Chapter 08 – Stock Valuation
Chapter 8
STOCK VALUATION
CHAPTER WEB SITES
Section Web Address
8.3 www.bloomberg.com
www.nyse.com
www.nasdaq.com
finance.yahoo.com
www.otcbb.com
www.pinksheets.com
CHAPTER ORGANIZATION
8.1 Common Stock Valuation
Cash Flows
Some Special Cases
Components of the Required Return
Stock Valuation Using Multiples
8.2 Some Features of Common and Preferred Stocks
Common Stock Features
Preferred Stock Features
8.3 The Stock Markets
Dealers and Brokers
Organization of the NYSE
Nasdaq Operations
Stock Market Reporting
8.4 Summary and Conclusions
ANNOTATED CHAPTER OUTLINE
1. Common Stock Valuation
A. Cash Flows
Stock valuation is more difficult than bond valuation because the
cash flows are uncertain, the life is infinite, and the required rate of
return is unobservable.
The cash flows to stockholders consist of dividends plus a future
sale price. You can illustrate that the current stock price is
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Chapter 08 – Stock Valuation
ultimately the present value of all expected future dividends:
P0 = D1/(1+R) + D2/(1+R)2 + D3/(1+R)3 + …
Ethics Note: The importance of the components of the valuation
model is brought into sharp focus in a discussion of pension
funding decisions. Pension and Investments reports that in
November, 1993, the Securities and Exchange Commission issued
a “new, unprecedented warning …to use only ‘high-grade’ market
rates for discounting” for valuing pension assets. The article
reports that many over-funded plans could “slip into underfunded
status.” A practical result of the use of inappropriate return
estimates is found in the case of Witco Chemical, which took large
charges against earnings in 1993 related to its use of an
inappropriate rate for computing its unfunded pension liability.
Students might first be asked to guess how one determines an
“appropriate” return estimate for pension funding purposes. Then,
ask them to whom the actuary owes greater responsibility – future
pension recipients, management, shareholders, or the Pension
Benefit Guaranty Corporation? It is easy to see that the ethical
issues underlying the actuarial calculations can become quite
complex.
Lecture Tip: Lively discussions can be generated in the area of
stock valuation and dividend cash flows. As the text points out, a
stock that currently pays no dividends may or may not have value;
a stock that will NEVER pay a dividend cannot have any value as
long as investors are rational. For a stock that currently pays no
dividend, market value derives from (a) the hope of future
dividends, and/or (b) the expectation of a liquidating dividend. In
the latter case, “never pays a dividend” really means “never pays
out cash in any form” to shareholders. Students will often argue
strenuously that a firm never has to pay a dividend because
investors can just rely on the increase in price. It’s important to
emphasize that the price won’t continue to increase forever. The
company will eventually run out of productive ways to use its cash.
When this happens, it will need to begin paying dividends. Another
way to think of this is that a company that never pays a dividend,
including a liquidating dividend, is essentially a perpetual zero-
coupon bond. It is a big, black hole where you put money in but
you never get anything back out.
B. Some Special Cases
Zero-growth – implies that D0 = D1 = D2 … = D
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Since the cash flow is always the same, the PV is that for a
perpetuity:
P0 = D / R
Example: Suppose a stock is expected to pay a $2 dividend each
period, forever, and the required return is 10%. What is the stock
worth?
P0 = 2 / .1 = $20
Constant growth – Dividends are expected to grow at a constant
percentage rate each period. D1 = D0(1+g); D2 = D1(1+g); in
general Dt = D0(1+g)t Note that this is really just a future value.
Example: If the current dividend is $2 and the expected growth
rate is 5%, what is D1? D5?
D1 = 2(1+.05) = $2.10
D5 = 2(1+.05)5 = $2.55
An amount that grows at a constant rate forever is called a growing
perpetuity. The present value of all expected future dividends
under this scenario can be expressed as follows:
P0 = D1 / (R – g) and more generally,
Pt = Dt+1 / (R – g)
Example: Consider the stock given above. If the required return is
10%, what is the expected price today? In 4 years?
P0 = 2.10 / (.1 – .05) = $42
P4 = 2.55 / (.1 – .05) = $51
Lecture Tip: In his book, A Random Walk Down Wall Street, pp.
