7- 1

CHAPTER 7 The Valuation and

Characteristics of Stock

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

7- 3The Return on an Investment in Common Stock

The future cash flows associated with stock ownership consists of

– Dividends and

– 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, your 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.

7- 4

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 industryDifferent investors with different cash flow

estimates will have different intrinsic values

7- 5Price versus Earnings

7- 6

Developing Growth-Based Models Realistically most people tend to forecast growth rates rather

than cash flows 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

7- 7

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

7- 8

What is a constant growth stock?

s

3

s

32

s

21

s

10

k1

D. . .

k1

D

k1

D

k1

DP̂

One whose dividends are expected togrow forever at a constant rate, g.

Stock Value = PV of Dividends:

7- 9

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:

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

7- 10

Constant Normal Growth Constant growth model can be simplified to

10

DP

gk

K must be greater than g.

D1 = D0(1+g)

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

gk

Ds

11

7- 11

The discount rate (ki) is the opportunity cost of capital, i.e., the rate that could be earned on alternative investments of equal risk.

ki = k* + IP + LP + MRP + DRP.

For Bonds:

For Stocks:

Ks = KRF + (KM – KRF)s

7- 12

Constant Normal Growth—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:

Exa

mpl

e 10

DP

k - g

$2.25 (1.06)

.11 - .06$47.70

7- 13

.gk requires gk

DP̂ s

s

10

What happens if g > ks?

We can’t use model unless (1) ks> g and (2) g is expected to be constant forever.

•If ks< g, get negative stock price, which is nonsense.

7- 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

7- 15

The Expected Return

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

1

0

D

Pk g

g is the expected capital gains (%)

The higher the expected growth in dividends the faster the price is expected to grow

Would this apply to farmland? How?

7- 16Basis for growth expectationsJust looking at past dividend growth is not very

informative because it can be distortedGrowth in EPS is the fundamental driver of

growth in dividends (get data on EPS growth)EPS growth greater than sales growth is not

sustainable over a long period (so get data on sales growth)

Consider industry factors that affect growth and market share

ROE times the retention rate is the fundamental driver of EPS growth (get data on ROE and retention rate)

Also look for expert opinion

7- 17

What’s the stock’s market value? D0 = 2.00, ks = 16%, g = 6%.

Constant growth model:

PD

k gs0

1 120 16 0 06

$2.. .

$2.

.$21. .

120 10

20

7- 18

What is the stock’s market value one year from now, P1?

D1 will have been paid, so expected dividends are D2, D3, D4 and so on. Then,

PD

k gs1

2 2470 16 0 06

47

$2.

. .$22. .

^

..$..

.$gk

DP

s

8223060160

382232

..$

...$

gkD

Ps

8223060160

382232

7- 19

Constant Growth Implications

Year Dividend Multiple Stock

Price

Growth

Rate

0 $2.12 10 $21.20 6%

1 $2.247 10 $22.47 6%

2 $2.382 10 $23.82 6%

Ks = 16%; g = 6%; 1/(.16-.06) = 10

7- 20

Find the expected dividend yield, capital gains yield, and total return

during the first year.

%.16%6%10return Total

%.6PD

kP

PP yldgains Cap.

%.1020.21$12.2$

PD

yldDividend

0

1s

0

01

0

1

7- 21

Then, ks = $2.12/$21.20+ 0.06= 0.10 + 0.06 = 16%.

Dividend yield+capital gain

Why do the dividend and capital gains returnsadd-up to the required rate of return?Rearrange model to rate of return form:

.gPD

k gk

DP s

s

0

110

7- 22

What would P0 be if g = 0?

The dividend stream would be a perpetuity.

PPMTk0

000 16

50 $2.

.$12. .

2.00 2.002.00

0 1 2 316%

7- 23

Two Stage Growth

At times a firm’s future growth may not be expected to be constantFor 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 timeUse the Gordon model to value the constant

portionFind the present value of the non-constant

growth periods

7- 24

Problem 9 from lab

Frazier Inc. paid a dividend of $4 last year (D0). The firm is expecting dividends to grow at 21% in years 1–2 and 10% in Year 3. After that growth will be constant at 8% per year. Similar investments return 14%. Calculate the value of the stock today.

a.$71.49b.$88.31c.$91.47d.$116.10

7- 25

ANS: C

D1 = 4(1.21) = 4.84

D2 = D1(1.21) = 5.8564

D3 = D2(1.10) = 6.442

D4 = D3(1.08) = 6.9574032

P3 = [D4]/(.14 – .08) = 115.956726.44 + 115.96 = 122.40Calculator Steps:

CFo = 0, C01 = 4.84, C02 = 5.86, C03 = 122.40; I = 14Solve for NPV = $91.37

7- 26

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.

