The Valuation and Characteristics of Stock

2

Common Stock

Corporations are owned by common stockholders Stockholders choose directors

Most large companies are “widely held’ Ownership spread among many investors.

Investors don’t think of a role as owner Interested mostly in future cash flows.

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The Return on an Investment in Common Stock

Income in a stock investment comes from: dividends gain or loss on the difference between the purchase and sale price

If you buy a stock for price P0, hold it for one year, receive a dividend of D1, then sell it for 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

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 a 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

For stockholders:Expected dividends and future selling price are not known with any precision

Similarity to bond cash flows is superficial – both involve a stream of small payments followed by a larger payment

When selling, investor receives money from another investor

For bondholders:Interest payments are guaranteed, constant

Maturity value is fixed

At maturity, the investor receives face value from the issuing company.

Comparison of Cash Flows from Stocks and Bonds

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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 Make assumptions about future dividends and selling

price 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 ValueExample 8.1

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?

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The Intrinsic (Calculated) Value and Market Price

A stock’s intrinsic value is based on assumptions about future cash flows made from fundamental analysis of the firm and its industry

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

9

Growth Models of Common Stock Valuation

Based on predicted growth rates since forecasting exact future prices and dividends is difficult

More likely to forecast a growth rate of earnings rather than cash flows

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• 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

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The Constant Growth Model

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

This 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 exponents get larger○ If k>g growth is normal○ If k<g growth is supernormal

• Can occur but lasts for limited time period

1i

i

i0

0)k1(

)g1(DP

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Working with Growth Rates Example 8.2

Q. Apex Corp. paid a dividend of $3.50 this year. What are its next three dividends if it is expected to grow at 7%?

A. SOLUTION: In this case D0 = $3.50 and g = .07, so (1+g) = 1.07. Then

D1 = D0(1+g) = $3.50(1.07) = $3.75,D2 = D1(1+g) = $3.75(1.07) = $4.01, andD3 = D2(1+g) = $4.01(1.07) = $4.29.

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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 8.3 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

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

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Two Stage Growth

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

The two-stage growth model values 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

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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 GrowthExample 8.5

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Two Stage GrowthExample 8.5

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 GrowthExample 8.5

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 estimated results since the inputs are approximations of reality

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

big difference in the decision Allow for a margin for error in estimations

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Practical Limitations of Pricing Models

Comparison to Bond Valuation

Bond valuation is precise because the inputs are precise.

Future cash flows are guaranteed in amount and time, unless firm defaults.

Stocks That Don’t Pay Dividends

Have value because of expectation that they will someday pay them.

Some firms don’t pay dividends even if they are profitableFirms are growing and using profits to finance the growth

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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 appoint middle/lower management

Board consists of top managers and outside directors (may include major stockholders)

In widely held corporations, top management in “control”

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Stockholders’ Claim on Income And Assets

Stockholders have a residual claim on income and assets

What is not paid out as dividends is retained for reinvestment in the business (retained earnings)

Common stockholders are last in line, they bear more risk than other investors

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Preferred Stock

A hybrid security with characteristics of common stock and bonds Pays a constant dividend forever Specifies the initial selling price and the

dividend No provision for the return of capital to the

investor

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Valuation of Preferred Stock

Since securities are worth the present value of their future cash flows, preferred stock is worth the present value of the indefinite stream of dividends.

p

p

kD

P

28

Preferred StockExample 8.6

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 - can’t pay common dividends unless cumulative preferred dividends are current

Never returns principal Stockholders cannot force bankruptcy Receives preferential treatment over

common stock in bankruptcy Lower priority than bondholders

No voting rights Dividend payments not tax deductible to the firm

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Securities Analysis

The art and science of selecting investments

Fundamental analysis looks at a company’s business to forecast value

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

The Efficient Market Hypothesis (EMH) - financial markets are efficient since new information is instantly disseminated Impossible to consistently beat the market

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Options and Warrants

Options Gives the holder the

temporary right to buy or sell an asset at a fixed price

Speculate on price changes without holding the asset

WarrantsSimilar but less common

Options and warrants make it possible to invest in stocks without holding shares

32

Stock Options

Stock options speculate on stock price movements

Trade in financial markets Call option — option to buy Put option — option to sell Options are Derivative Securities

Derive value from prices of underlying securities Provide leverage – amplifying returns

33

Writing Options

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

Option writers give up what option buyers make Covered option — writer owns underlying stock Naked option — writer does not own the

underlying stock Purchase it at the current price if exercised

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Warrants

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

Secondary market instruments

Warrants Issued by underlying company

When exercised – new stock is issued and company receives the exercise price

Primary market instruments while options are secondary market instruments

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Warrants

Similar to calls with a longer expiration period (several years vs. months)

Issued as a “sweetener” (especially for risky bonds)

Can generally be detached from another issue and sold separately

36

Employee Stock Options

More like warrants than traded options Expire after several years Strike price set far out of the money May receive options in lieu of salary increases

Wanted if future expectations are good

Companies offering options may pay lower salaries Attract employees not otherwise affordable

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Employee Stock Options

Executive Stock Option Problem Senior executives may receive most of the

stock options Provide an incentive for executives to

misstate financial statements and inflate stock prices Negatively impacts a firm’s pension plan if heavily

invested in its own stock As a result of overhauling financial reporting, companies

must recognize employee stock options as expenses when they are issued