Declassify their boards of directors
Student 601
M3-2.pdf
Slide 1
7-1
Cash Flows for Stockholders
• If you own a share of stock, you can receive cash in two ways
The company pays dividends
You sell your shares, either to another investor in the market or back to the company
• As with bonds, the price of the stock is the present value of these expected cash flows
Dividends → cash income
Selling → capital gains
In this module, we turn to the other major source of financing for corporations, common and preferred stock.
The goal of financial management is to maximize stock prices, so an understanding of what determines
share values is obviously a key concern. The dividends currently being paid are one of the primary factors
we look at when we attempt to value common stocks. This module explores dividends, stock values, and
the connection between the two.
A share of common stock is more difficult to value in practice than a bond, for at least three reasons.
First, with common stock, not even the promised cash flows are known in advance.
Second, the life of the investment is essentially forever, since common stock has no maturity.
Third, there is no way to easily observe the rate of return that the market requires.
However, we can come up with the present value of the future cash flows for a share of stock making some
assumptions.
Slide 2
7-2
One Period Example
• Suppose you are thinking of purchasing the stock of Moore Oil, Inc.
– You expect it to pay a $2 dividend in one year
– You believe you can sell the stock for $14 at that time.
– You require a return of 20% on investments of this risk
– What is the maximum you would be willing to pay?
Slide 3
7-3
One Period Example
• D1 = $2 dividend expected in one year
• R = 20%
• P1 = $14
• CF1 = $2 + $14 = $16
• Compute the PV of the expected cash flows
33.13$ 20.1
)142( P
0
Note, the calculation can also be done as:
FV = 14; PMT = 2; I/Y = 20; N = 1; CPT PV = -13.33
Slide 4
7-4
Two Period Example
• What if you decide to hold the stock for two years?
– In addition to the dividend in one year, you expect a dividend of $2.10 in two years and a stock price of $14.70 at the end of year 2.
– Now how much would you be willing to pay?
33.13$ )20.1(
)70.1410.2(
20.1
2 P
20
Calculator: CF0 = 0; C01 = 2; F01 = 1; C02 = 16.80; F02 = 1; NPV; I =
20; CPT NPV = 13.33
We can use uneven cash flow keys.
Slide 5
7-5
Three Period Example
• What if you decide to hold the stock for three years?
– In addition to the dividends at the end of years 1 and 2, you expect to receive a dividend of $2.205 at the end of year 3 and the stock price is expected to be $15.435.
– Now how much would you be willing to pay?
33.13$ )20.1(
)435.15205.2(
)20.1(
10.2
20.1
2 P
320
Calcultator: CF0 = 0; C01 = 2; F01 = 1; C02 = 2.10; F02 = 1; C03 = 17.64;
F03 = 1; NPV; I = 20; CPT NPV = 13.33
Slide 6
7-6
Developing The Model
• You could continue to push back the year in
which you will sell the stock
• You would find that the price of the stock is
really just the present value of all expected
future dividends
• So, how can we estimate all future dividend
payments?
In equilibrium, the required return, R, is the same as the “expected return.”
Slide 7
7-7
Stock Value = PV of Dividends
P0 = ^
(1+R)1 (1+R)2 (1+R)3 (1+R)∞
D1 D2 D3 D∞ + + +…+
1t t
t 0
)R1(
D P̂
How can we estimate all future dividend
payments?
Slide 8
7-8
Estimating Dividends Special Cases
• Constant dividend/Zero growth
– Firm will pay a constant dividend forever
– Like preferred stock
– Price is computed using the perpetuity formula
• Constant dividend growth/Goldon growth – Firm will increase the dividend by a constant percent
every period (growing perpetuity model)
• Supernormal growth/Nonconstant growth – Dividend growth is not consistent initially, but settles
down to constant growth eventually (Multistage model)
Three special cases of assumptions for estimating dividends allow us to value common stock.
Constant dividend implies zero dividends growth (constant dollar amount) and is valued like a perpetuity.
Constant dividend growth is the most fundamental and frequently used assumption. It describes a constant dividend growth percent.
Supernormal growth allows valuation of the stock of a company experiencing abnormal growth currently but expected to stabilize to a constant growth situation in the future.
