Chapter 07 Valuation & Characteristics of Stocks

Slides developed by:Pamela L. Hall, Western Washington University

The Valuation and Characteristics of Stock

Chapter 7

2

Common Stock

Background Stockholders own the corporation, but in

many instances the corporation is widely held• Stock ownership is spread among a large number

of people Because of this, most stockholders are only

interested in how much money they will receive as a stockholder

• Most equity investors aren’t interested in a role as owners

3

The Return on an Investment in Common Stock The future cash flows associated with stock ownership consists of

Dividends The eventual selling price of the shares

If you buy a share of stock for price P0, hold it for one year during which time you receive a dividend of D1, then sell it for a price P1, you return, k, would be:

1 1 0

0

1 01

0 0

dividend yield capital gains yield

D + P -Pk =

P

or

P -PDk = +

P P

A capital gain (loss) occurs if you sell the stock for a price greater (lower) than

you paid for it.

4

The Return on an Investment in Common Stock We can solve the previous equation for P0, the stock’s

price today:

0 1 1 0

0 0 1 1

0 1 1

1 10

kP

P kP

1 P

P1

D P P

D P

k D P

D P

k

The return on our stock investment is the interest rate that equates the present value of the investment’s expected future cash flows to the amount invested today, the price, P0

5

The Nature of Cash Flows from Stock Ownership Comparison of Cash Flows from Stocks and

Bonds The expected receipt of dividends and the future

selling price of stock is similar to what a bondholder expects in terms of interest and principal repayment

• However, with bondholders:• A guarantee is associated with their interest payments• Interest payments are constant• The maturity value of a bond is fixed• When the bond matures, the investor receives contracted par or

face value from the issuing company• When stock is sold, the investor receives money from another investor

6

The Basis of Value

The basis for stock value is the present value of expected cash inflows even though dividends and stock prices are difficult to forecast Must make assumptions about what the future

dividends and selling price will be• Discount these assumptions at an appropriate interest rate

0 1 k,1 2 k,2 n k,n n k,nP = D PVF D PVF D PVF P PVF

7

The Basis of Value—Example

Q: Joe Simmons is interested in the stock of Teltex Corp. He feels it is going to have two very good years because of a government contract, but may not do well after that. Joe thinks the stock will pay a dividend of $2 next year and $3.50 the year after. By then he believes it will be selling for $75 a share, at which price he'll sell anything he buys now. People who have invested in stocks like Teltex are currently earning returns of 12%. What is the most Joe should be willing to pay for a share of Teltex?

A: Joe shouldn’t pay more than the present value of the cash flows he expects: $2 at the end of one year and $3.50 plus $75 at the end of two years.

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0 12%,1 12%,2 12%,2P = $2 PVF $3.50 PVF $75 PVF

$2[0.8929] $3.50[0.7972] $75.00[0.7972]

$64.37

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The Intrinsic (Calculated) Value and Market Price A stock’s intrinsic value is based on

assumptions made by a potential investor Must estimate future expected cash flows

• Need to perform a fundamental analysis of the firm and the industry

Different investors with different cash flow estimates will have different intrinsic values

9

Growth Models of Common Stock Valuation Realistically most people tend to forecast

growth rates rather than cash flows Because forecasting exact future prices and

dividends is very difficult

10

Developing Growth-Based Models A stock’s value today is the sum of the present values of

the dividends received while the investor holds it and the price for which it is eventually sold

1 2 n n

0 2

D D D PP =

1 1 1 1n nk k k k

An Infinite Stream of Dividends Many investors buy a stock, hold for awhile, then sell, as

represented in the above equation• However, this is not convenient for valuation purposes

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Developing Growth-Based Models A person who buys stock at time n will hold it

until period m and then sell it Their valuation will look like this:

n + 1 m m

n m - n m - n

D D PP = +…+ +

1 + k 1 + k 1 + k

Repeating this process until infinity results in:

i

0 ii=1

DP

1 + k

Conceptually it’s possible to replace the final selling price with an infinite series of dividends

12

Working with Growth Rates

Growth rates work like interest rates If growth is expected to be 6% next year then

$100 experiencing a 6% growth will increase by $6, or $100 x 6%

• The ending value after 6% growth will be $106, or $100 + $6, or $100 x (1.06)

13

The Constant Growth Model

If dividends are assumed to be growing at a constant rate forever and we know the last dividend paid, D0, then the model simplifies to:

1

00 i

i=1

D 1 iP

1 + k

Which represents a series of fractions as follows

2 3

0 0 00 2 3

D 1 g D 1 g D 1 gP =

1 k 1 k 1 k

If k>g the fractions get smaller (approach zero) as the exponents get larger If k>g growth is normal If k<g growth is supernormal

• Can occur but lasts for limited time period

14

Constant Normal Growth—The Gordon Model Constant growth model can be simplified

to

10

DP

gk

K must be greater than g.

