate of return is 8% instead of 6%?
In this case, the stock is valued at its par value.
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Valuing Common Stock

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Valuing common shares involves several complications that
arise with respect to the appropriate future cash flows that
should be discounted.
One of the most popular discounted cash flow valuation
models, uses dividends.
 However, unlike bonds or even preferred shares, there is
no requirement that common shares pay dividends at all.
 In addition, the level of dividend payments is
discretionary, which implies we must make estimates
regarding the amount and timing of any dividend
payments.
The Basic Dividend Discount
Model (DDM)
We assume that common shares are valued according to the
present value of their expected future cash flows—specifically,
dividends. Based on this premise, we estimate today’s value, based
on an n-year holding period:
P0 = the value of a share of common stock today,
Dt = the expected dividend at the end of year t,
Pn = the expected share value after n years, and
re = the required return on the common shares.
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Example: The Basic Dividend
Discount Model
Problem:
Consider a stock that is expected to pay $2 at the end of the
first year and $3 at the end of the second year. If the stock is
expected to have a value of $20 at the end of 2 years, what is
the value of the stock today if the required rate of return is
8%?
Solution:
= $21.5707
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Valuation with Constant
Growth
It is impractical to estimate and discount all future dividends
one by one. Fortunately, we can simplify the equation into a
usable formula by making the assumption that dividends grow
at a constant rate (g) indefinitely.
This growth rate represents the annual growth in dividends, ad
infinitum.
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Constant growth
If growth is expected to be constant, the value of a share of
stock is:
D1
P=
re −g
where D1 = D0 x (1 + g)
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Example: constant growth
Problem:
If a company’s current dividend is $2 per share, its required
rate of return is 10%, and its expected growth in dividends is
4%, what is the value of a share of this company’s stock?
Solution:
(1+0.04) $2.08
P = $2
=
=$34.67
0.10 −0.04
0.06
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Example: constant growth
Problem:
If a company’s current dividend is $2 per share, its required
rate of return is 10%, and dividends are expected to decline 2%
per year, what is the value of a share of this company’s stock?
Solution:
$2 (1− 0.02) $1.96
P = 0.10
=
=$16.33
− −0.02 0.12
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Estimating the Required Rate
of Return
We can estimate the rate of return required by investors on a
particular share as follows:
The first term (D1 ÷ P0) is the expected dividend yield on the share
and the second term, g, as the expected capital gains yield (or,
simply, capital yield).
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Estimating the Required Rate
of Return
Example:
Consider a common stock that has an annual dividend of $2
per share. If the value of a share of this stock is $20 and the
expected growth rate is 4%, what is the required rate of
return?
Solution:
The dividend yield is $2 ÷ $20 = 10%, and the required rate of
return is 10% + 4% = 14%.
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Estimating the Value of
Growth Opportunities
Let’s assume that a company that has no profitable growth
opportunities should not reinvest residual profits in the
company, but rather should pay out all its earnings as
dividends.
 Under these conditions, we have no growth (that is, g =
0), EPS1 represents the expected earnings per common
share in the upcoming year, and earnings per share are
equal to dividends, D1 = EPS1.
 These assumptions give us the following expression:
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Estimating the Value of
Growth Opportunities
It is unlikely to find a company that has exactly “zero” growth
opportunities, but the point is that we can view the share
value of any common stock (that satisfies the assumptions of
the constant growth dividend discount model) as comprising
two components: without growth and with growth
We denote this as the present value of growth opportunities
(PVGO) and get the following equation:
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Estimating the Value of
Growth Opportunities
Example:
If a company’s common stock has a market value of $25, the
expected earnings per share for next year is $1 and the
required rate of return is 10%, what is the stock’s present value
of growth opportunities?
Solution:
Rearranging:
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Two-stage growth
What if the dividends are expected to experience
two different growth rates in the future?
We can use time value of money and the dividend
valuation model to value the stock.
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Example: Two-stage growth
Problem:
Suppose a stock currently pays a dividend of $3 per
share and investors require a 10% return on this
stock. And suppose the dividends are expected to
grow at a rate of 15% for three years and then 5%
thereafter. What is the value of the stock?
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Example, cont.
Growth rate
(from prior
year’s
Year dividend)
0
1
15%
2
15%
3
15%
4
5%
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Dividend
$3.00
$3.45
$3.97
$4.56
$4.79
Example, cont.
0
1
2
3
4
|
|
|
$3.45
$3.97
$4.56
5% growth
after period 3
|
$4. 79
𝑃3 =
$81.83
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$4.79
=$95.82
0.10−0.05
$3.45
$3.97
$100.38



Limitations of the Dividend
Discount Model
The dividend discount model is based on several assumptions
that are not met by a large number of companies. In
particular, it is best suited for companies that:

Pay dividends based on a stable dividend payout history that
they want to maintain in the future
Are growing at a steady and sustainable rate
As such, the model works reasonably well for large corporations in
mature industries with stable profits and an established dividend
policy.

