Unit 7 Stocks and Their Valuation
Overview
Common stock constitutes the ownership position in a firm. As owners, common stock holders
have certain rights and privileges, including the right to control the firm through election of
directors and the right to the firm’s residual earnings.
Corporate generally begin their corporate life as closely held companies, with all the
common stock held by the founding managers. Then, as the company grows, it is often necessary
to sell stocks to the general public to rise more funds. Eventually, the firm may choose to list its
stock on one of the physical location exchanges.
A common stock is valued as the present value of its expected future dividend stream. The
total company model is a valuation model used as an alternative to the dividend growth model to
determine the value of a firm, especially one that does not pay dividends or is privately held. The
total rate of return on a stock is comprised of a dividend yield plus a capital gains yield. If a stock
is in equilibrium, its total expected return must equal the average investor’s required rate of return.
Preferred stock is a hybrid——it is similar to bonds in some aspects and common stock in
others. The value of a share of constant dividend forever is found as the dividend divided by the
required rate of return.
Outline
The corporation’s common stockholders are the owners of the corporation, and as such, they have
certain rights and privileges.
□. In a large, publicly owned firm, the managers typically have some stock, but their personal
holdings are generally insufficient to give them voting control.
□. Managers of most publicly owned firms can be removed by the stockholders if the
management team is not effective.
□. Stockholders who are unable to attend annual meetings may still vote for directors by
mean of proxy. Proxies can be solicited by any party seeking to control the firm.
□. If earnings are poor and stockholders are dissatisfied, an outside group may solicit the
proxies in an effort to overthrow management and take control of the business. This is known as a
1
proxy fight.
□. A takeover is an action whereby a person or group succeeds in ousting a firm’s
management and taking over of the company.
□. A poison pill makes a possible acquisition unattractive and wards off hostile takeover
attempts.
The preemptive right gives the current shareholders the right to purchase any new shares
issued in proportion to their current holdings. The preemptive right may or may not be require by
state law.
□. The purpose of the preemptive right is twofold:
▪. It enables current shareholders to maintain their proportionate share of ownership an
control of the business.
▪. It also prevent the sale of shares at low prices to new stockholders, which would dilute the
value of the previously issued shares.
Special classes of common stock are sometimes created by a firm to meet special needs and
circumstances. If two classes of stock were desired, one would normally be called “Class A” and
the other “Class B”. Common stock that is given a special designation is called classified stock.
Class A might be entitled to receive dividends before dividends can be paid on Class B stock.
Class B might have the exclusive right to vote.
□. Note that Class A and Class B have no standard meanings.
Founders’ shares are stock owned by the firm’s founders that have sole voting rights but
restricted dividends for specified number of years.
Some companies are so small that their common stocks are not actively traded; they are owned by
only a few people, usually the companies’ managers. Such firms are said to be closely held
corporations. In contrast, most of whom are not active in management. Such companies are said to
be publicly owned corporations. Larger, publicly owned companies generally apply for listing on
physical location exchanges, and they and their stocks are said to be listed.
Stock market transactions may be separated into three distinct categories.
□. The secondary market deal with trading in previously issued, or outstanding, shares of
2
established, publicly owned companies. The company receives no new money when sales are
made in the secondary market.
□. The primary market handles additional shares sold by established, publicly owned
companies. Companies can raise additional capital by selling in this market.
□.the primary market also handles new public offerings of shares in firms that were formerly
closely held. Capital for the firm can be raised by going public, and this market is often termed the
initial public offering (IPO) market.
Common stocks are valued by finding the present value of the expected future cash flow
stream.
People typically buy common stock expecting to earn dividends plus a capital gain when
they sell their shares at the end of some holding period. The capital gain may or may not be
realized, but most people expect a gain or else they would not buy stocks.
The expected dividend yield on a stock during the coming year is equal to the expected

dividend, D1, divided by the current stock price, P0. ( P1  P0 ) / P0 is the expected capital gains
yield. The expected dividend yield plus the expected capital gains yield equals the expected total
return.
The value of the stock today is calculated as the present value of an infinite stream of
dividends. For any investor, cash flows consist of dividends plus the expected future sales price of
the stock. This sales price, however, depends on dividends expected by future investors:

Value of stock = P0 = PV of expected future dividends


Dt
D1
D2
D





.