Slide 9
7-9
Zero Growth
• Dividends expected at regular intervals forever = perpetuity
P0 = D / R
• Suppose stock is expected to pay a $0.50 dividend every quarter and the required return is 10% with quarterly compounding. What is the price?
20$
4 10.
50.0 0
P
If dividends are paid quarterly, then the discount rate must be a quarterly rate.
Zero-growth – implies that D1 = D2 = D3 … = D
Since the cash flow is always the same, the PV is that for a perpetuity:
P0 = D ⁄ R
Example: Suppose a stock is expected to pay a $2 dividend each period, forever, and the required return is
10%. What is the stock worth?
P0 = 2 ⁄ .1 = $20
Slide 10
7-10
Constant Growth Stock
D1 = D0(1+g) 1
D2 = D0(1+g) 2
Dt = D0(1+g) t
One whose dividends are expected to
grow forever at a constant rate, g.
D0 = Dividend JUST PAID
D1 to Dt = Expected dividends
Slide 11
7-11
Projected Dividends
• D0 = $2.00 and constant g = 6%
• D1 = D0(1+g) = 2(1.06) = $2.12
• D2 = D1(1+g) = 2.12(1.06) = $2.2472
• D3 = D2(1+g) = 2.2472(1.06) = $2.3820
Slide 12
7-12
Dividend Growth Model
“Gordon Growth Model”
t
t
R
gD
R
gD
R
gD
R
gD P
)1(
)1( ...
)1(
)1(
)1(
)1(
)1(
)1( 0
3
3
0
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00 0
1
1
2
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00 )1(
)1( ...
)1(
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)1( t
t
R
g
R
g
R
g DP
g
R
t
t
R
g DP
g
gR
)1(
)1( 1
)1(
)1()1( 00
Now multiply both sides by (1+R)/(1+g):
Subtract the first equation from the second and you get:
The term 1 – (1+g)t/(1+R)t goes to one as t approaches infinity, assuming R > g.
If we solve for P 0 , we get the dividend growth model.
Given our basic PV definition and using some advanced mathematics, we can derive the Dividend
Growth Model, also known as the Gordon Growth Model for the academic who did extensive work in this
area.
Slide 13
7-13
P0 = ^ D0(1+g)
R - g =
D1 R - g
1t t
t
00 )R1(
)g1( DP̂
Dividend Growth Model
“Gordon Growth Model”
Constant growth – Dividends are expected to grow at a constant percentage rate each period. D1 =
D0(1+g); D2 = D1(1+g); in general Dt = D0(1+g) t Note that this is really just a future value.
Example: If the current dividend is $2 and the expected growth rate is 5%, what is D1? D5?
D1 = 2(1+.05) = $2.10
D5 = 2(1+.05) 5 = $2.55
An amount that grows at a constant rate forever is called a growing perpetuity. The present value of all
expected future dividends under this scenario can be expressed as follows:
P0 = D1 ⁄ (R − g)and more generally,
Pt = Dt+1 ⁄ (R − g)
“g” is the growth rate in dividends; the subscripts denote the period in which the dividend is paid. This is
the formula for a growing perpetuity.
Slide 14
7-14
DGM – Example 1
• Suppose TB Pirates, Inc. is expected to pay a $2
dividend in one year. If the dividend is expected to
grow at 5% per year and the required return is 20%,
what is the price?
– D1 = $2.00
– g = 5%
– r = 20%
33.13$ 05.20.
00.2 P
gR
D P
0
1 0
We are finding a present value, so the dividend needed is the one that will be paid NEXT period, not the
one that has already been paid.
Slide 15
7-15
DGM – Example 2
• Suppose Big D, Inc. just paid a dividend of $.50. It is
expected to increase its dividend by 2% per year. If
the market requires a return of 15% on assets of this
risk, how much should the stock be selling for?
• D0= $0.50
• g = 2%
• R = 15%
92.3$ 02.15.