Exa

mpl

eTwo Stage Growth—Example

7- 27

Two Stage Growth—Example

We’ll develop a schedule of expected dividend payments:

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

Exa

mpl

e

32

2

D $3.05P $76.25

k - g .10 - .06

6%$3.053

20%$2.882

20%$2.401

GrowthExpected DividendYear

7- 28

Do time line and PV on the board

CF0 = 0

CF1 = 2.40

CF2 = 2.88 + 76.32 = 79.20

Ks = 10%

NPV =?= 67.64

7- 29

Have to project out the assumptions on a time line.

Apply the constant growth model after 3 years.

^

Another example: If we have supernormal growth of 30% for 3 yrs, then a long-run constant g=6%, what is P0? ks is still 16%.

7- 30

High growth followed by constant lower growth:

0 1 2 3 4ks=16%

NPV = 37.410 = P0

g = 30% g = 30% g = 30% g = 6%

D0 = 2.00 2.60 3.380 4.394 4.658

P34 658

0 16 0 0658

.. .

$46.

46.58CF0=0

CF1=2.6

CF2=3.38

CF3=50.97

I=16

7- 31

What is the expected dividend yield and capital gains yield at t = 0?

At t = 4?

%.055.9%95.6%16gain Cap.

:bemustgaincapitaltheTherefore

%.95.641.37$

60.2$ yield.Div

0

0

7- 32

During nonconstant growth, dividend and cap. gains yields are not constant, and capital gains yield is less than g.

After t = 3, g = constant = 6% = capital gains yield; k = 16%; so D/P = 16 - 6 = 10%.

7- 33

If g = -6%, would anyone buy the stock? If so, at what price?

Firm still has earnings and still paysdividends, so P0 > 0:

P

Dk g

D gk gs s

01 0 1

.^

$2. .. .

$1..

$8. .00 0 94

0 16 0 0688

0 2255

7- 34

What is the annual D/P and capital gains yield?

Capital gains yield = g = - 6.0%, Dividend yield = 16.0% - (-6.0%) =

22%. D/P and cap. gains yield are

constant, with high dividend yield (22%) offsetting negative cap. gains yield.

7- 35

super normal growth example

The XYZ corporation has had annual earnings and dividends increase at the rate of 75% recently and recently paid dividends of $4/share. The outlook is for continued high growth at 50% per year for the next three years, then a more modest growth rate of 5% per year for all future years.

The required return for a company of this risk is 15%.

7- 36

SUPER NORMAL GROWTH ANSWER

D1=6, D2=9, D3=13.50, D4=13.5(1.05)=14.175

P3=price of the stock at time 3, when the constant growth begins

P3=14.175[1/.15-.05]=14.175(10)

=$141.75Draw a time line.Using the CFj part of your calculator:

CF0=0, CF1=6, CF2=9, CF3=13.5+141.75=155.25, I=15

NPV=P0=$114.10

7- 37Super Normal Growth

Base Dividend

Growth rate

Num-ber of years

Constant growth rate

ks

$1 20% 5 3% 15%

$30 40% 3 4% 16%

$2 30% 2 5% 14%

2 30% 3 5% 14% 

7- 38

What is market equilibrium?

In equilibrium, stock prices are stable.There is no general tendency for people to buy versus sell.

In equilibrium, expected returns mustequal required returns:

.k D P g k k k k bRF M RF 1 0

7- 39

How is equilibrium established?

If k = (D1/ P0) + g > k, thenP0 is “too low,” a bargain.

Buy orders > sell orders;

P0 bid up; D1/P0 falls until

D1/P0 + g = k = k.

^

^

7- 40

Why do stock prices change?

gk

DP

i 1

0

1. ki could change: ki = kRF + (kM - kRF )bi

kRF = k* + IP

2. g could change due to economic or firm situation

3. D could change – usually due to earnings

4. Super-normal growth expectations could be formed or change.

7- 41

Feb. 4, 1994: Fed announcedincrease in interest rates at 11 a.m.

Result: Dow Jones fell 95 points.

PD

k gi0

1

ki = kRF + (kM - kRF )bi

kRF = k* + IP

7- 42

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

7- 43

What’s the Efficient Market Hypothesis?

EMH: Securities are normallyin equilibrium and are “fairlypriced,” given what is currently known. One cannot “beatthe market” except throughgood luck or inside info.

7- 44

1. Weak-form EMH:Can’t profit by looking atpast trends. A recent declineis no reason to think stockswill go up (or down) in thefuture. Seems empiricallytrue, but “technical analysis”is still used.

7- 45

2. Semi-strong form EMH:

All publicly available info. isreflected in stock prices, sodoesn’t pay to pore overannual reports looking forundervalued stocks. Largelytrue, but superior analystscan still profit by finding and using new information.

It is VERY hard to tell good luck from superior stock picking/timing ability.

7- 46

All information, even insideinfo, is embedded in stockprices. Not true--insiderscan gain by trading on the basis of insider information,but that’s illegal.

3. Strong-form EMH:

7- 47

Markets are efficient because:

1. 15,000 or so trained analysts; MBAs,

CFAs, Technical PhDs.

2. Work for firms like Merrill, Morgan,

Prudential, which have much money.

3. Have similar access to data.

4. Thus, news is reflected in P0 almost

instantaneously.