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Stock Valuation

Corporate Finance

Dr. A. DeMaskey

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Learning Objectives Questions to be answered:

What are the rights and privileges of stock ownership?

What types of common stock exist? How can stock market transactions be

classified? How are stocks valued? What is the total return on stocks? What does stock market equilibrium mean and

how is it established? What is preferred stock and how is it valued?

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Facts About Common Stock Represents ownership. Ownership implies control. Stockholders elect directors. Directors hire management. Management’s goal: Maximize stock

price.price.

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Basics of Common Stock Preemptive Right

Right to purchase new shares in proportion to current holdings.

Classified Stock Founders’ shares, with voting rights but

dividend restrictions. New shares might be called “Class A”

shares, with voting restrictions but full dividend rights.

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The Market for Common Stock

Secondary Market

Primary Market

Initial Public Offering (IPO) Market

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The Dividend Valuation Model Stock Value = PV of Expected Dividends

sss k

D

k

D

k

DP

1...

11ˆ

22

11

0

1 1tt

s

t

k

D

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Return on Stocks Total return = Dividend yield +

Capital gains yield Dividend yield = D1/P0

Capital gains yield = (P1 – P0)/P0

If dividends are paid quarterly, the annual return is

(1 + quarterly return)4 – 1.0

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Zero Growth Model Dividends are not expected to grow

over time. Value of a zero growth stock:

The expected rate of return:sk

DP 0̂

0P

Dks

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Constant Growth Model Dividends are expected to grow at

some normal, or constant rate forever.

For a constant growth stock, Dt = D0(1 + g)t

If g is constant, then

gk

D

gk

gDP

ss

100

1ˆ

D D gtt 0 1

PVD

D

kt

tt

1

If g > k, P0 !P PVDt0

$

0.25

Years (t)0

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

We cannot use the model unless (1) g ks and (2) g is expected to be constant forever. Because g must be a long-term growth rate, it cannot be ks.

.PD

k gg

s0

1

requires ks

What happens if g > ks?

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Growth Rate of Dividends The growth rate, g, can be stated in terms

of the dividend payout ratio:

The greater ks, the higher the expected growth rate of dividends.

The greater the dividend payout ratio, the lower the expected growth rate of dividends.

1

11EPS

Dkg s

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Total Expected Return on a Constant Growth Stock Rearrange the constant growth

model to rate of return form:

.PD

k g

D

Pg

s0

1 1

0

to ks

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Nonconstant Growth Model Find the present value of the dividends during the

period of non-constant growth. Find the price of the stock at the end of the non-

constant growth period, at which point it has become a constant growth stock, and discount this price back to the present.

Add these two components to find the stock’s present value.

P0 = PV of DIV during constant growth period + PV of DIV after the constant growth period to

infinity

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Summary of Dividend Valuation Model The greater the current dividend, the

grater the value of a share of stock. The greater the expected growth in

dividends, the greater the value of a share of stock.

The greater the uncertainty of dividends, the greater the discount rate and the lower the value of a share of stock.

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Stock Market Equilibrium In equilibrium, stock prices are

stable. There is no general tendency for people to buy versus to sell.

The expected price, P, must equal the actual price, P. In other words, the fundamental value must be the same as the price.

^

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Stock Market Equilibrium If the expected rate of return is less than the

required rate of return, investors will desire to sell the stock.

If the expected rate of return is greater than the required rate of return, investors will try to purchase the stock.

Only at the equilibrium price, where the expected returnsexpected returns and the required returnsrequired returns are equal, will the stock be stable.

If the expected rate of return is less than the required rate of return, investors will desire to sell the stock.

If the expected rate of return is greater than the required rate of return, investors will try to purchase the stock.

Only at the equilibrium price, where the expected returnsexpected returns and the required returnsrequired returns are equal, will the stock be stable.

ks = D1/P0 + g = ks = kRF + (kM - kRF)b.^

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How is stock market equilibrium established? If ks = (D1/P0) + g > ks, then P0 is “too

low.” If the price is lower than the fundamental

value, then the stock is a “bargain.” Buy orders will exceed sell orders, the

price will be bid up, and D1/P0 falls until

D1/P0 + g = ks = ks.

^ ^

^

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Why do stock prices change?

ki = kRF + (kM - kRF)bi could change Inflation expectations Risk aversion Company risk

g could change

PD

k gi0

1

^

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Preferred Stock Hybrid security. Similar to bonds in that preferred

stockholders receive a fixed dividend which must be paid before dividends can be paid on common stock.

However, unlike bonds, preferred stock dividends can be omitted without fear of pushing the firm into bankruptcy.

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Valuation of Preferred Stock The value of preferred stock is found as:

The greater the preferred dividend, the greater the value of a share of preferred stock.

The greater the required rate of return, the lower the value of preferred stock.

p

pp k

DV