)02.1(50.0 P
gR
)g1(D P
0
0 0
Slide 16
7-16
Stock Price Sensitivity to Dividend Growth, g
0
50
100
150
200
250
0 0.05 0.1 0.15 0.2
Growth Rate
S to
c k
P r ic
e
D1 = $2; R = 20%
As the growth rate approaches the required return, the stock price increases dramatically. From the DGM
formula, as g → R, the denominator → 0.
Slide 17
7-17
Stock Price Sensitivity to Required Return, R
0
50
100
150
200
250
0 0.05 0.1 0.15 0.2 0.25 0.3
Required Return
S to
c k
P r ic
e
D1 = $2; g = 5%
As the required return approaches (is decreased leftward toward) the growth rate, the price increases
dramatically. This graph is a mirror image of the previous one.
Slide 18
7-18
Gordon Growth Company - I
• Gordon Growth Company is expected to pay a dividend of $4 next period and dividends are expected to grow at 6% per year. The required return is 16%.
• What is the current price?
40$ 06.16.
00.4 P
gR
D P
0
1 0
Remember that we already have the dividend expected next year, so we don’t multiply the dividend by
1+g.
Slide 19
7-19
Gordon Growth Company - II
• What is the price expected to be in year 4?
50.50$ 06.16.
)06.1(00.4 P
)g1(DD
g-R
D
gR
)g1(D P
4
4
4
15
54 4
The dividend in the numerator is always for one period later than the price we are computing. This is
because we are computing a Present Value, so we have to start with a future cash flow.
We know the dividend in one year is expected to be $4 and it will grow at 6% per year for four more years.
So, D5 = 4(1.06)(1.06)(1.06)(1.06) = 4(1.06) 4
Slide 20
7-20
Gordon Growth Company - II
• What is the implied return given the change in price during the four year period?
50.50 = 40(1+return)4; return = 6%
4 N; -40 PV; 50.50 FV; 0 PMT; CPT I/Y = 6%
The price grows at the same rate as dividends
Slide 21
7-21
Constant Growth Model Conditions
1. Dividend expected to grow at g forever
2. Stock price expected to grow at g forever
3. Expected dividend yield is constant
4. Expected capital gains yield is constant and equal to g
5. Expected total return, R, must be > g
6. Expected total return (R): = expected dividend yield (DY)
+ expected growth rate (g)
= dividend yield + g
“How can g ever be assumed to be constant?”
The answer lies in the competitive equilibrium model of classical macroeconomics. Since g represents not
only the growth rate in dividends but also in earnings and sales, assuming no change in the firm’s cost
structure, we are simply assuming that the product market that the firm operates in “settles down” to a
steady state in which competing firms earn sufficient returns to remain in business, but not large enough
to attract outside capital. From a more practical standpoint, firms will often attempt to manage their
dividend policy so that there is a reasonably constant growth in dividends.
“Why do we assume that R > g?”
At least two answers are possible. First, R may be less than g in the short-run. The supernormal growth
problem is an example of this situation. Second, in equilibrium, high returns on investment will attract
capital, which, in the absence of technological change, will ensure that in succeeding periods, higher
returns cannot be earned without taking greater risk. But, taking greater risk will increase R, so g cannot
be increased without raising R.
Note that, from the equation itself, we can see that the growth rate must be less than the required return
else the denominator will be negative leading to a negative—and impossible—stock price
Slide 22
7-22
Nonconstant Growth
• Suppose a firm is expected to increase dividends by 20% in one year and by 15% in two years.
• After that, dividends will increase at a rate of 5% per year indefinitely.
• If the last dividend was $1 and the required return is 20%, what is the price of the stock?
• Remember that we have to find the PV of all expected future dividends.
This situation is quite common, especially among younger, startup companies that may experience a high
growth
Slide 23
7-23
R1
D . . .