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7.3 Using Multiples to Value
Equity
We can use relative valuation to estimate the value of common
shares by comparing the market values of similar companies,
relative to a common variable, such as earnings, cash flow,
book value, or sales.
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Using Multiples to Value Equity
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
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Because relative valuation relies on multiples, we refer to
this methodology as the method of multiples. Conceptually,
relative valuation appears simple to apply: All we need to do
is find a group of comparable companies and then use their
financial data and market values to infer the value of the
company in question.
However, finding comparable companies is difficult: what
company is similar to Microsoft, for example? Disney? GE?
Using the Price-Earnings Ratio

The most commonly used relative valuation multiple is
the price-earnings (P/E) ratio.

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The justified P/E is the multiple that is considered
sustainable over the long term.
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Represents the number of times investors are willing to pay
for a company’s earnings, as expressed in the share price, or
the share price divided by the earnings per share.
Implemented by estimating the company’s earnings per
share (EPS) and multiplying it by a justifiable P/E multiple.
The typical P/E formulation for valuation purposes uses
estimated earnings per share (EPS1) for the next 12 months.
Price-Earnings Ratio Limitations
Aside from the difficulties in estimating an appropriate P/E
ratio and in estimating future EPS, there are several other
practical concerns regarding the use of P/E ratios:
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The P/E ratio is uninformative when companies have negative
or very small earnings.
The P/E ratio may be highly variable across an industry.
The volatile nature of earnings implies a great deal of volatility
in P/E multiples. For example, the earnings of cyclical
companies fluctuate quite dramatically throughout a typical
business cycle.
Net income, and hence earnings per share, are susceptible to
the influence of accounting choices and earnings
management.
Practical approach to P/E
For these reasons, P/E ratios are often based on smoothed or
normalized estimates of earnings for the forecast year.
This is also why analysts use other, similar relative value
approaches along with a P/E analysis.
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Additional Multiples or Relative
Value Ratios
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The market-to-book (M/B) ratio is the market value per
share divided by the book value per share.
Equivalently, we can calculate the market-to-book ratio as
the ratio of the market capitalization of the common stock
divided by the book value of common equity.
Additional Multiples or Relative
Value Ratios
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Book value provides a relatively stable, intuitive measure of
value relative to market values that can be easily compared
with those of other companies, provided accounting
standards do not vary greatly across the comparison group.
Using book value eliminates several of the problems arising
from the use of P/E multiples because book values are rarely
negative and do not exhibit the volatility associated with
earnings levels.
Additional Multiples or Relative
Value Ratios
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The use of the M/B ratio fell out of favor in the 1980s and
1990s because of high rates of inflation that distorted the
M/B ratio.
 This is because using historical cost accounting in an
inflationary period results in understated carrying or
book values.
However, the low rate of inflation of the last 10 to 15 years
has removed most of these problems, whereas changes in
accounting standards have made the book value of equity
more useful.
Additional Multiples or Relative
Value Ratios

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Another commonly used relative valuation ratio is the priceto-cash-flow (P/CF) ratio, where cash flow (CF) is often
estimated as cash flow from operations.
By focusing on cash flow rather than on accounting income,
this ratio alleviates some of the accounting concerns
regarding measures of earnings.
Summary

A value of a share of stock is the future value of future cash
flows to that share.


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In terms of preferred and common stock, the value of a share is
the present value of expected future dividends.
The valuation of preferred stock is rather straightforward;
we typically use the present value of a perpetuity formula to
estimate the value of a share of preferred stock.
Summary

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Because the dividend rate on common stock is not set, but
rather the amount and timing of dividends is left to the
discretion of the board of directors, the valuation of a share
of common stock is more complicated than the value of
preferred stock.
 A useful model is the dividend discount model, assuming
a constant growth in dividends.
 This model can be modified to consider multiple stages of
growth, and other patterns of future dividends.
Problems
Problem 1
Suppose a company had dividends of $2.50
per share in 2013 and is expected to pay
dividends of $4 per share in 2018. What is
the average annual rate of growth of
dividends from 2013 to 2018?
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Problem 2
Suppose a stock has a current dividend of
$4.50 per share and dividends are expected
to increase at a rate of 5% a year, forever. If
investors require a 12% return on this stock,
what is the value of a share of this stock?
48
Problem 3
Suppose a stock has a current dividend of
$4.50 per share and dividends are expected
to increase at a rate of 5% a year, forever.
Investors required a 12% return on this
stock, but have now revised it to 15%
because of the company’s misfortunes. how
much is the value of this share expected to
change with this revision?
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