82 – 89, (1985, W.W. Norton & Company, New York), Burton
Malkiel gives four “fundamental” rules of stock prices. Loosely
paraphrased, the rules are as follows. Other things equal:
–Investors pay a higher price, the larger the dividend growth rate
–Investors pay a higher price, the larger the proportion of earnings
paid out as dividends
–Investors pay a higher price, the less risky the company’s stock
–Investors pay a higher price, the lower the level of interest rates
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If the required return, R, is looked at as a riskless rate of interest,
Rf, plus a risk premium, RP, (R = Rf + RP), it is easily shown that
Malkiel’s rules have counterparts in the dividend growth model
that exert just these effects on the stock price. Of course, the tricky
part is estimating the growth rate and required return. So, while
the model is precise, its predictions may be substantially different
from observed stock prices depending on the values used.
Lecture Tip: If your students have had some calculus, you might
find it useful to derive the dividend growth model.
P0=D0(1+g)
(1+R)+D0(1+g)2
(1+R)2+D0(1+g)3
(1+R)3+. ..+D0(1+g)t
(1+R)t
Now multiply both sides by (1+R)/(1+g):
(1+R)
(1+g)P0=D0
[
1+(1+g)
(1+R)+(1+g)2
(1+R)2+...+(1+g)t−1
(1+R)t−1
]
Subtract the first equation from the second and you get:
[
(1+R)−(1+g)
(1+g)
]
P0=D0
[
1−(1+g)t
(1+R)t
]
The term 1 – (1+g)t/(1+R)t goes to one as t approaches infinity,
assuming R > g. If we solve for P0, we get the dividend growth
model.
Lecture Tip: Students often ask:
1. “How can g ever be assumed to be constant?” The answer lies
in the competitive equilibrium model of classical
macroeconomics. Since g represents not only the growth rate in
dividends but also in earnings and sales, assuming no change
in the firm’s cost structure, we are simply assuming that the
product market that the firm operates in “settles down” to a
steady state in which competing firms earn sufficient returns to
remain in business, but not large enough to attract outside
capital. From a more practical standpoint, firms will often
attempt to manage their dividend policy so that there is a
reasonably constant growth in dividends.
2. “Why do we assume that R > g?” At least two answers are
possible. First, R may be less than g in the short-run. The
supernormal growth problem is an example of this situation.
Second, in equilibrium, high returns on investment will attract
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capital, which, in the absence of technological change, will
ensure that in succeeding periods, higher returns cannot be
earned without taking greater risk. But, taking greater risk will
increase R, so g cannot be increased without raising R.
Lecture Tip: In this example P3 = D4 / (.1-.05). Some students
have a tendency to incorrectly discount P3 by (1 + R)4 instead of (1
+ R)3. This is probably because they already have a cash flow at
time 3 or because they used D4 to determine P3. It should be
stressed that we are always bringing the next dividend back one
period. The timing of P3 determines the time period for the factor
used.
C. Components of the Required Return
Rearrange P0 = D1 / (R – g) to find R:
R = (D1 / P0 ) + g
Dividend yield = D1 / P0
Capital gains yield = g, and
R = dividend yield + capital gains yield
International Tip: An interesting question arises as to the relative
importance of the components of required (or total) return in the
stocks of different countries when one considers the differences in
dividend yields and P/E ratios in US and Japanese stocks. The
Financial Times reports that, near the end of 1993, the average
dividend yield on Japanese stocks was approximately .8 percent,
or about one-third that of US stocks. On the other hand, the P/E
ratios of US stocks ranged in the mid-‘20s, while the same story
reports that Japanese P/E ratios nearing 90 were not uncommon.
You may wish to ask students to speculate on why such differences
could arise. This facilitates discussion of differential tax laws,
accounting rules, market interest rates, etc. In this context, you
might wish to ask students to evaluate a statement from a
contemporaneous article in the South China Morning Post:
“Japanese companies pay comparatively smaller dividends, so net
earnings per share takes on less importance” to investors.
Ethics Note: The increase in Internet usage has brought a lot of
benefits from an information standpoint; however, students need to
recognize that not everything they read on the Internet is true. It is
incredibly easy for individuals to post fake press releases on the
Internet and move the price of a stock. Unfortunately, even
reputable news organizations often pick up these phony press
releases and run them before they have checked the facts. This
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Chapter 08 – Stock Valuation
“news” may have a major impact on stock prices. Stephen Sayre
was arrested for posting buy recommendations on eConnect. The
stock price went as high as $22 per share on March 9, 2000, and
was trading as low as $1 by April 24, 2000. Phony press releases
can also be used to move prices down. The case of Emulex,
discussed earlier in the instructor’s manual (Chapter 3), is an
excellent example. In this case, the individual had shorted the
stock and placed a phony press release with bad news on the
Internet. The stock price dropped over 62%. It rebounded after it
was discovered that the press release was false, but many investors
lost a substantial amount of money on the way down. An excellent
article discussing this issue can be found in the April 24, 2000
issue of BusinessWeek (Investors, Beware the Press Release, pp.