R1
D
R1
D
R1
D P̂
3
3
2
2
1
1 0
Nonconstant + Constant
growth
gR
D P̂ 1t
t
Basic PV of all Future Dividends Formula
Dividend Growth Model
Slide 24
7-24
2 2
2
2
1
1 0
)R1(
P
R1
D
R1
D P̂
gR
D P
then 2,t after constant g If
)R1(
D P Because
3 2
3t t
t 2
Nonconstant + Constant growth
Slide 25
7-25
0 1 2 3R = 20%
= P0
g = 20% g = 15% g = 5%
D0 = 1.00 D1 D2 D3
D3P2 = ^
R – g
Nonconstant growth followed by constant growth:
Slide 26
7-26
Nonconstant Growth – Solution • Compute the dividends until growth levels off
D1 = 1(1.2) = $1.20
D2 = 1.20(1.15) = $1.38
D3 = 1.38(1.05) = $1.449
• Find the expected future price at the beginning of
the constant growth period:
P2 = D3 / (R – g) = 1.449 / (.2 - .05) = 9.66
• Find the present value of the expected future cash
flows
P0 = 1.20 / (1.2) + (1.38) / (1.2) 2 + (9.66) / (1.2)2 = 8.67
Calculator: CF0 = 0; C01 = 1.20; F01 = 1; C02 = 11.04 (=1.38 + 9.66); F02 =
1; NPV; I = 20; CPT NPV = 8.67
P2 is the value, at year 2, of all expected dividends year 3 on.
The final step is exactly the same as the 2-period example at the beginning of the chapter. We can look at
it as if we buy the stock today and receive the $1.20 dividend in 1 year, receive the $1.38 dividend in 2
years and then immediately sell it for $9.66.
Slide 27
7-27
0
1.0000
0.9583
6.7083
1 2 3R = 20%
8.6667 = P0
g = 20% g = 15% g = 5%
D0 = 1.00 1.20 1.38 1.449
$1.449 P2 = ^
0.20 – 0.05 = $9.66
Nonconstant growth followed by constant growth:
Slide 28
7-28
Quick Quiz: Part 1
• What is the value of a stock that is expected to pay
a constant dividend of $2 per year if the required
return is 15%?
• What if the company starts increasing dividends by
3% per year beginning with the next dividend? The
required return remains at 15%.
33.13$ 15.
00.2 P
0
17.17$ 03.15.
)03.1(00.2 P
0
Slide 29
7-29
Finding the Required Return Example
• A firm’s stock is selling for $10.50. They
just paid a $1 dividend and dividends
are expected to grow at 5% per year.
• What is the required return?
Slide 30
7-30
Using the DGM to Find R
Start with the DGM:
g P
D g
P
g)1(D R
g-R
D
g - R
g)1(D P
0
1
0
0
10 0
Rearrange and solve for R:
Rearrange P0 = D1 ⁄ (R − g) to find R:
R = (D1 ⁄ P0 ) + g
Dividend yield = D1 ⁄ P0
Capital gains yield = g, and
R = Dividend yield + Capital gains yield
Slide 31
7-31
Finding the Required Return Example
• P0 = $10.50
• D0 = $1
• g = 5% per year
• What is the dividend yield?
1(1.05) / 10.50 = 10%
• What is the capital gains yield?
g = 5% Dividend Capital Gains
Yield Yield
%1505. 10.50
1.00(1.05) R
g P
D R
g P
g)1(D R
0
1
0
0
Slide 32
7-32
Stock Valuation Using Multiples
• For stocks that don’t pay dividends (or have erratic dividend growth rates), we can value them using the price-earnings (PE) ratio and/or the price-sales ratio:
(multiply a benchmark PE ratio by earnings per share (EPS) to come up
with a stock price)
Price at time t = Pt = Benchmark PE ratio X Earnings per sharet
Price at time t = Pt = Benchmark price-sales ratio X Sales per sharet
• The price-sales ratio can be especially useful when earnings are negative.
How to find PE?
Benchmark PE come from similar companies (Industry average) or from a firm’s historical values.
The price-sales ratio is often used to value newer companies that do not pay dividends and are not yet
profitable (meaning that earnings are negative).
Slide 33
7-33
Stock Valuation Using Multiples Example
• Suppose we are trying to value the company Inactivision, a video game developer that does not pay dividends. If the appropriate industry PE for this type of company is 20 and you predict earnings to be $2.50 per share for the coming year, then the forecasted stock price for a year from now, or target price, is the following:
Target price = 20 x $2.50 = $50
Slide 34
7-34
Table 7.1
Slide 35
7-35
Features of Common Stock
• Voting Rights
– Stockholders elect directors
– Cumulative voting vs. Straight voting
– Boards are often staggered, or “classified”
– Proxy voting
• Classes of stock
– Founders’ shares
– Class A and Class B shares
Shareholders have the right to elect the board of directors and vote on other important issues.
