Equity Securities
© Dallas Brozik, Marshall University
Equity securities are what you think about when you hear the word "Investments".
This is stock, common stock, preferred stock, convertible stock, and all the other types that
might exist now or in the future. If you own stock, you own a piece of the action. Your
return in some way depends on how well the company does in its market of "things" and
people. Stock represents a piece of the American dream; you can get rich if you invest
your money intelligently. And therein lies the problem.
Intelligent investment requires a knowledge of the contract, what the contract entitles
the holder to, any restrictions on the contract, the condition of the underlying firm and its
markets, the conditions of the market for the equity contracts, and..... Well, it should be
obvious that there is no magic formula for getting rich in the stock market. If you want to
be an investor, you should also understand that each of the individual parts of the problem
is manageable, once you have done your homework.
A word of caution. The analysis of equity securities seems to appeal to all sorts of
people, including some who will tell you which stocks to buy by reading tea leaves or the
entrails of small furry animals. Everybody seems to have a system, and almost everybody
will be willing to tell you about it, for a price. It is up to you to find a technique for analysis
that makes sense to you; it could be your own system or someone else's (but please be
kind to small furry animals). It is your money, and you will have to live with your decision.
Make sure you do not rely too heavily on someone else's advice without a full
understanding of what this advice is based upon. You can be just as good as anyone else.
The Financial Contract
The equity contract is simply a set of forward contracts. This financial security gives
the owner a specific claim on a certain set of future cash flows generated by a firm. The
time line for the cash flows associated with equity is shown below:
Dividends are the periodic payment made by a firm to its shareholders from money
earned by the firm. The equity contract has no expiration date, so the string of forward
contracts represented by the dividends is potentially infinite. This infinite string of dividends
is the financial gain the shareholder earns from his "piece of the action". The focus here
is on financial returns. A shareholder may get some psychic benefit out of being a
shareholder, but that benefit is unmeasurable.
Always remember that the success of a firm ultimately depends on the "things" it
makes and sells and the people involved in the making and selling. It is these "things" that
generate the "action" that the stockholders get a "piece of". If a firm cannot make a product
that is of value to someone else, it will be a failure. Money can only come into the firm from
the outside, and if outsiders are going to give a firm their hard-earned money, they expect
some "thing" in return.
The difference between the interest payments made to bond holders and the
dividends paid to shareholders is that the dividends may not be fixed. The amount paid as
a dividend may vary. This variability of the size of the payment received by the shareholder
contributes to the variability of the distribution of the returns earned by the shareholder.
This is the long way of saying that the dividends to the shareholder are more variable than
the interest payments to the bondholder. Stock, in general, is riskier than bonds. The
shareholders who bear this additional risk expect to earn a higher return than bondholders
in the same firm.
Liability
One of the most important features of the equity contract is limited liability. This is
a legal concept, but it does affect the financial characteristics of the contract. The owner
of a sole proprietorship or a general partner in a partnership is liable for all of the actions
of the firm, whether he personally performs these actions or not. The owner of a grocery
store is liable for the actions of the driver of his delivery truck. If the delivery truck is
involved in an accident, the resulting damages could be so great as to cause the store
owner to lose his business and all his accumulated wealth. Even if the driver is not at fault,
the grocery store owner could face substantial losses.
Liability makes it difficult for firms to raise money by selling ownership positions. If
you become partners with someone, you become liable for his actions. This is a major step
for most individuals, and most investors seem to prefer a more passive position. Someone
who has a day job wants to invest money and earn a return on that investment; she does
not want to gamble with his probably modest fortune. Large firms with the capability of
making lots of big "things" have lots of different ways for mistakes to be made, hence lots
of potential liability. Small investors typically would not want to risk everything on someone
else, so it would be virtually impossible to build a large company that could trade in world
markets if liability were not limited.
The equity contract solves this problem by providing the investor with limited liability.
Incorporation allows firms to sell equity with limited liability in order to raise the funds
necessary to build the firm. The most that an investor can lose is the amount invested in
the stock1. If the firm has problems, those with claims against the firm cannot reach into
the bank accounts of the shareholders. This level of exposure to liability is acceptable to
most investors. A bad or unlucky investment should not mean the end of a person's
financial world. Most investors will consider investing in large corporations only if this level
of protection is offered. This is the reason that most large organizations are of the
corporate form. Limited liability is a fundamental aspect of equity investments and the
reason why equity securities exist in the first place.
1
This is a legal concept and could be subject to change.
shareholders have been held to other standards of liability.
In the past in the US,
The Contract and the Firm
The equity contract has implicit characteristics that must be viewed from two sides,
the side of the firm and the side of the investor. A given characteristic of the contract may
be a benefit or a burden for either side. Limited liability is a benefit for both sides of the
contract since it makes the whole thing possible. The claim on the cash flows of the firm
may be a benefit for the shareholders, but the need to pay dividends may limit the growth
of the firm.
The cash flows that are called dividends are generated by the firm as a result of its
business activities. The firm produces and sells "things", pays off creditors and the tax
man, and the remaining money belongs to the owners of the firm, the shareholders. Equity
is sometimes called "residual" ownership since the shareholders only get what is left over
after everyone else has received payment. Recall that the Income Statement for the firm
looks like this:
INCOME STATEMENT
-
Sales
Cost of Goods Sold
Gross Profit
Fixed Costs
Depreciation
Earnings Before Interest and Taxes
Interest
Earnings Before Taxes
Taxes
Net Income
Preferred Dividends
Available to Common Shareholders
Common Dividends
Retained Earnings
The residual money available for the payment of all dividends is called the net
income. The net income is the result of one period of the firm's business activities, and
belongs to the shareholders.
This Income Statement shows that there are two main classes of shareholders,
preferred shareholders and common shareholders. These two forms of residual ownership
have different legal and financial characteristics.
From the financial side, preferred
shareholders have a senior claim on the net income (they get paid first), but in return for
the head-of-the-line privileges the preferred shareholders get only a fixed dividend.
Common shareholders have a claim on all the money left over after the preferred
shareholders are paid.
One important characteristic of equity securities is that the dividend payments do not
have to be made.
If there is no net income, there is no money available to pay
shareholders, preferred or common. This does not create a legal problem for the firm since
shareholders know that this is one possible outcome of owning the stock. Shareholders
own a "piece of the action", and if there is no action, there is nothing gained from this
ownership.
It is important to note that even when there is net income the firm may not pay out
all the available net income as dividends. The goal of the firm is to maximize the
shareholders wealth, and the managers of the firm may think that wealth maximization can
best be achieved by keeping as much of the net income as possible within the firm and
reinvesting it in additional plant and equipment. This is what happens with growth firms.
These companies produce "things" much in demand by the market, and additional
investment now can result in additional net income in future periods. If the management
of the firm feels that the wealth of the shareholders can be maximized by retaining the net
income, then it may do so. When management retains earnings, it should mean that the
discounted present value of the additional dividends that will be earned in the future due
to the additional investment exceeds the value of the earnings retained now.
From a practical point of view, managers will seldom if ever attempt to retain the net
income due to the preferred shareholders as dividends, even if there is some
super-fantastic investment available to the firm. The firm is contractually liable for the
dividend payments, but the management of the firm does have the ability to defer such
payments. If the preferred dividend is skipped, it is accrued and must be paid to the
preferred shareholders at a later date. The firm's implied obligation to the preferred
shareholders is that the preferred dividend will be paid, except in times of financial distress.
The preferred stock contract has some legal aspects that make it unlikely the managers
would withhold the preferred dividend if it can be paid. For all intents and purposes, the
greatest amount of net income that can be retained by the firm is the amount called
“available to common shareholders”.
Any time that the firm retains any money due to the shareholders, the managers of
the firm are forcing the shareholders to increase their investment in the firm. Money that
belongs to the shareholders from their "piece of the action" is being kept from them. Not
only must the managers have a good reason for holding this money back, they must also
account for the money held back. Money is not allowed to evaporate. The money that is
not paid to the common shareholders shows up on the firm's Balance Sheet as retained
earnings. If the firm decided to withhold the dividends due to the preferred shareholders,
this would also have to be recorded as a liability on the Balance Sheet with an account
name like “accrued preferred dividends”. (This type of an accrual account would be rare
since its existence would mean that the managers of the firm had either been forced to
miss the dividend due to very bad business conditions or that the managers were violating
the implied nature of the preferred stock contract.)
Balance Sheet
Cash and Equivalents
Accounts Receivable
Inventory
Current Assets
Gross Fixed Assets
- Accumulated Depreciation
Net Fixed Assets
Total Assets
Accounts Receivable/Accruals
Notes Payable
Current Liabilities
Long-Term Debt
Preferred Stock
Common Stock
Retained Earnings
Total Liabilities and
Owners' Equity
The right side of the Balance Sheet represents sources of funds that are invested
in the assets on the left side of the Balance Sheet. The money in the retained earnings
account is used to purchase inventory and equipment. This money will not be kept as cash
since the firm has no reason simply to keep cash away from its owners, the shareholders2.
There are reasons why a firm might choose to retain earnings as cash, but these are very
specific and typically relate to future purchases of inventory and equipment. Regardless
of whether the purchases are immediate or in the future, an increase in the amount of
retained earnings represents an involuntary additional investment in the firm on the part of
the shareholders. This does not mean that the shareholders would not agree to the
investment if they were asked, but they are not asked.
It is important to remember that the retained earnings account does not represent
cash.
Retained earnings is the level of involuntary investment that the common
shareholders have made in the firm due to the actions of the firm's managers. The money
that was retained is used for plant and equipment and assets that are used to make the
"things" whose sale will augment the Net Income on future Income Statements. Under
certain conditions, it may be necessary to change the level of this account to adjust for
changes elsewhere in the Balance Sheet, like when a stock dividend is issued, but it is not
possible to "take cash out of retained earnings". Retained earnings reflects ownership, not
cash levels.