The Gordon model is a simple expression for forecasting the price of a stock that’s expected to grow at a constant, normal rate

15

Constant Normal Growth—The Gordon Model—Example

Q: Atlas Motors is expected to grow at a constant rate of 6% a year into the indefinite future. It recently paid a dividends of $2.25 a share. The rate of return on stocks similar to Atlas is about 11%. What should a share of Atlas Motors sell for today?

A:

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DP

k - g

$2.25 (1.06)

.11 - .06$47.70

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The Zero Growth Rate Case—A Constant Dividend If a stock is expected to pay a constant,

non-growing dividend, each dollar dividend is the same

Gordon model simplifies to:

0

DP

k

A zero growth stock is a perpetuity to the investor

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The Expected Return

Can recast Gordon model to focus on the return (k) implied by the constant growth assumption

1

0

D

Pk g

The expected return reflects investors’ knowledge of a company If we know D0 (most recent dividend paid) and P0

(current actual stock price), investors’ expectations are input via the growth rate assumption

18

Two Stage Growth

At times a firm’s future growth may not be expected to be constant For example, a new product may lead to temporary

high growth The two-stage growth model allows us to value

a stock that is expected to grow at an unusual rate for a limited time Use the Gordon model to value the constant portion Find the present value of the non-constant growth

periods

19

Q: Zylon Corporation’s stock is selling for $48 a share according to The Wall Street Journal. We’ve heard a rumor that the firm will make an exciting new product announcement next week. By studying the industry, we’ve concluded that this new product will support an overall company growth rate of 20% for about two years. After that, we feel growth will slow rapidly and level off at about 6%. The firm currently pays an annual dividend of $2.00, which can be expected to grow with the company. The rate of return on stocks like Zylon is approximately 10%. Is Zylon a good buy at $48?

A: We’ll estimate what we think Zylon should be worth given our expectations about growth.

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Two Stage Growth—Example

We’ll develop a schedule of expected dividend payments:

Next, we’ll use the Gordon model at the point in time where the growth rate changes and constant growth begins. That’s year 2, so:

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2

D $3.05P $76.25

k - g .10 - .06

6%$3.053

20%$2.882

20%$2.401

GrowthExpected DividendYear

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Two Stage Growth—Example

Then we take the present value of D1, D2 and P2:

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0 1 k, 1 2 k, 2 2 k, 2

10, 1 10, 2 10, 2

P D PVF + D PVF + P PVF

$2.40 PVF + $2.88 PVF + $76.25 PVF

$2.40 0.9091 + $2.88 0.8264 + $76.25 0.8264

$67.57

Compare $67.57 to the listed price of $48.00. If we are correct in our assumptions, Zylon should be worth about $20 more than it is selling for in the market, so we should buy

Zylon’s stock.

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Practical Limitations of Pricing Models Stock valuation models give approximate results

because the inputs are approximations of reality Bond valuation is precise because inputs are exact

• With bonds future cash flows are contractually guaranteed in amount and time

Actual growth rate can be VERY different from predicted growth rates Even if growth rates differ only slightly, it can make a big

difference in our decision

So, it’s best to allow a margin for error in your estimations

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Practical Limitations of Pricing Models Stocks That Don’t Pay Dividends

Some firms don’t pay dividends even if they are profitable

Many companies claim they never intend to pay dividends

• These firms can still have a substantial stock price Firms of this type typically are growing and are using

their profits to finance their growth• However rapid growth won’t last forever• When growth slows, the firm will begin paying dividends

• It’s these distant dividends that impart value

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Some Institutional Characteristics of Common Stock Corporate Organization and Control

Controlled by Board of Directors (elected by stockholders) Board appoints top management who then appoint middle/lower

management Board consists of: top management and outside members

(major stockholders, top executives at other firms, former presidents, etc.)

In widely held corporations, top management is effectively in control of the firm because no stockholder group has enough power to remove them

Preemptive Rights If firm issues new shares, existing shareholders have right to

purchase pro rata share of new issue Common, but not required by law

25

Voting Rights and Issues

Each share of common stock has one vote in the election of directors, which is usually cast by proxy A proxy fight occurs if parties with conflicting

interests solicit proxies at the same time

26

Majority and Cumulative Voting

Majority voting gives the larger group control of the company

Cumulative voting gives minority interest a chance at some representation on the board