1
2
(1  k  ) t 1 (1  k s ) t
(1  k s ) (1  k s )
Here ks is the discount rate used to find the present value of the dividends.
Dividends can be rising, falling, fluctuating randomly, or can even be zero for several years.
The generalized equation above can be used to value the stock. With a computer spreadsheet this
equation can easily be used to find a stock’s intrinsic value for any dividend pattern, the hard part
is getting an accurate forecast of the future dividends.
For many companies, earnings and dividends are expected to grow at some normal, or
constant, rate. Dividends in any future year t may be forecasted as Dt  D0 (1  g ) t ,
where D0
is the last dividend paid and g is th4e expected growth rate. For a company that last paid a $2.00
3
dividend and has an expected 6 percent constant growth rate, the estimated dividend one year
from now would be D1= 2.00 (1.06) = 2.12; D4 = 2.00 (1.06)4 = 2.525. Using this method of
estimating future dividends, the current price,P0, is determined as follows:
 D (1  g )
D1
P0  0

.
ks  g
ks  g
This equation for valuing a constant growth stock is often called the constant growth model, or the
Gordon Model, after Myron J. Gordon, who developed it.
□. A necessary condition of this equation is that ks > g. If the equation is used in situations
when ks is not greater than g, the results will be both wrong and meaningless.
□. Growth in dividends occurs primarily as a result of growth in earnings per share.
▪. Earnings growth results from a number of factors, including inflation, the amount of
earnings the company retains and reinvests, and the rate of return the company earns on its equity
(ROE).
□. The constant growth model is often appropriate for mature companies with a stable history
of growth.
▪. Expected growth rates vary somewhat among companies, but dividend growth for most
mature firms is generally expected to continue in the future at about the same rate as nominal
gross domestic product.
The constant growth model is sufficiently general to handle the case of a zero growth stock,
where the dividend is expected to remain constant over time. If g = 0, then the stock can be valued
as P0 = D/ks.
□. This is the same equation as that used for perpetuity.
For all stocks, the total expected return is composed of an expected dividend yield plus an
expected capital gains yield. For a constant growth stock, the formula or the total expected return
can be written as:

D
k s  1  g.
P0
□. For a constant growth stock, the following conditions must hold:
▪. The dividend is expected to grow forever at a constant rate, g.
▪.the stock price is expected to grow at this same rate.
4
▪. The expected dividend yield is a constant.
▪. The expected capital gains yield is also a constant, and it is equal to g.

▪. The expected total rate of return, k s , is equal to the expected dividend yield plus the

expected growth rate: k s  DividendYi eld  g .
Firms generally go through periods of non-constant growth, after which time their growth
rate settles to a rate close to that of the economy as a whole. The value of such a firm is equal to
the present value of its expected future dividends. To find the value of such a stock, we proceed in
three steps:
□. Find the present value of the dividends during the period of non-constant growth.
□. Find the price of the stock at the end of the non-constant growth period, at which point it
has become a constant growth stock, and discount this price back to the present.

□. Add there two components to find the intrinsic value of the stock, P0 .
▪. Supernormal growth firms are firms that are in that part of their life cycle in which they
grow much faster than the economy as a whole.
▪. The terminal date is the date when the growth rate becomes constant. At this date it is no
longer necessary to forecast the individual dividends.
▪. The terminal, or horizon, value is the value at the horizon date of all individends expected
thereafter.
The total company, or corporate value, model is a valuation model used as an alternative to the
dividend growth model to determine the value of a firm, especially one that does not pay
dividends or is privately held. This model discounts a firm’s free cash flows at the WACC to
determine its value.
The value of a firm’s stock is directly linked to a firm’s total value.
The steps to this approach are the follows:
□. Find the total value of the firm.
□. Subtract out the market value of the debt and preferred stock from the firm’s total value.
□. Divided the total value of the common equity by the number of shares outstanding to
obtain an estimate of the value per share.
▪. This estimate should, in theory, be identical to the share value found using the discounted
5
dividend model.
The market value of any company can be expressed as follows:
Vcompany = PV of expected future free cash flow