The Details of the Contract
The equity contract comes in two forms, preferred stock and common stock. Both
types of equity represent ownership of the firm, and both types have a claim on the firm and
its assets. The difference between preferred and common stock is in the priority of the
claim. Preferred shareholders get priority in dividends and liquidation, and they pay for this
privilege by having a limit on the size of their claim. Common shareholders get everything
left over after all creditors and the preferred shareholders have been paid.
2
There actually is a reason for a firm to retain earnings as cash, but it has to do with
income tax avoidance on the part of the shareholders. The Internal Revenue Service takes
a very dim view of such behavior.
Preferred Stock
Preferred stock is the equity contract that has first claim on the Net Income of the
firm. A firm does not necessarily have to issue preferred stock, and most firms do not. The
holders of preferred stock get their money before the common shareholders, but they must
give something to the common shareholders for this "head-of-the-line" privilege. One
privilege that the preferred shareholders give away is the privilege to vote for the Board of
Directors. The Board of Directors is responsible for hiring the firm's managers, so the
Board has a direct impact on the way that the firm is run and the priorities of the managers.
Except under certain extreme circumstances, the directors are elected only by the common
shareholders.
The preferred stock contract is similar to a bond in that the dividend payment is
fixed. But while a bond has a finite life, the life of a preferred stock is infinite, unless the
preferred stock is callable and can be retired or has a specified life. Most preferred stocks
are perpetual; they have no specified retirement date. This is because equity investments
are ownership positions and not merely loans. Preferred stock is an ownership position of
the firm and should last as long as the firm lasts. Preferred stock that has a fixed
retirement date is actually acting as a substitute for debt.
The fixed nature of the preferred dividend makes the preferred stock very similar to
debt, and since the financial characteristics of the contract are very important to the
investors the nature of this payment should make a big difference in the way the preferred
stock is priced. Firms that have a history of paying preferred dividends on time find that the
preferred stock is priced like a bond and that this price reflects a low level of risk to the
investor. If a firm occasionally misses a preferred dividend, the cash flows from security
are seen as riskier, and the preferred stock is priced accordingly. The market does indeed
consider the quality of the cash flows when pricing a preferred stock.
Another difference between bonds and preferred stock is the source of the money
used to make the required payments. Interest payments on the bonds are allowed to be
deducted from the income stream before taxes while the money for the preferred dividends
is taken from the income stream after taxes. The reason that the two payments are treated
differently is that bondholders only lend money to the firm and are considered to be
creditors, not owners, of the firm. The owners of the firm, preferred and common alike, only
have claim on the money that is left over after all other payments are made, including tax
payments.
The preferred stock contract has a stated value, a par value, just like bonds.
Though this amount can vary, the typical par value for a share of preferred stock is $100
per share. This is an accounting item and may not have any bearing on the price that the
shares sell for in the market. The par value also has a practical application in some cases.
In those events where a firm is shut down or liquidated, the preferred shareholders receive
the par value of the preferred stock as the liquidation value of their investment. It makes
no difference if the stock originally cost the investor $20 or $200, on liquidation the
repayment to the shareholder is the par value. If during the liquidation process there is not
enough money to pay all preferred shareholders fully, each receives a pro rata share of the
available funds. Under such circumstances, there would be no money left to distribute to
the common shareholders, but that is another reason why this type of equity is called
preferred stock.
Preferred stock has a dividend rate, similar to the interest on bonds. For example,
a share of preferred stock in Little Joe's Chicken Plucking Company (LJCP) may have a
stated par value of $100 and a dividend rate of 8%. Each share of LJCP preferred would
be entitled to receive a dividend of 8% of $100 per year, or $8. Since most preferred
stocks do have a par value of $100, the interest rate and the payment are used
interchangeably. The LJCP stock could be called either an "$8 preferred" or an "8%
preferred"; both terms imply an annual payment of $8 per share. Firms may have several
different issues of preferred stock outstanding just as there might be several bond issues.
The dividend rates carried by each issue could be different, possibly reflecting the
conditions in the financial markets at the time of their issuance.
Though the preferred stock has a fixed dividend payment, the management of the
firm is not obligated to make that payment. Management could withhold payment if there
were no money available or for other reasons. Preferred shareholders protect themselves
from losing wealth due to the non-payment of dividends in two ways. First, most preferred
stock contracts specify that the dividend is cumulative. This means that if a dividend is
missed for any reason, the missing dividend(s) and all current dividends must be paid to
the preferred shareholders prior to any dividend payment to the common shareholders.
There is still a difficulty for the holder of the cumulative preferred stock because the
company is not obligated to pay interest on the money withheld. The managers of a
company could conceivably withhold all net income and reinvest it for the benefit of the
common shareholders without paying any interest to the preferred shareholders for the use
of their money. This is an example of the agency problem that exists when the managers
of the firm have control over both the preferred and common shareholders' money, but the
managers work directly for the common shareholders. This could become a real problem
if the managers' compensation was tied to a figure like the earnings per share which would
benefit from the additional investment.
The second level of protection that the preferred shareholders have is also
contractual. It is theoretically possible that the preferred dividend could be withheld even
when money exists so that it could be paid. Most preferred stock contracts also include a
restriction on the managers that makes such action undesirable. In order to get the first
claim on net income, the preferred shareholders had to give up their rights to vote for the
Board of Directors of the company. If the company misses a certain number of preferred
dividend payments, say three or four, the preferred shareholders can regain these voting
rights, possibly even having more voting power than the common shareholders. Once the
preferred shareholders get these voting rights, they can elect directors who will see to it
that the preferred shareholders get fair payment. Managers who play silly little games with
preferred shareholders will eventually find themselves facing the representatives of the
preferred shareholders.
The contract for preferred stock may also include features like callability and
convertibility. A callable preferred stock can be retired under the specified conditions at the
option of the firm. The firm may want this feature as part of the contract to provide latitude
in restructuring the company's Balance Sheet at a later date. Since this is a benefit for the
firm, the call price of the stock should be higher than the par value of the stock to
compensate the preferred shareholders for agreeing to having their stock called. For
example, the LJCP 8% preferred stock has a par value of $100 but could be callable at
$110 per share.
Such stock may also carry a higher-than-market dividend rate as
additional compensation for the shareholders.
Preferred stock may also be convertible into another security, typically common
stock3. This feature can be a benefit to both the preferred shareholders and the firm. The
preferred shareholders would benefit if the value of the shares of common stock into which
the preferred stock could be converted exceeded the value of the preferred stock. For
example, assume that a share of the LJCP preferred stock can be converted into two
shares of LJCP common stock. If the LJCP common stock is selling for $60 per share, the
value of the LJCP preferred stock would have to be at least $120 per share. Even if the
preferred shareholder chose not to convert the preferred stock it would still sell for at least
$120 since it could be converted and would then be worth that much as common equity.
The preferred shareholder will voluntarily convert preferred stock to common only
if the total dividend that should be received from the common shares would be greater than
the preferred dividend. Recall that the LJCP preferred stock pays the holder $8 per year.
This is $8 at the head of the line, not back with the common shareholders. To give up the
head-of-the-line privileges voluntarily, the preferred shareholder would have to make more
than $8 from the dividends on the common stock. This means that there would be no
reason for a holder of a share of $8 LJCP preferred stock, which is convertible into two
3
Virtually any type of security may be convertible, except common stock. Convertibility
usually implies that the security can be traded for a more junior security, that is, a security
with a less senior claim on the firm's earnings or assets under the conditions specified in
the contract.
shares LJCP common stock, to convert to the common stock unless the common stock
were paying a dividend in excess of $4 per share per year.
The holder of a preferred stock might be "forced" to convert the shares, however.
If the LJCP common stock is selling for $60 per share, the preferred stock is worth $120
as common, and the price of the preferred stock will reflect this fact. If Little Joe decides
to restructure the Balance Sheet by calling the preferred stock, the preferred shareholder
would be faced with the choice of cashing in the preferred stock for, say, $110 or
converting the preferred stock to common stock worth $120. Preferred shareholders are
wealth maximizers just like all other investors, and under these conditions, and will convert
their preferred stock to common stock rather than lose money. Those who do not want to
hold the LJCP common stock can sell it and use the money to buy a more suitable
investment. Little Joe would have succeeded in changing the preferred stock into common
stock without spending a dime. The convertibility feature when coupled with callability can
be a real benefit to the management of the firm in restructuring an existing Balance Sheet.
In some cases a preferred stock may have a sinking fund. A sinking fund is more
typically associated with a bond in that at the end of the life of the bond there is a balloon
payment of the principal due to the bondholders. Preferred stock usually has an infinite life
which means no balloon payment is due. Any preferred stock issue with a sinking fund has
an implied maturity date. From the point of view of the investor, a sinking fund makes
sense if there is the possibility that the firm may fail; the sinking fund means that money will
be available for the repayment of the par value of the preferred shares. Preferred shares
with a sinking fund are therefore "safer" than those without one and will carry a lower
dividend rate to reflect this greater degree of safety. Firms might offer a preferred stock
sinking fund just to get the lower dividend rate. In general, a sinking fund for a perpetual
preferred stock does not make a lot of sense. This fund would represent money that the
firm would have to sequester and restrict from productive uses. The firm and all its
shareholders are better off if the firm is directing its efforts to making the "things" that sell
in the market.
Common Stock
Common stock is the purest and most prevalent form of equity ownership; a firm
does not necessarily have preferred stock, but it does have common stock. Common stock
is the common denominator of ownership within a firm. Each share of common stock has
an equal claim on the firm, except in a few special cases. It is important to remember that
this is a residual claim. Common shareholders only get what is left over after everyone
else, including the preferred shareholders, has been paid off.