Shares With Different Voting Rights Different classes of stock can be issued with different

rights• Some stock may be issued with limited or no voting rights

27

Stockholders’ Claim on Income And Assets Stockholders have claim on the firm’s net

income What is not paid out as dividends is retained

(Retained Earnings) for investment in new projects Leads to future growth

Common stockholders are last in line to receive income or assets, and bear more risk than other investors However, residual interest is large when firm does

well

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Preferred Stock

Preferred stock is often referred to as a hybrid between common stock and bonds because: No maturity date (like common stock) Fixed dividend payment (similar to bond

interest payment)

29

Valuation of Preferred Stock

There is no growth rate in preferred stock dividends, so growth rate equals 0

The dividend at time 1 is the same as the dividend at time 0, so there is usually no time period associated with the numerator Valuation is that of a perpetuity

p

p

kD

P

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Preferred Stock—Example

Q: Roman Industries’ $6 preferred originally sold for $50. Interest rates on similar issues are now 9%. What should Roman’s preferred sell for today?

A: Just substitute the new market interest rate into the preferred stock valuation model to determine today’s price:

0

$6 $66.67P

.09

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Characteristics of Preferred Stock Cumulative Feature

Common dividends can’t be paid unless the dividends on cumulative preferred are current

Preferred stock never returns principal (like a bond does upon maturity)

Preferred stockholders cannot force a firm into bankruptcy (like bondholders)

Preferred stockholders received preferential treatment over common stockholders in the event of bankruptcy, but have a lower priority than bondholders

Preferred stockholders do not have voting rights (like common stockholders do)

Dividend payments to preferred stockholders are not tax deductible to the firm

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Securities Analysis

Securities analysis is the art and science of selecting investments

Fundamental analysis looks at a company and its business to forecast value

Technical analysis bases value on the pattern of past prices and volumes

The Efficient Market Hypothesis says information moves so rapidly in financial markets that price changes occur immediately, so it is impossible to consistently beat the market to bargains

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Options and Warrants

Option gives the option holder the temporary right to buy (or sell) an asset from another party at a fixed price

For instance, a company may be interested in building a new factory on a tract of land, but it is still unsure if it wants to build the factory However, it plans to make a final decision in six months The company could buy an option contract giving it the right to

buy the land at a fixed price by the end of the six months• If the company pursues the factory project, it would exercise the

option• If the company decided not to go ahead with the factory project it

would not have to exercise the option• But what if the value of the land had risen substantially above the price

fixed by the option—it could exercise the option and sell the land for a profit thus benefiting even though it didn’t own the land during the period of the option

34

Stock Options

Stock options are purchased to speculate on stock price movements

Can be traded in financial markets Call option (call)—an option to buy a stock Put option (put)—an option to sell stock Known as a derivative—derives its value

from the price of an underlying security

35

Call Option

Basic call option Gives owner the right to buy stock at a fixed

price (called the exercise or strike price) for a specified time period

• Usually 3, 6 or 9 months Option expires at the end of the time period Price of the option is less than the price of the

underlying stock

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Figure 7-3: Basic Call Option Concepts

If the option is selling for $1 and the stock’s price increased to $63 the option could be exercised and the stock immediately

sold, resulting in a profit of $3 less the price of the option contract (a $2 profit on a $1 investment, or a 200% return). If the stock price doesn’t exceed $60 before the option expires, the $1

is lost (a 100% loss).

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Call Options

The more volatile the stock’s price the more attractive the option The stock’s price is more likely to exceed the

strike price before the option expires The longer the time until expiration the

more attractive the option The stock’s price is more likely to exceed the

strike price before the option expires

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The Call Option Writer

The option writer is the person who creates the contract Agrees to sell the stock at the strike price if

the option is exercised The original writer must stand ready to

deliver on the contract regardless of how many times the option is sold

Call writer hopes stock price will remain the same

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Intrinsic Value

A call option’s intrinsic value is the difference between the underlying stock’s current price and the option’s strike price

If the option is out-of-the-money then the intrinsic value is zero

Option will always sell for intrinsic value or above Difference between option’s intrinsic value

and price is known as time value

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Figure 7-4: The Value of a Call Option

41

Options and Leverage

Financial leverage Technique that amplifies return on investment

• Improves positive returns and worsens negative returns

Options offer leveraging potential due to the lower price at which you can buy an option compared to the price of the underlying stock The higher the price of the option the less the

leverage potential

42

Options that Expire

Option investing is risky because options expire after a limited time

If the option was purchased out-of-the-money and the stock price never exceeds the strike price prior to the expiration date the option will expire worthless Resulting in a 100% loss

As the expiration date approaches an option’s time value approaches zero

43

Trading in Options

Options can be bought and sold at any time prior to expiration Chicago Board Options Exchange (CBOE) is the largest, oldest

and best known options exchange Price volatility in the options market

As the price of the underlying stock changes the price of the option changes but by a greater relative movement due to the lower price of the option compared to the stock

Options are rarely exercised before expiration If the call option owner believes a stock is unlikely to increase

further he is likely to sell the option rather than exercise it as he would lose any time premium if he were to exercise the option

44

Writing Options

People write options for the premium income, hoping that the option will never be exercised

Option writers lose whatever option buyers win Take the opposite side of a bet

Covered option—the writer owns the underlying stock

Naked option—the writer does not own the underlying stock and must purchase it at the current price should the option be exercised

45

Option Example

The following information refers to a three-month call option on the stock of Oxbow, Inc.