FCF1
FCF2
FCF


.
1
2
(1  WACC) (1  WACC)
(1  WACC) 
□. Free cash flow represents the cash generated in a given year minus the cash needed to
finance the capital expenditures and working capital needed to support future growth.
FCF = NOPAT – Net new investment in operating capital.
▪. Free cash flow is the cash generated before making any payments to common or preferred
stockholders, or to bondholders, so it is the cash flow that is available to all investors.
□. Therefore, the FCF should be discounted at the company’s weighted average cost of debt,
preferred stock, or the WACC.
To find the firm’s total value, proceed as follows:
□. Assume the firm will experience non-constant growth for N years, after which it will grow
at some constant rate.
□. Calculate the expected FCF for each of the N non-constant growth years, and find the PV
of these cash flows.
□. After year N growth will be constant. Thus, use the constant growth formula to find the
firm’s value at Year N. this terminal value is the sum of the PV of the FCFs for N + 1 and all
subsequent years, discounted back to Year N. then, the Year N value must be discounted back to
the present to find its PV at year 0.
□. Sum all the PVs, those of the annual free cash flows during the non-constant period plus
the PV of the terminal value, to find the firm’s value.
Estimates of intrinsic value will often deviate considerably from the actual stock price.
deviations occur because the forecaster’s assumptions are different from those of marginal
investors in the marketplace.
Much can be learned from the corporate value model, so analysts today use it for all types of
valuations.
The relationship between a stock’s required and expected rates of return determines the
6
equilibrium price level where buying and selling pressures will just offset each other.
The marginal investor is a representative investor whose actions reflect the beliefs of those
people who are currently trading stock. It is the marginal investor who determines a stock’s price.
If the expected rate of return is less than the required rate, investors will desire to sell the
stock; there will also be a tendency for the price to decline.
When the expected rate of return is greater than the required rate, investors will try to
purchase the shares of stock; this will drive the price upward.
Only at the equilibrium price, where the expected and required rates are equal, will stock be
stable.
Equilibrium will generally exist for a given stock because security prices, especially those of
large companies, adjust rapidly to new developments.
Change in the equilibrium price can be brought about (1) by a change in risk aversion, (2) by
a change in the risk-free rate, (3) by a change in the stock’s beta coefficient, or (4) by a change in
the stock’s expected growth rate.
The Efficient Markets Hypothesis (EMH) holds that stocks are always in equilibrium and
that it is impossible for an investor to consistently “beat the market”.
□. The weak form of the EMH states that all information contained in past price movements
is fully reflected in current market prices.
□. The semi-strong form of the EMH states that current market prices reflect all publicly
available information. If this is true, no abnormal returns can be gained by analyzing stocks.
Another implication of semi-strong form efficiency is that wherever information is released to the
public, stock price will respond only if the information is different from what had been expected.
□. The strong form of EMH states that current market prices reflect all pertinent information,
whether publicly available or privately held. If this form holds, even insiders would find it
impossible to earn abnormal returns in the stock market.
Empirical tests have shown that EMH is, in its weak and semi-strong forms, valid. However,
the strong form of EMH does not hold, so abnormal profits can be made by those who possess
inside information.
Anyone who has ever invested in the stock market knows that there cn be, and generally are, large
7
differences between the expected and realized prices and returns.
Investors always expect positive returns from stock investments or else they would not buy
them. However, in some years negative returns are actually earned.
Even in bad years, some individual stocks do well, and the “name of the game” in security
analysis is to pick the winners. Financial managers are trying to take those actions that will help
put their companies in the winners’ column, but they don’t always succeed.
When investing overseas, you are making two bets: (1) that foreign stocks will increase in
their local markets and (2) that the currencies in which you will be paid will rise relative to the
dollar.
Preferred stock is a hybrid—it is similar to bonds in some respects and to common stock in other
respects.
Preferred dividends are similar to interest payments on bonds in that they are fixed in amount
and generally must be paid before common stock dividends can be paid.
If the preferred dividend is not earned, the directors can omit it without throwing the
company into bankruptcy. So, although preferred stock has a fixed payment like bonds, a failure to
make this payment will not lead to bankruptcy.
Most preferred stocks entitle their owners to regulate fixed dividend payments. If the
payments last forever, the issue is a perpetuity whose value, Vp, is found as follows:
Vp 
Dp
ks
.
□. Here Dp is the dividend to be received in each year and kp is the required rate of return on
the preferred stock.
Questions
1. The preemptive right protects stockholders against loss of ____________ of the corporation as
well as ___________ of market value from the sale of new shares below market value.
2.
The trading of previously issued shares of a corporation takes place in the __________
market, while new issues are offered in the ___________ market.
3. securities traded on the physical location exchanges are known as __________ securities.
8
4. Preferred stock is referred to as a hybrid because it is similar to ___________ in some respects
and to __________ _________ in others.
5. The __________ _________ __________ holds that stocks are always in equilibrium and that
it is impossible for an investor to consistently “beat the market”.
6. The ___________ _____________ give the current shareholders the right to purchase any
new shares issued in proportion to their current holdings.
7. The __________ ____________ is a representative investor whose actions reflect the beliefs
of those people who are currently trading a stock and determines a stock’s price.
8. _______ ________ __________ is the cash generated before making any payments to
common or preferred stockholders, or bondholders, so it is available to all investors.
9. __________ ________ are stock owned by the firm’s founders that have sole voting rights but
restricted dividends for a specified number of years.
10. The constant growth model is often appropriate for __________ companies with a(n)
__________ history of growth.
Problems
1. Stability Inc. has maintained a dividend rate of $4 per share for many years. The same rate is
expected to be paid in future years. If investors require a 12% rate of return on similar
investments, determine the present value of the company’s stock.
a. $15.00
b. $30.00
c. $33.33
d. $35.00
e. $40.00
2. Your sister-in-law, a stockbroker at Invest Inc., is trying to sell you s stock with a current price
of $25. the stock’s last dividend (D0) was $2.00, and earnings and dividends are expected to
increase at a constant rate of 10 percent. Your required return on this stock is 20 percent. From
a strict valuation standpoint, you should:
a. Buy the stock; it is fairly valued.
b. Buy the stock; it is undervalued by $3.00.
c. Buy the stock; it is undervalued by $2.00.
d. Not buy the stock; it is overvalued by $2.00.
e. Not buy the stock; it is over valued by $3.00.
3. Lucas Laboratories last dividend was $1.50. Its current equilibrium stock price is $15.75, and
its expected growth rate is a constant 5 percent. If the stockholders require rate of return is
9
15%, what is the expected dividend yield and expected capital gains yield for the coming
year?
a. 0%; 15%
b. 5%; 10%
c. 10%; 5%
d. 15%; 0%
e. 15%; 15%
4. The Canning Company has been hard hit by increased competition. Analysts predict that
earnings (and dividends) will decline at a rate of 5 percent annually into the foreseeable future.
If Canning ’s last dividend (D0) was $2.00, and investors’ required rate of return is 15 percent,
what will be Canning ’s stock price in three years?
a. $8.15
b. $9.50
c. $10.00
d. $10.42
e. $10.96
5. Assume that the average firm in your company’s industry is expected to grow at a constant
rate of 7 percent and its dividend yield is 8 percent. Your company is about as risky as
average firm in the industry, but it has just successfully completed some R&D work that leads
you to expect that its earnings and dividends will grow at a rate of 40 percent [D1 = D0 (1+g) =
D0 (1.40)] this year and 20 percent the following year, after which growth should match the 7
percent industry average rate. The last paid (D0) was $1. What is the return value per share of
your firm’s stock?
a. $22.47
6.
b. $24.15
c. $21.00
d. $19.48
e. $22.00
Today is December 31,2001. the following information applies to Harrison Corporation:
a. After-tax operating income [EBIT(1-T)] for 2002 is expected to be $950 million.
b. The company’s depreciation expense for 2002 is expected to be $190 million.
c. The company’s capital expenditures for 2002 are expected to be $380 million.
d. No change is expected in the company’s net operating working capital.
e. The company’s free cash flow is expected to grow at a constant rate of 4 percent per year.
f. The company’s cost of equity is 13 percent.
g. The company’s WACC is 9 percent
h. The market value of the company’s debt is $5.2 billion.
i. The company has 250 million shares of stock outstanding.
Using the free cash flow approach, what should the company’s stock price be today?
a. $35.00
b. $40.00
c. $37.50
d. $43.50
e. $52.50
Answers for questions (Stocks and their valuation)
1.control; dilution
2. secondary; primary
10
3. listed
4. debt; common stock
5. Efficient Markets Hypothesis
6. preemptive right
7. marginal investor
8. Free cash flow
9. Founders’ shares
10. mature; stable
Answers for problems (Stocks and their valuation)

