The Valuation and Characteristics of Stock

Chapter 7

© 2003 South-Western/Thomson Learning

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 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

8

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

9

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

10

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

11

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)

12

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

13

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

14

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

15

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

16

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

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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

18

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

19

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

20

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

21

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

22

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

23

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)

24

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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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