Price of the underlying stock: $30Strike price of the three-month call: $25Market price of the option: $8

Q: What is the intrinsic value of the option? A: The intrinsic value represents by how much the option is in-the-

money. Since the stock price is $30 and the call option’s strike price is $25, the option is in-the-money by $5, which is the intrinsic value.

Q: What is the option’s time premium at this price?A: The time premium represents the difference between the

market price of the option and the intrinsic value, or $8 - $5 = $3.

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Option Example

Q: If an investor writes and sells a covered call option, acquiring the covering stock now, how much has he invested?

A: The premium ($8) that the writer receives for the option will offset some of the purchase price of the stock ($30), therefore the investor has invested $30 - $8 = $22.

Q: What is the most the buyer of the call can lose?A: The buyer can lose, at most, 100% of his investment which is

the purchase price of the option of $8.Q: What is the most the writer of a naked call option on this stock

can lose?In theory since the stock price can rise to any price the writer can lose an infinite amount. However, a prudent writer would limit his losses by purchasing the stock once it started to rise in value.

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Option Example

Just before the option’s expiration Oxbow is selling for $32.Q: What is the profit or loss from buying the call?A: The buyer would exercise the option paying $25 for the stock and

simultaneously selling the stock for $32, resulting in a gain of $7. However, this gain would be offset by the $8 premium paid for the option, resulting in an overall loss of $1.

Q: What is the profit or loss from writing the call naked?A: A naked writer would have to buy the stock for $32 and sell it to the

option owner for $25, resulting in a loss of $7. However, this loss would be offset by the premium received on the writing of the option of $8, resulting in an overall gain of $1.

Q: What is the profit or loss from writing the call covered if the covering stock was acquired at the time the call was written?

A: The call writer bought the stock for $30 and sold it for $25, resulting in a loss of $5, but the loss is offset by the $8 premium received for writing the option. The overall gain is $3.

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Put Options

An option to sell an underlying asset at a specified price by a specified date

Would buy a put if you thought the price of the underlying asset were going to fall

Intrinsic value is how much the option is in-the-money

Option is in-the-money if the strike price is lower than the current stock price

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Figure 7.5: Basic Put Option Concepts

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Figure 7.6: The Value of a Put Option

51

Option Pricing Models

Option pricing model is more difficult than pricing models for stocks and bonds

Fischer Black and Myron Scholes developed the Black-Scholes Option Pricing Model Determines option’s price based on

• Price of underlying stock• Strike price of option• Time remaining until expiration of option• Volatility of underlying stock’s market price• Risk-free interest rate

52

Warrants

Options trade between investors, not between the companies that issue the underlying stocks

Warrants are issued by the underlying companies When the warrant is exercised the company

issues new stock and receives the exercise price

• Thus, warrants are primary market instruments while options are secondary market instruments

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Warrants

Similar to call options but have a longer expiration period (several years vs. months)

Usually issued as a “sweetener” (for bonds, for instance)

Warrants can generally be detached from another issue and sold separately

54

Employee Stock Options

More like warrants than traded options Don’t expire for several years Strike prices are set far out of the money Employees who receive options generally receive a

lower salary than they would otherwise If a company is expected to have a good future

employees may want to receive options Companies like paying with options because

they can pay the employees a lower salary Argue that options allow up-and-coming companies

to attract talented employees that they couldn’t otherwise afford

55

The Executive Stock Option Problem Senior executives are usually the people

who receive the most stock options Tactic has been criticized recently

May cause executive to try to increase stock price in unethical ways

• Manipulating financial results driving the stock price higher

• Market should eventually realize the problem and drive the stock down but executives have already exercised their stock options and sold the stock at the inflated price

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The Executive Stock Option Problem This can negatively impact a firm’s pension plan if it is

heavily invested in its firm’s own stock In the early 2000s investors realized that auditors

couldn’t (or wouldn’t) always report financial manipulations Enron, WorldCom, Tyco Resulted in a loss of investor confidence in corporate

management One result of the overhaul of financial reporting is the

requirement that companies recognize employee stock options as expenses at the time they are issued Problem is that no one knows how high the stock will rise in

value at the time the options are issued