Common stock can be thought of in terms of the characteristics it does not possess.
It does not possess the "right" to a dividend; dividends can be paid only if earned and if
declared by the Board of Directors. Common stock is not callable. Common stock is not
convertible. Common stock has no sinking fund. Common stock has no guarantee
whatsoever. But common stock does have everything else.
Common shareholders have the right to elect the members of the Board of Directors.
The board oversees the management of the firm and assures that the shareholders are
getting good managers to run their firm. The firm belongs to the common shareholders,
and they get to have a say in how it is run. If the common shareholders become
dissatisfied with the management of the firm, the directors can act on that information or
be voted out in the next election. Given that the ability to vote for the directors is one of the
special characteristics, it may be surprising to note that in many elections the majority of
the eligible shares do not vote.
In some cases, large shareholders, like the trust
department of a major bank, may not vote intentionally in order to prevent a conflict of
interest between the trust department and the lending department of the bank. Most of the
lack of interest seems to be simple inertia on the part of individual shareholders; they feel
that their few votes will not make a difference so they abstain. Somewhat like national
politics.
Though the basic structure of common stock is the same for all firms, there are
occasionally special types of shares which are similar to common stock, but not quite.
These shares arise due to specific circumstances within a specific firm. For example, if
LJCP grows into a megabusiness and dominates chicken plucking on a worldwide scale,
it is doubtful whether Little Joe and even Big Joe have enough money to finance the
necessary expansion of assets. Firms sell common stock in order to raise money for
expansion, but with the sale of the stock control is diluted. LJCP was Little Joe's creation,
and he might want to keep control of it without having a bunch of outsiders telling him how
to pull feathers. This attitude could be the result of an overinflated ego or the realization
that Little Joe really is the only person who understands the ins and outs of this business.
The solution to this problem is the creation of classified stock.
Classified stock is common stock with missing pieces. If Little Joe wants to keep
control of the company, he has to control the Board of Directors. The only way that control
of the Board can be guaranteed is with a majority of the voting shares of common stock.
Notice that the emphasis is on "voting" shares. Little Joe currently owns all 1,000 shares
of LJCP common stock. These shares have voting rights, and Joe uses those votes to
make sure he has control of the Board of Directors. When selling new shares, Joe has two
methods by which to maintain control of the board. The common shares could be sold with
all the rights and privileges of normal common stock, except voting rights; sometimes these
are called Class A or Class B stocks. LJCP could sell a million shares of this type of stock,
and Little Joe would still have control of the company because he has the only shares with
voting privileges. Some investors are wary about buying such "incomplete" shares; even
outside investors might want the ability to talk to the management and have the
management listen. Without a vote, the shareholder has no way to make the managers
pay attention.
If the market really wants voting rights, LJCP could issue a million shares of normal
common stock and simultaneously issue another million or two million shares of "founders
stock" to Little Joe. Founders stock is common stock that has been stripped of all
privileges except voting rights. These shares do not have a claim on any of the money that
LJCP might make, so they do not have get in the way of the outside shareholders getting
their fair share of the earnings. But when it comes time to vote for the board, Little Joe will
have the majority of shares and can elect the majority of the directors, who should then let
him do what he wants.
Under this method, Joe still retains control, but the other
shareholders will be able to elect some members of the board, though not a majority. The
outside shareholders will have a way to make their voices heard at the highest levels of the
company.
The classification of common stock may or may not make a material difference in
the performance of the stock. If classified stock means that an incompetent group of
managers has control of the firm and cannot be dislodged, it is the wise investor who seeks
other investments. If classified stock means that earnings are being divided up in some
manner other than equal amounts per share, the potential investor can factor that into the
pricing decision. Classification is neither good nor bad in and of itself, but the existence of
classified stock should lead the potential investor to ask what the classification really means
and find out if it will have an impact on the performance of the stock.
Analysis of the Contract
The purchase of an equity security entitles the owner of that security to certain cash
flows, the dividends. Since these dividends are the result of the operations of the
underlying firm, they may have differing "quality". The idea that $1 in dividends from one
company is worth more than $1 from another company may at first seem strange; after all,
a dollar is a dollar is a dollar.... But remember that investors also consider risk in their
decision about how much to pay for a stock. When risk is taken into account, a dollar here
might not be worth a dollar there.
One of the problems in financial analysis (or any kind of analysis) is the use of
history. The fact that a firm has a strong record of earnings does not guarantee that there
will be earnings in the future, but the financial securities that investors purchase are claims
on those uncertain future earnings. Only the past is known, but the fortune of the company
lies in the future. For strong companies with a long history of paying dividends, there is a
good chance that the firm will be able to pay the next dividend. The quality of the dividend
is said to be "high"; these are the types of companies that attract investors who require a
steady income. Since the investor is confident that the next dividend will come, she is
willing to pay more for the security since she "knows" that she will be getting her money
back. Companies that have more variable earnings might not always be able to pay
dividends, and because of this these dividends would be less certain and more risky.
Investors would pay less for these stocks due to the uncertainty of the returns.
This is just another way of saying "risk and return". The firm with historically more
uncertain cash flows would be considered riskier than the firm that consistently pays
dividends. Because of the additional risk, investors will pay less for each dollar of dividends
from the firm with the greater uncertainty. When investors pay less for each dollar of
dividends, they set themselves up to get a higher return for each of their invested dollars.
Recall that the return on an investment is inversely related to the amount paid for the
investment.
To get this additional return, however, the investor must take a greater chance that he will
get no return. Just like in any game of chance, the higher the odds, the more is won; if the
investor wins.
Risk and Return
Consider two companies in the same line of business, Consolidated Cable Company
(CCC) and the Wimpy Wire Works (WWW). Consolidated has been around for years and
is a leader in the business of turning lumps of metal into long, strong strands. CCC is
always on the cutting edge and attracts customers who know that CCC will have what they
need, or be able to make it for them. Wimpy, on the other hand, deals with certain
specialty products and tends to follow the market rather than lead4. Because of its limited
product line, WWW sometimes has to turn away potential customers.
4
Playing "follow the leader" is not always a bad business strategy. Remember, the earliest
Christians got the hungriest lions.
Here is where the effect of the overall economy must be appreciated. During
periods of economic expansion, both CCC and WWW could be just fine. When the
economy is doing well, any good company should be able to find a market for the "things"
that it produces, especially if those "things" are components of or used in the manufacturing
of "things" made by other companies. Both companies could have more than enough
business and be very profitable. Both companies could make money, and the investors in
both firms could receive dividends.
But when the economy softens (hits the skids, goes south, takes a nosedive....),
there would be fewer customers for both CCC and WWW. A common occurrence during
rough economic times is that those customers that do buy tend to buy proportionately more
of the basic commodities. When money is short, only necessities will be purchased all
along the chain of production and consumption. Suppliers, like CCC and WWW, more
actively seek out customers, and larger firms have larger product lines to offer and can
possibly make better deals with respect to price and/or credit terms.
In a weak economy, CCC would probably fare better than WWW. Consolidated's
larger product line (one of the "invisible assets") means that the customer base is broader
and that many of the products might be considered necessary by other companies.
Though business might drop off, CCC would still be able to make some sales. Because
CCC maintains an active research and development program, new products could be
created to meet the needs of the changing market. Though earnings might drop, there
could still be earnings.
A weak economy might spell trouble for the Wimpy Wire Works. As business falls
off, there are few products to maintain sales or draw new customers. Existing customers
will probably cut back on their purchases, and some might even begin to purchase goods
from WWW's competitors if those competitors offer good enough deals. The restricted
product line and the lack of R&D means that WWW will not be able to field new products
to attract what customers remain in the market. Earnings will drop, and the firm could
experience losses. When there is no money, the equity investor gets no dividend.
The weakened economy and loss of business does not necessarily mean that WWW
will fail. Many firms make it through rough times by laying off workers and cutting expenses
(which, of course, reduces the overall level of economic activity even further). If WWW cuts
back enough, it might be able to hold on until business once again picks up. This might
require that the company keep all the money it makes or even borrow some money from
outsiders. Whatever happens, the equity investors probably will not get any dividends. The
goal of the firm is to maximize the shareholders' wealth, and this means that the firm must
take the steps necessary to survive into the next period. Once a firm closes, there will
never be any further dividends for shareholders.
The changes in the economy that lead to changes in demand for goods and services
cause the variability in a company's earnings that result in the variability of dividends paid
to investors. It is this variability in returns that makes investors uncomfortable; they cannot
be sure when or if they will get their money back or make a profit. It is this variability that
is related to risk since a greater variability of returns is related to investors' perceptions of
greater risk. Investors would undoubtedly feel more comfortable if this cause of variability
could be reduced, but that would mean someone or something would have control over the
entire economy. The economy is just too large to be controlled by anyone, no matter how
large, how intelligent, or how well intentioned5; there will always be economic fluctuations,
and there will always be this source of risk, even for the strongest companies.
Consider the risks faced by investors in CCC or WWW. For simplicity, assume that
the economy can only have three possible conditions, and that the probability of each of
these states of the economy is known. Further assume that the earnings per share (EPS)
for the two firms in each state of the economy are as shown below. Since all possible
states of nature are known, the probabilities of those states of nature are known, the sum
5
The experiences of the economies of Eastern Europe are a good case in point.
Regardless of political reasons, these governments thought they could control the economy
for the good of the people. They failed. Miserably. It will take many years to pick up the
pieces and restore a reasonable quality of life to these people. An individual's failure to
understand the real meaning of economic principles can have disastrous effects on
personal wealth, too.
of the probabilities is 1.00 (meaning one of the possible outcomes will happen), and the
outcome of each state of nature is known, the distributions for the returns for the two firms
are by definition risk distributions. Had any of these conditions not been met, it would not
be possible to utilize statistical tools to analyze this situation.