1. c. This is a zero growth stock, or perpetuity: P0  D / k s  $.00 / 0.12  33.33
2. e.
 D (1  g ) 2.00(1  0.1)
P0  0

 22.00
ks  g
0.20  0.10
3. c. DividendYi eld 
D0 (1  g ) 1.50(1  0.05)

 0.10  10%.
P0
15.75
CapitalGainYield 
P0 (1  g )  P0
 g  5%.
P0
 D (1  g ) 2.00(1  0.05)
4. P0  0

 9.50.
ks  g
0.15  (0.05)


P3  P0 (1  g ) 3  9.50(1  0.05) 3  8.15.

Another way is to use the Gordon model: P3 
Year 0
1
D4
2.00(1  0.05) 4

 8.15.
ks  g
0.20
2
3
ks = 15%
g = 40%
Dividend
g = 20%
1.40
gn = 7%
1.68
1.7976
1.22
___22.47
__18.26
24.15
19.48
5.
d. D0 = $1.00; ks = 8% + 7% =15%; g1 = 40%; g2 =20%; g3 = 7%.
11

P2 
1.7976
 22.47
0.15  0.07
6. b.
FCF = EBIT(1-T) + Depreciation – Capital Expenditures – △(Net operating working capital)
= 950,000,000 + 190,000,000 – 380,000,000 – 0 = 760,000,000.
FirmValue 
FCF
760,000,000

 15,200,000,000.
AACC  g
0.09  0.04
This is the total firm value. Now find the market value of its equity.
MVequity = MVtotal – MVdebt = 15,200,000,000 – 5,200,000,000 = 10,000,000,000
This is the market value of all the equity. Divided by the number of shares to find the price
per share. 10,000,000,000/250,000,000 = 40.00
12