153 – 54).
D. Stock Valuation Using Multiples
For stocks that do not currently pay dividends, a common
valuation approach is to make use of the PE ratio. For instance,
using a benchmark PE ratio for a firm and their current earnings
per share, we can calculate a projected price for the firm:
Price at time t = Pt =Benchmark PE ratio x EPSt
2. Some Features of Common and Preferred Stocks
A. Common Stock Features
Shareholders have the right to elect corporate directors who set
corporate policy and select operating management.
1. Cumulative voting –the directors are all elected at once. Total
votes that each shareholder may cast equal the number of shares
times the number of directors to be elected. In general, if N
directors are to be elected, it takes [1 / (N+1)] percent of the stock
to assure a deciding vote for one directorship. Good for getting
minority shareholder representation on the board.
2. Straight (majority) voting – the directors are elected one at a
time, and every share gets one vote. Good for freezing out minority
shareholders.
3. Staggered elections – directors’ terms are rotated so they aren’t
elected at the same time. This makes it harder for a minority
shareholder group to elect a director and complicates takeovers.
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Chapter 08 – Stock Valuation
4. Proxy voting – grant of authority by a shareholder to someone
else to vote his or her shares. A proxy fight is a struggle between
management and outsiders for control of the board, waged by
soliciting shareholders’ proxies.
Lecture Tip: Large institutions, such as mutual funds and pension
funds, used to remain on the sidelines when it came to corporate
control. However, several institutions have become much more
active in recent years and have worked to force companies to
operate in the shareholders’ best interests. CalPERS, the pension
plan for California public employees, has been at the forefront of
the corporate governance movement. Management for the fund
takes their job as “shareowners” so seriously that they
have a section of their web site devoted to corporate governance
issues. For more information, see http://www.calpers-
governance.org/forumhome.asp. This issue has become even more
important in recent years, given the number of scandals related to
corporate management by Boards of Directors and executive
officers.
Other rights usually include:
1. Sharing proportionately in dividends paid
2. Sharing proportionately in any liquidation value
3. Voting on matters of importance (e.g., mergers)
4. The right to purchase a pro rata share of any new stock sold –
the preemptive right
Real-World Tip: The importance of the preemptive right was
driven home in November, 1996, to the shareholders of Marvel
Entertainment Group, the company that produces Marvel Comics.
(Marvel’s stable of characters includes Spider-Man, the Fantastic
Four, and the Incredible Hulk, among others.) Despite Marvel’s
dominance of the comic book market, the declining size of the
market, as well as a heavy debt load, caused Marvel to run the risk
of default. In order to obtain needed funds, Ron Perelman, who
(through his other firms) owned approximately 80% of the
outstanding shares, proposed that Marvel issue 410 million new
shares at a price of $0.85 per share. The effect of the
announcement was to drive the price of the outstanding 20% of the
shares Perelman didn’t own from $4.625 to less than $2.50. To add
insult to injury, according to The Wall Street Journal, Perelman
had the power, as the majority shareholder, to force the plan
through. Subsequently, Marvel filed for bankruptcy reorganization
and Carl Icahn sought to gain control of the firm. Ultimately,
Marvel merged with Toy Biz, much to Icahn’s displeasure. This
combined company was then purchased by Disney in 2009.
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1. Payment of dividends is at the discretion of the board. A firm
cannot default on an undeclared dividend, nor can it be forced to
file for bankruptcy because of nonpayment of dividends.
2. Dividends are not tax deductible for the paying firm.
3. Dividends received by individuals are taxed based on the
holding period of the stock (see the Lecture Tip below), while
dividends received by a corporation are at least 70% tax-exempt.
Lecture Tip: The tax laws regarding dividends received by
individuals were revised for dividends received after 2002.
Qualified dividends are taxed at the capital gains rate of 15% if
the tax rate on ordinary income is 25% or higher and at 5% if the
tax rate on ordinary income is less than 25%. According to the
Internal Revenue Service, all of the following requirements must
be met:
1. The dividends must have been paid by a U.S. corporation or
qualified foreign corporation.
2. The dividends are not of the type listed under “Dividends that
are not qualified dividends.”