State of the
Economy
Probability of the State
of the Economy
CCC Expected
Earnings per Share
WWW Expected
Earnings per Share
Great
.30
$2.00
$3.00
Mediocre
.50
$1.50
$1.50
Terrible
.20
$1.00
-$1.00
During the good times, both CCC and WWW do well. In fact, WWW even has
higher earnings per share. During the terrible times both firms have a severe drop in
earnings, and WWW actually loses money (as shown by the negative earnings per share).
The variability of the earnings per share is the risk. But just looking at a table of numbers
does not give a good picture of the risk implicit in these investments. Risk can actually be
seen if these values are graphed, as shown below.
The difference in the risk associated with the expected earnings of the two firms can
be seen by looking at the spread of the distributions. The WWW distribution is wider than
that of CCC; WWW is riskier than CCC. CCC is not safe, though, since the distribution
does have a spread. This is evidenced by the basic statistics for the two distributions. The
distribution of the expected returns of the CCC stock has a mean of $1.55 and a standard
deviation of $.35. The distribution for the WWW returns has a mean of $1.45 and a
standard deviation of $1.39.
The concepts of risk and return are always present in any type of financial analysis.
This comparison of CCC and WWW shows that the equity securities of any firm within any
industry can exhibit a risky distribution of returns, whether the firm is an industry leader or
a follower. Investors must always be aware of risk, especially when it is not obvious. Risk
is always there and must be considered in any financial decision.
Valuation
The basic contract represented by common stock is an infinite series of forward
contracts. Unlike debt contracts, the forward payments in equity contracts are subject to
variability. If the company does not make any money, there is no residual value to be
distributed among the shareholders. Recall that the time line for the cash flows associated
with the basic equity contract looks like this:
The shareholder is entitled to all the future dividends that are paid, and since the
share of stock has a theoretically infinite life, the dividends can run forever. Note that it is
only the dividends that count. Money that is held within the firm as retained earnings might
"belong" to the shareholder, but since it is still held by the firm, it does not count. The only
money that matters is the money that the shareholder actually gets. This is a very
important concept for all types of investments. Only money in the hand counts.
This may seem to be a rather restricted view of the value of the firm since it does not
include the concept of liquidation value, but for most firms liquidation would mean that the
firm had failed. Once a firm has failed, there is usually little or no money left for common
shareholders due to the claims of senior creditors.
Though this dividend model is
potentially incomplete for firms with liquidation on the horizon, it is satisfactory for firms
viewed as going concerns.
The real question for the investor is how much to pay for the share of stock. The
purchase price, a present cash outflow, should in some way reflect the value of the
dividends to be received, future cash inflows. This is where present value techniques come
into play. A fair price for the stock would be that price at which the discounted value of the
future cash flows would be equivalent to the current share price. If the discounted value
of all the dividends from a share of stock is $30, $30 is a fair price for that share of stock.
If the stock actually is selling for $25 a share, it is a bargain. If the stock is selling for $40
a share, it is overpriced. The calculation of the present value of the future cash flows
therefore gives an idea of what a proper price is for a given share of stock.
It is good to recall at this point that value and price are different concepts. Value is
how much a "thing" is worth and price is how much the "thing" costs. Value is inherent to
the "thing" while price is related to the market for the "thing". It is easy to think that the
price of an object is its value; it is also a mistake. Investors must always be aware of the
difference and take advantage of it when the opportunity presents itself.
Finding the present value is conceptually easy, but the practical aspects of the
calculation can be a bit stickier. Recall that the time value of money problem has four
pieces, and to calculate the present value a person needs to know the future value of the
dividend cash flows, the times at which these cash flows occur, and an interest rate that
reflects the amount of risk being borne by the investor.
where:
i = discount rate, t = time period
The greatest difficulty lies in trying to find a crystal ball that will give accurate values
of the future dividends. These values are all parts of future probability distributions, and
these probability distributions depend on a firm, its products, the managers, the local
economy, the international economy, and maybe even the price of tea in China. Anyone
who says he has an exact answer to this aspect of the problem is full of beans. Anyone
who is looking for exact answers should stay away from stocks, because those answers
simply do not exist. People who hold stocks must understand that this variability of future
income streams is the risk that they are being paid to bear.
An absolutely 100% exact solution to the valuation equation is out of the question,
but that does not mean that a decent estimate cannot be calculated. It is better to know
that a stock should be worth something like $30 a share than to know nothing at all. In
order to make the mathematics work, it is necessary to make some assumptions. Making
assumptions is often an important part of many activities that involve the planning for the
future. The key to the process is to make sure that the assumptions are reasonable and
to identify any situations in which the assumptions break down.
Since the dividend cash flows present the biggest problem in estimation, it is
necessary to make some sort of assumption concerning them. Dividends can differ from
year to year, depending on the fortunes of the firm. Management decides how much of net
income goes for dividends and how much is retained, so the behavior of the managers is
also important in this part of the problem. Managers often try to behave consistently in the
declaration of dividends. Shareholders like to know what is going to happen, and the firm's
management often tries to make sure the dividends are reasonably consistent. Sometimes
this may mean holding back a little more money than really necessary as retained earnings,
and sometimes firms have even been known to borrow money just to have the cash
available to pay dividends. The point is that management often tries to smooth the dividend
cash flows so that shareholders can make decent estimate.
Preferred Stock
If dividends are constant as they are with preferred stock, the solution present value
problem is relatively simple.
Preferred stock dividends are all the same size, so the equation becomes
The infinite series on the right side of the equation has a finite solution if the value
for i is greater than zero. This is one of those places where an assumption is being made,
and it is imperative that the assumption be reasonable. Since it does seem reasonable that
an investor would want a positive return, it is reasonable that the discount rate i is greater
than zero. This is actually a fairly innocuous assumption, but it is an assumption made so
that the mathematics will work. Even innocuous assumptions must be remembered.
Another assumption lying in the mathematical weeds is that the discount rate i
remains constant forever. It is extremely unlikely that the discount rate will remain
constant. The history of financial markets indicates that interest rates, and hence discount
rates, do indeed move through time. It could be argued that there is some long-run
average discount rate that is stable across time, but forever is a long time, and it might be
a stretch to make an assumption of that sort. This is not a reasonable assumption, but it
must be tolerated if the problem is to be solved. In a stable economy interest rates do not
oscillate too wildly, and by assuming that this rate is constant it is assumed that the
economy will probably go on about like it is going now. Without information to the contrary,
it is customary to make this assumption.
Given that the discount rate is constant and greater than zero, the equation
becomes
That's right. After all that work and two assumptions, the value of the infinite series of
dividends from a share of preferred stock that are the same size is simply
For a contract like preferred stock that pays a constant dividend from now until
forever, the value of that set of cash flows is merely the size of the dividend received
divided by the discount rate. Just to make things interesting, when referring to the discount
rate used for equity securities, many times the letter k is used instead of the letter i. There
are some minor historical reasons for doing this, none of which are important here. The
usual way the Preferred Stock Valuation Model is written is:
This is a nice little equation, and easy enough solve, but another assumption just
sneaked into the whole process. This equation equates the price of the stock with the
discounted value of the dividends. Price and value are NOT the same thing. The price of
any object is set in the market by the forces of demand and supply. This change reflects
the fact that in most cases the price of a security is based on its value.
The solution to the equation only gives a fair value for the discounted future cash
flows. The price of the stock in the market might be quite different. Most investors are
really trying to find such instances of mispricing. If a stock that has a value of $30 is selling
for $25, the smart investor will buy the stock, tell everybody how great the stock is and
convince them that the stock is really worth $30, and then sell the stock when the rest of
the market recognizes that the stock really is worth $30 and adjusts the price accordingly.
Just finding an underpriced stock is not enough; the market must be made to realize that
the stock is underpriced so that the price will go up. Money cannot be made in the market
by keeping secrets. The same logic can be applied to overpriced stocks using a technique
know as short-selling. Either way, there may be difference between price and value that
can be exploited by the astute investor.
It should also be obvious that the value of the future dividends depends on the
discount rate used in the equation. The preferred stock dividend is fixed, so the discounted
value of the dividend stream is an inverse function of the discount rate. If the discount rate
doubles, the value of the stream of future dividends is cut in half. This explains why
investors in fixed income securities like preferred stocks and bonds are very concerned
about market interest rates. If money gets tight so that the cost of borrowing increases, the
cost of capital increases to all investors, and the value of fixed income securities drops.
When interest rates drop, the value of fixed income securities increases, and the price
follows upward. Anyone who thinks he has a good way to predict interest rates can do very
well with fixed income securities. Of course, if the crystal ball is wrong once in a while, the
same investor can get burned.
The effect of the interest rate also explains why different investors have different
opinions concerning the value of a preferred stock. Consider a share of preferred stock in
Little Joe's Chicken Plucking Company (LJCP). This stock pays an annual dividend of $8
per share, and there is virtually no chance that the payment will be missed since the
business is doing very well. This stock might look like a good investment to Cousin Clyde
who has been putting his money in the bank and earning 10% interest per year. If Clyde
were to use money from his savings account to buy this stock, the value of the future cash
flows to Clyde would be
Clyde could pay up to $80 for a share of this stock and still get a return equivalent
to what he would earn by leaving the money in the bank [ ($80.00) (.10) = $8.00 ]. If Clyde
could buy the stock more cheaply, it would give him a return higher than he could earn at
the bank.
If Uncle Bubba has investable money in an account that only pays him 5% per year,
this same share of LJCP preferred stock would be worth more to him than to Clyde.