Cumulative voting—when the directors are all elected at once. Total votes that each shareholder may cast
equals the number of shares times the number of directors to be elected. In general, if N directors are to be
elected, it takes 1 / (N + 1) percent of the stock + 1 share to assure a deciding vote for one directorship.
Increases the likelihood of minority shareholder representation on the board.
Straight (majority) voting—the directors are elected one at a time, and every share gets one vote. Can
freeze out minority shareholders.
Staggered elections—directors’ terms are rotated so they aren’t elected at the same time. This makes it
harder for a minority to elect a director and complicates takeovers.
A staggered board is a governance practice in which only a fraction (typically a third) of the members of
the board of directors is elected each year, rather than all.
A staggered board consists of a board of director whose members are grouped into classes; for example,
Class 1, Class 2, Class 3, etc.
Proxy voting—grant of authority by a shareholder to someone else to vote his or her shares. A proxy fight
is a struggle between management and outsiders for control of the board, waged by soliciting
shareholders’ proxies.
Shareholders can come to the annual meeting and vote in person, or they can transfer their right to vote to
another party.
Different classes of stock can have different rights. Owners may want to issue a nonvoting class of stock
if they want to make sure that they maintain control of the firm.
Ford Motor Company has always had two classes of stock: Class B or “Founders’ Shares” are owned by
the Ford family and carry 40% of the voting rights though they represent only 10% of the shares
outstanding.
Google has Class A shares that are publicly traded and carry one vote per share. Class B shares are held
by insiders and carry 10 votes per share.
Slide 36
7-36
Features of Common Stock
• Other Rights
– Share proportionally in declared dividends
– Share proportionally in remaining assets during liquidation
– Preemptive right
• Right of first refusal to buy new stock issue to maintain proportional ownership if desired
Other rights usually include:
Sharing proportionately in dividends paid.
Sharing proportionately in any liquidation value.
Voting on matters of importance (e.g., mergers).
The right to purchase any new stock sold – the preemptive right.
In addition to the right to vote for directors, shareholders usually have the following rights:
1. The right to share proportionally in dividends paid.
2. The right to share proportionally in assets remaining after liabilities have been paid in a liquidation.
Essentially, a preemptive right means that a company that wishes to sell stock must first offer it to the
existing stockholders before offering it to the general public
Slide 37
7-37
Dividend Characteristics
• Dividends are not a liability of the firm until declared by the Board of Directors
A firm cannot go bankrupt for not declaring dividends
• Dividends and Taxes Dividend payments are not considered a business
expense; therefore, they are not tax deductible.
The taxation of dividends received by individuals depends on the holding period.
Dividends received by corporations have a minimum 70% exclusion from taxable income.
Characteristics of dividends:
• Payment of dividends is at the discretion of the board. A firm cannot default on an undeclared dividend, nor can it be forced to file for bankruptcy because of nonpayment of dividends.
• Dividends are not tax deductible for the paying firm. • Dividends received by individuals are taxed based on the holding period of the stock, while dividends
received by a corporation are at least 70% tax-exempt.
Dividend exclusion: If corporation A owns less than 20% of corporation B stock, then 30% of the
dividends received from corporation B are taxable. If A owns between 20% and 80% of B, then 20% of
the dividends received are taxable. If A owns more than 80%, a consolidated statement can be filed and
dividends received from B are essentially untaxed.
Slide 38
7-38
Features of Preferred Stock
• Dividends Stated dividend that must be paid before dividends can be
paid to common stockholders
Dividends are not a liability of the firm, and preferred dividends can be deferred indefinitely.
Most preferred dividends are cumulative – any missed preferred dividends have to be paid before common dividends can be paid.