3. The proper holding period is met.
The “proper holding period” requires the stockholder to own the
shares for at least 61 days during the 121 day period surrounding
the ex–dividend date (60 days before, the ex-dividend date, 60 days
after). Preferred stock may have slightly different requirements in
certain circumstances.
Dividends that are NOT qualified include:
1. capital gains distributions
2. dividends paid on deposits with banks or credit unions that
should be included in interest income
3. Dividends from a tax-exempt corporation or farmer’s
cooperative
4. Dividends paid on stock owned through an employee stock
ownership plan
5. Dividends paid on short sale or similar positions where the
shareholder is obligated to make related payments for positions in
similar or related property
6. Payments in lieu of dividends
Resource: www.irs.gov “What are Qualified Dividends?” article
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B. Preferred Stock Features
Preferred stock has precedence over common stock in the payment
of dividends and in liquidation. Its dividend is usually fixed, and
the stock is often without voting rights. The stated value is the
value paid to preferred stockholders in the event of liquidation.
Cumulative dividends – current preferred dividend plus all
arrearages (unpaid dividends) to be paid before common stock
dividends can be paid. Non-cumulative dividend preferred does not
have this feature.
Preferred stock represents equity in the firm, but has many features
of debt, including a stated yield, preference in terms of cash flows
and liquidation, and some issues are callable and/or convertible
into common shares.
Real-World Tip: Here’s a gruesome-sounding security – the
“death spiral.” Actually, the name refers to convertible preferred
shares that have a floating conversion ratio. That is, the
conversion ratio varies with the price of the firm’s common stock.
Also known as “toxic convertibles,” The Wall Street Journal
reports that, when the issuer’s common stock falls, more shares
must be issued to redeem the convertible securities, so this dilution
pushes the common stock price down further. Hence, the “death
spiral” appellation.
3. The Stock Markets
A. Dealers and Brokers
Primary market – the market in which new securities are originally
sold to investors
Secondary market – the market in which existing securities trade
among investors
Lecture Tip: Some students find it hard to grasp the relative
importance of primary and secondary market transactions.
Suggest that they consider automobile sales rather than stocks.
New automobiles are sold through a network of dealers and
salesman (brokers) to the public. In any given year, however, the
majority of transactions are between people buying and selling
existing automobiles, i.e., the secondary (used) car market. As with
secondary market transactions in stocks, used car purchases do
not directly benefit the issuer/manufacturer. You can also introduce
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Chapter 08 – Stock Valuation
the notion of information asymmetry and signaling at this point,
see the classic article by George Akerlof titled “Market for
Lemons.”
Broker – one who arranges security transactions among investors
Dealer – one who buys and sells securities from inventory
Bid price – the price at which a dealer is willing to buy a security
Ask price – the price at which a dealer is willing to sell a security
Spread – the difference between the bid and ask prices
Video Note: The “Financial Markets” video discusses how capital is raised and shows
an open-outcry market at the Chicago Board of Trade.
B. Organization of the NYSE
Prior to 2006, the exchange consisted of 1,366 members, said to
own seats. Since going public, there are 1,366 licensees who pay
an annual fee to trade.
Designated market maker (DMM) – NYSE members who act as
dealers in particular stocks. Formerly known as “specialists.”
Supplemental liquidity providers (SLPs) – investment firms that are
active participants in stocks assigned to them. Their job is to make
a one-sided market (i.e., offering to either buy or sell).
Floor brokers – NYSE members who execute orders for buys and
sellers
Floor traders – those who trade for their own accounts, trying to
anticipate and profit from temporary price fluctuations
Order flow – the flow of customer orders to buy and sell securities
DMM’s post – fixed place on the exchange floor where the
specialist operates
Trading in the crowd – trading that occurs directly between floor
brokers around the DMM’s post
C. Nasdaq Operations
NYSE operations represent a premier example of the trading of
“listed” securities. Nasdaq operations, on the other hand, represent
the evolution of “over-the-counter” trading of securities that do not
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Chapter 08 – Stock Valuation
rely on a physical market place.
Nasdaq – National Association of Securities Dealers Automated
Quotation system – computer network of securities dealers who
disseminate timely security price quotes to Nasdaq subscribers.
D. Stock Market Reporting
Lecture Tip: A useful assignment is to require students to obtain a
recent Wall Street Journal and examine the financial section. Have
the students examine the dividend column for various stocks and
point out the number of non-dividend paying stocks. Also have
them identify the information available in each quote. This allows
them to see more information at once than they would normally
see with online quotes.
4. Summary and Conclusions
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