If there were only one share of stock available and both Clyde and Bubba were bidding for
it (remember, this is a market), Clyde would bid the price up to $80. If Bubba were to bid
the price up to $81, Clyde should drop out since he gets a better deal by leaving his money
in the bank. In this case Bubba got one heck of a deal, and on his investment he will earn
In the example above, once Clyde dropped out of the bidding, Bubba got the stock
at a price that provided him a return only slightly lower than the return acceptable to Clyde.
Bubba could have paid quite a bit more for the stock, but even Bubba is not crazy enough
to raise his own bid. No rational investor ever pays anymore than he has to for any
investment (unless he is like Big Joe and is using his money to keep Little Joe busy).
If this investor only has enough money for a few shares of stock, the price of the
next shares could be significantly different. Once Bubba had purchased all the shares he
wanted, Clyde would be bidding against someone else for any remaining shares. This is
one reason why stocks with small capitalizations or stocks in closely held companies can
have seemingly wild price swings. The demand/supply curves in the market are relatively
steep, and any movement away from the last price is a real movement.
The diagram below illustrates how price can change in a thin market. For a given
supply of stock and some demand at T=0, there is a market equilibrium price at T=0. If
there should be an increase in demand such that the demand curve shifts to DemandHigh,
the price will shift to PriceHigh. A similar argument holds for a decrease in demand. The
relative slope of the demand curves and the supply curve will dictate the amount the price
will change. If all the curves are fairly flat, there will be little price change. This would be
consistent with a market with a lot of demanders and suppliers for the same "thing", in this
case a share of stock. If either or both sides of the market are thin, the curves would have
steeper slopes, as shown below, and any change in either the demand or supply
characteristics of the market could have a dramatic effect on stock prices.
For most stocks that are actively traded in the market, all members of the population
of potential investors have pretty much the same cost of capital. The big players can
borrow money at market rates and invest it in stocks. Or if they do not borrow the money,
their choices for investing are pretty much the same, so once again they face the same
cost (or opportunity cost) of capital. That is the reason that most widely traded stocks hold
their value, unless, of course, something really changes.
Common Stock
The calculation of the value of the future dividends of preferred stocks is really so
easy that it would be nice if it were as simple for common stock. After all, the value of a
share of common stock is still the discounted value of the future common stock dividends.
The only real difference between preferred and common stock is that the dividend
on common stock can change.
In fact, most common stock investors expect their
dividends to grow over time. The changing dividend makes it mathematically inappropriate
to factor out the dividend as was done with the preferred stock.
All is not lost, however, if another assumption is made. The change in the dividend
may not be the same from year to year, but it could be assumed that there is some long-run
average growth rate for the dividend. Since the set of dividends is infinite anyway, a longrun average growth rate might even be the most appropriate rate to use. If it is assumed
that the dividends do indeed have a long-run average growth rate, called g, it is possible
to rewrite the dividend terms in the previous equation. For reference purposes, the initial
dividend, Div0, is used. The purchaser of the stock will not actually receive this dividend
since it was paid to the previous owner of the stock. Under these conditions, the terms for
the dividends can be written as:
Div1 = Div0 (1+g)
Div2 = Div1 (1+g)
Div3 = Div2 (1+g)
:
:
DivN = DivN-1 (1+g)
This is a neat little series that shows each dividend growing at the rate g from the
previous dividend, but it does not really help the problem of solving the infinite series unless
the following mathematical substitution is made.
Div1 = Div0 (1+g)
Div2 = Div1 (1+g)
= Div0 (1+g) (1+g)
= Div0 (1+g) 2
Div3 =
=
=
=
:
DivN =
Div2 (1+g)
Div1 (1+g) (1+g)
Div0 (1+g) (1+g) (1+g)
Div0 (1+g) 3
Div0 (1+g) N
With this substitution (and using k instead of i), the valuation equation becomes:
This still looks like something only a mathematician could love. With one more
assumption, it can be made reasonable. The series of terms inside the brackets is an
infinite series, just as it was for the preferred stock calculation, but the numerators of the
terms are not as simple as in the preferred stock case. An infinite series will converge if
and only if the terms decrease (each term is smaller in magnitude than the preceding term),
which means each of the terms inside the brackets must be less than one. For each term
to be less than one, the value of g must be less than the value of k. This means that the
growth rate of the dividends must be less than the discount rate used on the dividends.
With this assumption, the equation becomes:
The substitution in the last step was carried out for the convenience of the user. In
the second from the last step, there is a "+g" in the numerator and a "-g" in the
denominator. Making the substitution of [ Div1 ] for [ Div0 (1+g) ] in the numerator makes
it less likely to confuse the signs. This equation is usually written in the form where price
is substituted for value.
This is known as the Gordon-Shapiro Dividend Discount Model and is one of the
most famous and most useful stock pricing models ever developed. It recognizes that only
the money received by the shareholder counts as wealth and that rational investors will not
pay anymore for a share of stock than the discounted value of these cash flows that accrue
in the future.
The denominator of the Gordon-Shapiro Model shows an interesting result of the
assumptions that were made and the mathematics that was performed. The growth rate
of the dividends (g) must be less than the discount rate (k). If the two were equal, the
denominator would be zero, and the fraction would be undefined. If g were greater than
k the denominator would be negative and so the whole fraction would be negative. Even
on an intuitive level, it would not make sense to pay someone to take a stock away if the
stock dividends are growing at a high rate. This relationship between the growth rate of
dividends and the discount rate is one weakness of the Gordon-Shapiro Model, though it
is not a fatal weakness.
There are times when the growth rate of dividends may exceed the cost of capital
for a firm. During periods of start-up or rapid expansion, or if the firms "things" happen to
be doing very well, the firm can realize very good earnings and thus a high growth rate of
dividends. The question is whether or not the long-run growth rate can exceed the cost of
capital. In the long run, the growth rate of any firm cannot exceed the growth rate of the
economy; if it did, the firm would eventually become the economy. The long run growth
rate of a firm, and therefore its dividends, is constrained to be equal to or less than the
growth rate of the overall economy. Investors seek a real return on their investments and
so price financial securities to earn more than just enough to keep up with the economy.
In the long run, the pricing behavior of investors assures that the cost of capital will be
greater than the growth rate of dividends, though there could be periods where the
relationship does not hold.
Recall that the dividend on a share of preferred stock is constant. Since the
preferred dividend does not grow, its growth rate is zero. When the Gordon-Shapiro Model
is used to price preferred stock, a growth rate of zero is used, and the resulting formula is
the same as the one derived earlier for preferred stock. The Preferred Stock Valuation
Model is just a special case of the Gordon-Shapiro Model.
The Gordon-Shapiro Model seems to assume that the stock will be held forever, and
this is not very realistic. As it turns out, though, the projected holding period has no effect
on the model. Assume that an investor is considering the purchase of a share of stock and
plans to hold for three years and then sell at the prevailing market price. The cash flows
that would accrue to the investor from this investment would look like:
The price of the stock today should reflect the discounted value of these projected
cash flows. The big question is what the price of the stock will be three years from now.
If the investor were to sell the stock at that time, a fair price for the stock would be the value
of all future dividend cash flows.
This time line looks just like the original time line used in developing the GordonShapiro Model. The only difference is that instead of being at time=0, the analysis is
performed at time=3. But the stream of dividends after time=3 is still infinite, and using the
same assumptions as before, the price of the stock at time=3 would be
The price at time t=3 is the value of all the future dividends discounted back to
time=3. Since Price3 is discounted back to time=0, all the dividends that were discounted
back to time=3 are actually discounted back to time=0. The net effect is that all dividends
are still discounted back to time=0 if there is a three year holding period, or a holding period
of any length.
The time line below shows the entire time line for this problem. When this stock
value at time=3 is discounted back to time=0, the net effect is the same as if all dividends
had been discounted back to time=0.
This is a very good result to have. All stock buyers and sellers, regardless of their
planned holding periods, will price the stock in the same way and come to the same price.
There should be no premium or discount paid just because someone has a different holding
period. That means that the stock market will operate more smoothly than if all the players
used different pricing models. Under the assumptions of the Gordon-Shapiro model, all
investors use the same pricing model which results in a continuity of prices in the market.
Examples
It may seem that all the work presented so far makes the pricing of equity securities
into a big, complicated procedure. Pricing equities is actually pretty easy, as long as the
boundary conditions of the Gordon-Shapiro Dividend Discount Model are met. A few
examples will show just how easy things really are.
Preferred Stock
(Be warned that this is really a simple problem, but it is going to be beaten severely around
the head and shoulders to make it submit to several different types of solution. The reason
this is being done is to illustrate that the principles of valuation hold no matter how they are
approached. There are usually many ways to analyze a problem, even a simple problem
like this one, and any technique if done properly, will result in the same solution. Do not
lose sight of the fact that this is a simple problem being tortured until it confesses.)
P1.
Little Joe's Chicken Plucking Company (LJCP) has an issue of 8% perpetual
preferred stock outstanding. This stock has a par value of $100 per share, so the
annual dividend is $8 per share. Aunt Agnes feels that this stock would make a
good addition to her portfolio, if it is fairly priced. Agnes intends to hold the stock for
five years until she cashes in her portfolio and moves to Aruba. The LJCP preferred
stock has never missed a dividend nor does it appear that business in the future will
be so bad that a dividend will ever be missed. The money that Agnes would use to
purchase the stock is currently in a certificate of deposit (CD) at her bank that earns
6% per year. Under these conditions, what is the most that Aunt Agnes should be
willing to pay for this LJCP preferred stock?
The first step in any valuation problem is to determine what valuation model is
appropriate to use.
The discounted cash flow model, shown below, is always an
appropriate model to use, but at times it can be a little messy.
where:
i = discount rate
t = time period
The time line for solving this problem would look like this:
There is still a piece missing, the price that Aunt Agnes will receive in five years.