• Preferred stock generally does not carry voting rights
Preferred stock is similar to bonds since interest payments on bonds are quite similar to dividends on
preferred stock. The difference is that most of the bonds have a finite maturity while preferred stock pays
a constant dividend in perpetuity. Its dividend is usually fixed, and the stock is often without voting
rights. Preferred stock has a state liquidating value, usually, $100 per share and it pays a cash dividend
expressed in terms of dollars per share. (e.g., Google' "$7 preferred," paying an annual cash dividend of
$7, translates to a dividend yield of 7% of stated liquidating value). The stated value is the value paid to
preferred stockholders in the event of liquidation.
Cumulative dividends – current preferred dividend plus all arrearages (unpaid dividends) to be paid
before common stock dividends can be paid. Non-cumulative dividend preferred stock does not have this
feature.
Preferred stock represents equity in the firm, but has many features of debt, including a stated yield,
preference in terms of cash flows and liquidation, and some issues are callable and/or convertible into
common shares.
Corporations that own stock in other corporations are permitted to exclude 50 percent of the dividend
amounts they receive and are taxed on only the remaining 50 percent (the 50 percent exclusion was
reduced from 70 percent by the Tax Cuts and Jobs Act of 2017).
Slide 39
7-39
The Stock Markets
• Primary vs. Secondary Markets Primary = new-issue market
Secondary = existing shares traded among investors
• Dealers vs. Brokers Dealer: Maintains an inventory
Ready to buy or sell at any time
Think “Used car dealer”
Broker: Brings buyers and sellers together
Think “Real estate broker”
Primary market – the market in which new securities are originally sold to investors
Secondary market – the market in which existing securities trade among investors
A dealer is an agent who buys and sells securities from inventory. In contrast, a broker is an agent who
brings buyers and sellers together but does not maintain an inventory (An agent who arranges
security transactions among investors).
Bid price – the price at which a dealer is willing to buy a security
Ask price – the price at which a dealer is willing to sell a security
Spread – the difference between the bid and ask prices
Slide 40
7-40
• Dealers vs. Brokers
• New York Stock Exchange (NYSE: https://www.nyse.com/index)
Largest stock market in the world
License holders (1,366) • Designated market makers (DMMs)
• Floor brokers
• Supplemental liquidity providers (SLPs)
Operations
Floor activity
Stock Market
Organization of the NYSE:
Prior to 2006, the exchange consisted of 1,366 members, said to own seats. Since going public, there are
1,366 licensees who pay an annual fee to trade.
• DMMs, formerly known as “specialists,” act as dealers in particular stocks. A DMM maintains an
inventory and stands ready to trade at quoted bid (DMM posts the price at which they will buy) and
ask (DMM posts the price at which they will sell) prices. They make their profit from the difference
between the bid and ask prices, called the bid-ask spread. The smaller the spread, the more competition
and the more liquid the stock. The move to decimalization allows for a smaller bid-ask spread. There
will be more discussion of this later.
• DMM’s post – fixed place on the exchange floor where the specialist operates
• Trading in the crowd – trading that occurs directly between floor brokers around the DMM’s post
• Floor broker: a broker matches buyers and sellers. They perform the search function for a fee
(commission). They do not hold an inventory of securities.
• Floor traders: those who trade for their own accounts, trying to anticipate and profit from temporary
price fluctuations
• SLPs: investment firms that agree to be active participants in stocks assigned to them. They trade
purely for their own accounts. Unlike DMMs and floor brokers, SLPs do not operate on the floor of
the stock exchange.
• Order flow – the flow of customer orders to buy and sell securities
Slide 41
7-41
• Not a physical exchange – computer-based quotation system
• Multiple market makers
• Electronic Communications Networks
• Three levels of information Level 1 – median quotes, registered representatives
Level 2 – view quotes, brokers, and dealers
Level 3 – view and update quotes, dealers only
• Large portion of technology stocks
NASDAQ
NYSE operations represent a premier example of the trading of “listed” securities. Nasdaq operations, on
the other hand, represent the evolution of “over-the-counter” trading of securities that do not rely on a
physical market place.
Nasdaq – National Association of Securities Dealers Automated Quotation system – computer network of
securities dealers who disseminate timely security price quotes to Nasdaq subscribers
The NASDAQ market site in Times Square is NOT an exchange. It is just offices and basically a place for
reporters to report on what is happening with Nasdaq stocks.