Since she plans to sell this stock along with the rest of her portfolio, it is reasonable to
assume that she will be able to sell the stock for the then fair market price. (This
assumption is made frequently when valuing equity securities, but it is an assumption
nonetheless.) The fair price for this LJCP stock in five years would be the discounted value
of all future dividends to be paid by the stock. The time line of dividends to be paid to any
stockholder in five years time would look like
This stream of cash flows constitutes an infinite annuity. The formula for solving an
infinite annuity is merely an application of the Present Value Annuity Factor formula for
annuities not listed on the table
where:
N = number of periods, k = discount rate
When N is very large, the denominator of the fraction in the numerator becomes very
large for any positive value of k (and the discount rate is a positive number, namely 6%).
This large denominator of the fraction makes the fraction very small. As N approaches
infinity, the value of the fraction in the numerator approaches 0. The Present Value Infinite
Annuity Factor (PVIAF) becomes
where:
k = discount rate
The astute reader may have noticed how similar the PVIAF is to the formula for
valuation of a preferred stock. A preferred stock is an infinite annuity, so the similarity
should come as no surprise. In fact, this PVIAF value is going to be used to find the value
of a share of preferred stock (remember Aunt Agnes?), but in this structure of the problem
the solution will be obtained through a strict Present Value approach.
Recall that the problem at this point is to find the value of an infinite annuity of $8
dividends discounted back to time=5. This should be the market value of Aunt Agnes'
share of LJCP 8% preferred stock when she sells it in five years. The big question now is
what the appropriate discount rate will be in five years. Trying to guess the interest rate
five years from now for any investment requires a very powerful crystal ball, and if anybody
out there has such a device he is not telling (if you owned that crystal ball, would you
REALLY tell the world about it?).
An assumption is required regarding the future discount rate, and in the absence of
contrary information, the practice is to use the discount rate being used for the rest of the
analysis. Aunt Agnes has a cost of capital of 6%, which results in a PVIAF of
Since the annuity tables are standardized to a payment of $1 per period, the present
value of an infinite annuity of $1 evaluated at a discount rate of 6% is $16.67. This may
seem like a small value since $1 per year for sixteen years is equal to $16, and an infinite
stream of money lasts a lot longer than sixteen years. This example once again illustrates
that a dollar today is not the same as a dollar next year or later. Time really does make a
difference, and a dollar a thousand years from now is not worth a whole lot today. The
actual, total, complete value of an infinite stream of one dollar bills really is just $16.67
when the discount rate is 6%. Different discount rates will naturally give other values.
The time line for the value of all the $8 dividend payments beyond time=5 shown as
an annuity and evaluated to time=5 looks like
A fair market price for the LJCP 8% preferred stock five years from now is $133.33
given a discount rate of 6%. Using this value in the time line for the cash flows Aunt Agnes
will receive, the time line looks like
While it is certainly acceptable to evaluate this time line as separate cash flows, it
can also be viewed as a five period annuity and a lump sum and evaluated as follows:
The most Aunt Agnes should pay for a share of the LJCP 8% preferred stock is
$133.33 (there is a penny of rounding error in the diagram above due to rounding in the
Present Value tables). But wait, that is the same price the stock will be in five years. And
it is the same price the stock will be in one year or a hundred years or at any time.
Regardless of where a person is on the time line, this stock has an infinite future and is
being evaluated at the same discount rate; the discounted value of the future cash flows
must be the same at all points on the line. This share of 8% preferred stock when
evaluated with a discount rate of 6% will always be worth $133.33.
The process shown above is absolutely correct at each step. All assumptions are
stated, and all the mathematics are done properly. But this is one miserable way to find
out how much Aunt Agnes should pay for the stock. It would make the problem easier if
some assumptions could be made before the analysis began. The right assumptions might
allow the use of another valuation model, one that is simpler.
The valuation model that was derived for preferred stock was of the form
This model assumed an infinite stream of equal payments and a single discount rate. All
of those assumptions attain for Aunt Agnes, so with this model the value of the stock is
That was a lot easier, but the only reason it worked was that all the mathematics
was done prior to putting the first number in the formula. The assumptions concerning the
size, pattern, and duration of the payments and the constancy of the interest rate were
already built into the model. It is extremely important to remember what assumptions are
in the model before the model is used; if the assumptions of the model do not match the
situation it is time to choose another model.
It was previously noted that the Preferred Stock Valuation Model was actually a
special case of the Gordon-Shapiro Dividend Discount Model. Aunt Agnes could use that
valuation technique, if the underlying assumptions are appropriate. It appears reasonable
to assume that the dividends will be paid on time and go on forever, so dividends can be
regarded as an infinite series of cash flows. Since the preferred stock contract specifies
a fixed dividend, the growth rate of the dividend is zero. Aunt Agnes is going to hold the
stock for five years when she plans to sell it along with the rest of her portfolio. Five years
is not forever, but if she sells the stock at the market price she will receive the discounted
value of all future dividends, and it has been shown in the derivation of the Gordon-Shapiro
model that the planned holding period has no effect on the model. The discount rate is
based on the rate paid on a bank CD which is assumed to be constant. These are the very
conditions it takes to use the Gordon-Shapiro Model. The most Agnes should pay for a
share of the LJCP preferred stock is:
These three approaches to finding the value of the LJCP preferred stock have
resulted in identical answers. Since each approach is based on present value techniques,
the result had better be the same. The difference in the three approaches was the
assumptions being made and at what step they were being made. In the Present Value
approach, the assumptions were made during the analysis. In the Gordon-Shapiro model
and its derivative the Preferred Stock Valuation Model, the assumptions were made prior
to the application of the model to the problem. The assumptions implicit in some models
may not always be appropriate for the problem at hand, and the wise analyst will
understand the implicit assumptions in every model before it is applied.
Each technique found that the value of the LJCP 8% Preferred Stock was $133.33
to someone like Aunt Agnes who has a cost of capital of 6%. Aunt Agnes' decision on
whether or not to purchase the stock will depend on its price. Since price is determined in
the market, it could be quite different from $133.33. The market price at which the LJCP
preferred sells tells the cost of capital for the market as a whole for a stock of this quality.
The valuation equation provides the ability to identify the market's opinion of the
discount rate appropriate for the LJCP preferred stock. It is only necessary to use a little
bit of algebra to turn the valuation equation inside out. The Preferred Stock Valuation
Model is:
By performing appropriate, simple algebraic manipulations, the formula becomes:
This expression of the relationship between dividend and price results in the
discount rate implied by the price. If the market price of the LJCP 8% preferred stock is
$80 per share, the implied discount rate for the stock is
The market is pricing the LJCP stock to provide a return of 10%. This level of return
could reflect the general price of money to the market participants, or it could reflect the risk
that the market perceives to be associated with the cash flows from the stock. Now it is
time for Aunt Agnes to make her decision. If she really believes that the LJCP preferred
stock is safe and will have the cash flows that she projected, then the stock is priced to
provide her a significantly higher return (10%) than she is now earning on her CD (6%).
Agnes could cash in the CD and buy the stock.
The other possibility is that the market has actually recognized that the LJCP 8%
Preferred Stock does indeed have a certain level of risk.
It could be that new
hypoallergenic fibers are displacing chicken feathers in the pillow stuffing market at such
a rate that Little Joe might have a tough time in the future keeping the company profitable.
The higher level of return could be caused by the market paying a low price for the stock.
When the market prices any stock to yield a higher-than-expected return, the prudent
investor should investigate the reasons why, especially if the projected return is higher than
other firms in the same business.
It is not unusual for high quality preferred stocks to provide yields higher than bank
CDs. Banks have to earn money for their stockholders, too, so the interest paid on CDs
is as low as competitively possible. But CDs often are insured by the federal government,
and for some investors this insurance is sufficiently important to miss a couple of points of
interest. Stocks have no guarantee, and history has shown that even strong companies
can fall on hard times. Even high quality preferred stocks have the potential of becoming
risky sometime in the future, so there is some reason for investors to expect a higher return
from preferred stock over bank CDs.
It should be noted that many professionally managed portfolios, like those of
insurance companies, pension funds, and conservatively managed mutual funds, do
contain high quality preferred stock. These managers apparently feel that the excess
return more than compensates for any additional risk. There is one disadvantage for the
small investor with respect to investing in preferred stocks. These large portfolios, under
certain conditions, do not have to pay taxes on all of the dividends paid on the preferred
stock they hold. This means that the large investors can bid the price of the stock up a bit
higher than if the dividends were fully taxed and still receive an "appropriate" after-tax
return. Small investors will receive a slightly lower than "appropriate" return on preferred
stocks that are favored by the large portfolio managers. It may be difficult for small
investors to beat the professionals in the market, but it is possible for small investors to
earn returns in the market higher than possible from alternative sources like commercial
banks.
Common Stock
P2.
Aunt Agnes might also be interested in the LJCP common stock for a part of her
portfolio. She has learned that the LJCP common just paid an annual dividend of
$2.00 per share and that this dividend was consistent with the long-run dividend
growth rate of 5% that has characterized LJCP common stock. Since the common
stock will always be subject to some variability of returns, it is a riskier investment
than bonds or preferred stock. Agnes feels that a discount rate of 15% is sufficient
to compensate for the additional risk. Aunt Agnes plans to hold this stock five years
before she sells it and sails off to her Caribbean retirement. Under these conditions,
what would be a fair price for Aunt Agnes to pay for the LJCP common stock?
After all the manipulations conducted on the analysis of the preferred stock, this
should be very simple. The underlying assumptions need to be considered in this analysis
just as they do in every analysis. The model used as the starting point for the valuation of
common stock is the Gordon-Shapiro Dividend Discount Model that has already been
derived. The Gordon-Shapiro model assumes that a dividend is paid (it is), that the
dividend has a stable long-run growth rate (it does), and that the discount rate is constant.
Once again, since there is no contrary information available, it is customary to assume that
the current discount rate will be constant. Since the boundary conditions of the model (the
assumptions) are met, the model can be used. Under these conditions, a fair price for Aunt
Agnes to pay for the LJCP common stock would be:
Aunt Agnes' projected holding period makes no difference since the price she will
receive at time=5 will be the discounted value of the future dividends, just as was the case
for the preferred stock. Once these dividends are discounted back to time=0, the net effect
is the same as if Aunt Agnes had had an infinite holding period.
This solution to the Gordon-Shapiro Model shows the relationship between the price
and the dividend. The price on the left side is today's price, but the dividend on the right
side is the next dividend. Recall that this convention to eliminate any confusion from having
a "+g" term in the numerator and a "-g" term in the denominator. When the next dividend
is not given directly, it is a simple task to calculate what it will be since the current dividend
and the growth rate of the dividend are already specified. This was done above to show
that it really is easy once each piece is in its proper place.
People new to the analysis of investments sometimes get confused by the fact that
today's price should depend on the next dividend. It might be easy to remember the time
relationship of the price and dividend terms by realizing that if a share of stock is purchased
today, the invested money needs to be at risk for a while before a dividend can be earned.
If the stock is purchased at time=0, the first dividend that will be earned will be the dividend
paid at time=1. A bank does not pay interest on a CD up front, so it is reasonable that the
dividend on the common stock should have the same structure with respect to the
dividend7.
Back to Aunt Agnes. She has now figured out that the value of a share of LJCP
common stock to her is $21.00. The price of the stock is whatever the market says the
price of the stock is. If the price is above the $21.00, Aunt Agnes should look for better
7
The reason that the preferred stock valuation model does not specify the next dividend
is because all dividends are the same size.
investments. But if the price is below $21.00, the decision to purchase is not automatic.
Suppose that LJCP common stock is selling for $15.00. Either Aunt Agnes is getting
one great deal, or there is something going on that Aunt Agnes is not aware of. A good first
step in examining this aspect of the problem is to find the implied discount rate that the
market is using for evaluating the stock. The Gordon-Shapiro model is:
The right side of the equation contains three separate terms, the dividend, the
growth rate of dividends, and the discount rate, that could affect the answer on the left side,
the price. If it is assumed that the dividend and its historical growth rate, which are both
items of historical record, are the same for all investors, the only factor that can make a
difference in price is the individual investor's discount rate k. A little algebraic manipulation
shifts the terms of the model around until it reads
This little piece of mathematics provides a real insight to the process of stock pricing.
All investors are seeking to earn a return, k. This equation shows that the return can come
in one of two forms. The first term on the right side of the equation it the expected dividend
payout rate for the common stock (like the dividend rate for preferred stock). The
difference in the times for the two terms is consistent with the notion that an investor will
wait one period before realizing a return on his invested money.
The second term on the right side is the growth rate of the dividends. In a long-run
environment, the growth rate of the dividends will be the same as the growth rate of the
stock price (the proof of that is a bit messy). The Gordon-Shapiro Model assumes an
infinite holding period, which is about as long-run as possible.
This term not only
represents the growth rate of the dividends, but it also represents the growth rate of the
stock price; this term is the expected capital gains that will be realized by holding the stock
for one period. This is the percentage amount by which the stock price should change.
This new equation shows that investors can take their return in either one of two
ways, either as a dividend that is paid out directly or as a capital gain in the price of the
stock8. The investor should be indifferent to which way the return occurs. Money paid out
directly as dividends can be reinvested if the investor chooses to do so. If the money is
retained in the firm, the stock price will rise, and the investor can sell the stock to reap the
capital gains if he should so choose. From a theoretical viewpoint, it should make no
difference to the investor whether the firm pays dividends or retains the money and lets the
price of the stock increase.
Theory is very nice, but often it does not describe reality. The way that the return
is earned, dividends or capital gains, has an effect on the type of investor that buys the
firm's stock. In practice, some firms try to pay out money as dividends while others retain
the money and let the stock price rise. Most firms do a little of each. A firm that pays
generous dividends will attract investors who need periodic cash payments, like widows
and orphans and pensioners. These folks would rather get a check in the mail than have
to go through the trouble of selling a few shares of stock to get the money they need.
Investors who do not need the money right now, like doctors and lawyers and others whose
current income exceeds current needs, will tend to buy stocks in companies that keep the
money and reinvest it in the firm. This causes the stock price to grow, and these investors
do not have to worry about reinvesting the dividends each period.
This difference between the types of investors and the way a company pays
dividends is called clientele theory. Different dividend payment practices attract different
clients (investors). These investors are shareholders with votes, so once a firm has
8
This statement and the following discussion assume that the investor lives in a world
without taxes. Even equal tax rates on dividends and capital gains does not work since the
taxes on capital gains can be deferred while the taxes on dividends must be paid
immediately. For the purposes of this discussion, taxes are completely ignored.
attracted a certain clientele it is sort of stuck with its dividend payment policy. A firm that
had attracted clients by paying dividends would be hard pressed to begin retaining all
dividends since the shareholders would get upset and vote in a new Board of Directors.
The whole area of dividend theory is a quagmire. It is one of the most studied and least
understood areas of finance. The decision about what size dividend to pay affects the
amount of money that the firm has available to reinvest, which affects the way a firm has
to raise money in the capital markets, which affects the Balance Sheet and Income
Statement of the firm, which affects the amount of money available to pay dividends, and
so on and so on. The problem with dividend theory is that everything relates to everything
else; there is no simple starting point as there was in present value analysis. While an
investor may wonder why a firm chooses to pay dividends or not, it is best to just take the
action as a given and try not to worry about the why. Such thinking causes headaches and
probably will not result in a satisfactory answer, anyhow.
Back to Aunt Agnes. She had calculated that the LJCP common stock was worth
$21.00 per share while the market price was $15.00 per share. At this price and with the
next dividend expected to be $2.10, the implied discount rate for the LJCP stock for the
market as a whole is:
Aunt Agnes now has to figure out why the market has a different valuation of the
LJCP common stock than she does, and there are only two possible sources of
disagreement. The calculation above shows the implied dividend payout and the implied
capital gains rate on the basis of the market price. If Aunt Agnes' stock value of $21.00 had
been used instead, the values would have been:
It should be no surprise that the answer came out to be 15% for Aunt Agnes since
that was the cost of capital she had assumed in arriving at the price of $21.00 in the first
place. It is important to note the differences between the terms for dividend payout and
capital gains. If both Aunt Agnes and the market accept 5% as the growth rate of the
dividends, the difference in the stock price is due to the difference in the dividend payout.
Aunt Agnes feels that a 10% dividend payout is appropriate, but the market wants 14%.
Maybe the market knows something that Aunt Agnes does not. The extra 4% return
demanded by the market could be to compensate for some risk unknown to Agnes. Or it
could be that the cost of money for the market is 4% higher than it is for Aunt Agnes and
that the stock is priced so that the investors with the higher cost of capital still get a fair
return. The answer is not obvious from these simple calculations, but now Aunt Agnes can
ask questions regarding the riskiness of the dividend cash flows.
The other possible source of difference between the prices is the growth rate of the
dividends. Solving the Gordon-Shapiro Model for g involves a bit of algebra, but the
answer is so messy that it does not help at this level of interpretation9. Both Aunt Agnes
and the market might feel that the risk associated with the dividend payments is the same,
but they might have different opinions concerning the growth rate of the dividends. If
Agnes feels that the dividends will grow faster than the market thinks possible, she should
be willing to pay more to get a piece of the larger future action. This implies that Agnes
knows something the market does not and thinks that the dividends will grow faster than
the historical rate. Of course, the market could have reason to expect that the dividends
will grow more slowly than indicated by the historical rate and therefore pay a lower price
for the stock. A difference of opinion concerning the growth rate of dividends can have a
substantial difference in the prices different investors will pay for a given share of stock.
9
OK, if you really want to see it:
Aunt Agnes' decision whether or not to purchase the LJCP stock may not be all that
simple. If the price she is willing to pay for the stock differs significantly from the price
being paid in the market, either she or the market is wrong, though only the future will show
which is correct. An investor who finds himself betting against the market can get either
very rich or very poor, very quickly. When the market and an investor disagree about the
value of a share of stock (or any asset), the investor would do well to explore all the
possible reasons why the disagreement exists. Investing without knowing as much as
possible is foolish, and while it might be that all questions cannot be answered (this is risk,
after all), it is the responsibility of the investor at least to ask the questions.
When Things Change
The previous discussions concerning the valuation of preferred and common stock
carried with them the assumptions that growth rates and discount rates were constant
forever. In the absence of contrary information, it is customary to make such assumptions,
but when contrary information is available it cannot be ignored. The contrary information
may be either good or bad, but it needs to be worked into the process in order to get a
more accurate valuation of the securities in question.
Aunt Agnes originally valued the LJCP preferred stock under the assumption that
the discount rate would remain constant forever. The LJCP preferred stock pays a
dividend of $8 per year, and since Agnes had a cost of capital of 6% the value of one share
to her was $133.33. Agnes only plans to hold the stock for five years and then sell it at the
market rate, but it was assumed that the market rate would be the same in five years as
it is today.
The reason that Aunt Agnes is going to liquidate her portfolio and move to Aruba in
five years is because she feels that in five years the domestic economy is going to be in
the pits. She has been following the news and reading the various publications put out by
the federal government, and she really believes that there will be inflation and
unemployment and civil unrest; that is why she is going to a nice, warm beach for a number
of years. Suppose that under these conditions, Agnes feels that when she sells the LJCP
preferred stock in five years the appropriate discount rate for the stock will be 12% instead
of 6%. This is new information that will affect her valuation calculation for the stock and
possibly her decision whether or not to buy the stock.
It is important to realize at this point that neither the Preferred Stock Valuation Model
nor the Gordon-Shapiro Model can be used directly since the boundary conditions
(assumptions) associated with the models do not exist. It might be possible to make use
of these models for pieces of the solution, but they cannot be used for the entire solution.
The only model that can be used is the Discounted Cash Flow model, complete with
time lines and arrows. This model is always applicable. All other models are special cases
of it. The cash flows that the LJCP Preferred will bring to Agnes are the same as before.
Since the discount rate will be different at time=5, it will be necessary to calculate
the value of the stock in that future market. It has been assumed that the market at that
time will be discounting all the future dividends at 12%. This is equivalent to saying that
after time=5 the discount rate will once again be constant, and now the Preferred Stock
Valuation Model can be used. The value of the LJCP preferred stock at time=5 is
The discount rate has doubled, so the price is halved. The time line now becomes
There is now the question of what discount rate should be used to discount these
cash flows in order to obtain the present value. Aunt Agnes' discount rate right now is 6%,
but the market rate in five years will be 12%. This question can be answered by noting that
the money to be spent on the purchase of the stock is Agnes' money, right here, right now.
The cost associated with that money is 6%, so the appropriate discount rate is 6%. The
value of the cash flows (the five year annuity and the lump sum) Agnes will receive from
this share of stock under these conditions is
The maximum price that Agnes would be willing to pay for the LJCP preferred stock
under these conditions is some $50 less than if the discount rate had remained constant.
Information that differs from the assumptions can really make a different in the calculated
value of a security.
A major assumption in the valuation of common stock is that the growth rate of
dividends is constant and that the growth rate is less than the discount rate. This might be
a reasonable assumption with an established firm, but companies that are just beginning
can experience very high short term growth rates. For example, a new firm that pays a
total of $1 in dividends its first year and $2 in dividends the second year has shown a 100%
growth in dividends simply by paying out one additional dollar. If this firm were to pay an
additional dollar the next year, dividends would go from a total of $2 to $3, an increase of
50%10. Firms that are new or experiencing unusual growth need a more detailed type of
analysis than the simple Gordon-Shapiro model since the boundary conditions of the model
are not met.
Little Joe's Chicken Plucking Company has only been in existence for a few years,
and during the first several periods the growth of the firm was funded by Big Joe. Now that
LJCP has just gotten that lucrative government contract for feather bed stuffing, the firm
will grow at a very fast rate, for a while. Extreme growth rates cannot last forever due to
competitive and regulatory forces. A good estimate for the future growth of LJCP and the
dividends paid by the firm is that for the next three years the growth rate will be 20% per
year after which a stable growth rate of 5% per year will resume. These growth rates will
apply to the dividends, the most recent of which was $2 per share. The discount rate that
reflects the risk associated with these cash flows is 15%.
Once again it is necessary to revert to the basic discounted cash flow valuation
model. The dividends that will be paid for the next several years will be
D1 = D0 (1+g) = ($2.00)(1.20) = $2.40
D2 = D1 (1+g) = ($2.40)(1.20) = $2.88
D3 = D2 (1+g) = ($2.88)(1.20) = $3.46
D4 = D3 (1+g) = ($3.46)(1.05) = $3.63
D5 = D4 (1+g) = ($3.63)(1.05) = $3.81
:
10
One of the difficulties in using percentages is that in the calculation of the percentage
one number is compared to another. Percentages are relative measures, and sometimes
absolute magnitudes are more relevant to the decision making process.
This is an infinite set of dividends, and on the time line they look like
Since this is an infinite set of dividends, it is going to take a very long time to do the
calculation. It would be nice if a short cut like the Gordon-Shapiro Model could be used.
While the entire time line may not meet the Gordon-Shapiro boundary conditions, part of
it does, the section of the time line beyond time=3. An investor standing at time=3 and
looking into the future would see a set of dividends growing at a constant rate which is less
than the discount rate. Someone at this point in time would be justified in using the
Gordon-Shapiro Model.
This is one of the major "tricks" in time value of money analysis. Though an entire
time line might not meet the boundary requirements of a specific model, part of the time line
might. Appropriate use of the right model on portions of the time line can save a lot of
work, especially when the portion of the time line treated in this manner is the infinite
portion that goes off to the right. This is one reason why drawing out the time line is a
worthwhile exercise. The drawing allows the analyst to "see" relationships that might be
difficult to visualize in a table of numbers. Graphical analysis of this form is really an
advanced form of analysis, and it should be regarded as such.
The relevant portion of the time line for an analyst standing at time=3 would be the
dividends occurring from time=4 onward as shown below.
The Gordon-Shapiro model does not require that the infinite series of dividends
begins at time=0. The model merely calculates the value of all future dividends at a point
one period before the first dividend is paid.
The relationship is normally stated in terms of time=0 and time=1, but in this specific
instance of the LJCP common stock, the normal period of dividend growth does not occur
for three years. The Gordon-Shapiro model can be restated for this application as
The appropriate relationship between the time of the first payment and the date at
which the present value of all future dividends is totaled remains correct at one period
apart. From the data provide for the LJCP common stock, the value of all the dividends
from time=4 onward discounted back to time=3 would be
This value can now be inserted into the original time line so that the calculations can be
completed.
A share of LJCP common stock with a three year supernormal dividend growth
period of 20% followed by a constant dividend growth of 5% has a fair value of $28.41 at
a 15% cost of capital. While the Gordon-Shapiro Model was not sufficient in and of itself
to solve this supernormal growth problem, it did assist in getting the final answer.
The Decision
All of these examples have concentrated on finding the value of a set of future cash
flows. In these examples, the cash flows have been the dividends from equity securities,
and at times some short cut formulas have helped in determining this value.
The
identification of value is not the same as the decision to purchase, however. Valuation
results in a numerical answer like $12.00; the purchase decision is either "yes" or "no".
Valuation and purchase are two separate steps in the investing process.
The decision to purchase a security will depend on the individual and the relationship
of the value that that individual places on the security and the price of the security in the
market. The market price may or may not be similar to the value of the security to a
specific individual. In those cases where price and value are significantly different, there
is some information that is not known to either the market or the individual. If the individual
has superior analytical ability or some other pipeline to the truth, he may have a "better"
sense of the value of the security than the market. If the individual has no special claim to
knowledge, he would be wise to find out just what is really going on before making an
investment, even if a security seems underpriced.
Especially if a security seems
underpriced. The market may not know everything right away, but it does have the ability
to identify the pieces of information relevant to the pricing of a security. The individual
investor should always be very careful when betting against the market.
It is really important to keep the valuation calculation and the purchase decision as
two separate steps in the investment process. Trying to combine the two will result in
mistakes that could prove fatal to the small investor.
Profit and Loss Diagrams
The profit and loss diagram for a share of stock is straightforward. The owner of the
share of stock is long the security, which is a set of forward contracts. The profit and loss
diagram for the entire security is thus similar to a long forward contract.
Since the stock can pay dividends, it is necessary to include these as part of the
benefit of owning the stock. In general, any dollar of dividends or increase in stock price
represents a dollar of profit. Even if the stock price drops, the dividends paid could be
enough to earn a profit on the investment. By including both dividends and price changes,
this profit and loss diagram is consistent with the manner in which returns are calculated.
This profit and loss diagram agrees with the old adage "Buy Low, Sell High". The
only way a profit can be made is if the price of the stock increases or if dividends are paid
in excess of any stock price decrease. The stock market has a procedure which allows the
process to be reversed to "Sell High, Buy Low". This is still a profitable situation, but it
would seem impossible to sell any stock before it is owned. This reversal of order can be
accomplished through a short sale. A short sale occurs when shares of stock are borrowed
and sold with the promise to replace them at in the future.
Short sales are speculative in nature since it is a decrease in price that will make the
deal valuable rather than the returns generated by a long-run investment. A investor who
thinks that the price of LJCP common stock is going to fall should sell his stock. But if
someone who does not already own the stock thinks that it is due for a price drop wants
to get in on this action, he can borrow the shares and sell them (there are rules governing
this type of trade that will be discussed in a later chapter). Once the shares have been
sold, the seller is liable to replace the shares and pay any dividends to the owner of the
stock that was sold. If the stock price does fall, the speculator can buy the shares back at
the lower price, return them to the person from whom the were borrowed, and keep the
difference in the price (less any dividends paid) as profit. If the stock price goes up, the
shares will still have to be repurchased, but this would represent a loss to the speculator.
The profit and loss diagram for a short sale looks like this:
This position is similar to a short forward contract and completes the "long-short" pair
that typically exists with forward contracts. Short sales provide the opportunity for equity
speculators to make profits in a down market, but these contracts can be hazardous to the
casual player and should be approached with caution.
It is appropriate to note that the profit and loss diagrams do not account for the time
value of money. Each dollar of dividend and each dollar of capital gain are counted the
same, regardless of where they come in time. Because of this characteristic, the profit and
loss diagrams are not appropriate for valuation analysis. Profit and loss diagrams like
these are best used at a point in time when analyzing complex financial securities. In this
case, a financial security that had equity as one of its components would have this type of
profit and loss diagram as a component of the overall profit and loss diagram.
Summary
Equity securities give the holder an ownership position in the firm. Common
stockholders also have the privilege of electing the Board of Directors that hires the
managers who run the firm. The pricing of equity securities, preferred or common, is really
just an exercise in present value calculations, and under some conditions these
calculations can be reduced to a simple formula, like the Gordon-Shapiro model. Use of
any model requires that the underlying assumptions be met. If these boundary conditions
are not present, then the basic present value technique, possibly in conjunction with one
of the models, can be used to find the value of the security. Once a security has been
properly valued, the individual can make an informed purchase decision.