Financial Markets and Institutions (2-downloads)

will pay dividends someday. Most of the time a firm institutes dividends as soon as

it has completed the rapid growth phase of its life cycle. The stock price increases

as the time approaches for the dividend stream to begin.

The generalized dividend valuation model requires that we compute the pres-

ent value of an infinite stream of dividends, a process that could be difficult, to

say the least. Therefore, simplified models have been developed to make the cal-

culations easier. One such model is the Gordon growth model that assumes con-

stant dividend growth.

The Gordon Growth Model

Many firms strive to increase their dividends at a constant rate each year. Equation 4

rewrites Equation 3 to reflect this constant growth in dividends.

(4)

where

D

0

= the most recent dividend paid

g = the expected constant growth rate in dividends

k

e

= the required return on an investment in equity

P

0

⫽

D

0

⫻ 11 ⫹ g2

1

11 ⫹ k

e

2

1

⫹

D

0

⫻ 11 ⫹ g2

2

11 ⫹ k

e

2

2

⫹ p ⫹

D

0

⫻ 11 ⫹ g2

q

11 ⫹ k

e

2

q

P

0

⫽ a

q

t

⫽1

D

t

11 ⫹ k

e

2

t

$50

>11.12

75

2 ⫽ $0.01

P

0

⫽

D

1

11 ⫹ k

e

2

1

⫹

D

2

11 ⫹ k

e

2

2

⫹ p ⫹

D

n

11 ⫹ k

e

2

n

⫹

P

n

11 ⫹ k

e

2

n

---

310

Part 5 Financial Markets

Equation 4 has been simplified using algebra to obtain Equation 5.

2

(5)

This model is useful for finding the value of stock, given a few assumptions:

1. Dividends are assumed to continue growing at a constant rate forever.

Actually, as long as they are expected to grow at a constant rate for an

extended period of time (even if not forever), the model should yield rea-

sonable results. This is because errors about distant cash flows become small

when discounted to the present.

2. The growth rate is assumed to be less than the required return on equity,

k

e

. Myron Gordon, in his development of the model, demonstrated that this

is a reasonable assumption. In theory, if the growth rate were faster than the

rate demanded by holders of the firm’s equity, in the long run the firm would

grow impossibly large.

P

0

⫽

D

0

⫻ 11 ⫹ g2

1k

e

⫺ g2

⫽

D

1

1k

e

⫺ g2

2

To generate Equation 5 from Equation 4, first multiply both sides of Equation 4 by

and subtract Equation 4 from the result. This yields

Assuming that k

e

is greater than g, the term on the far right will approach zero and can be dropped.

Thus, after factoring P

0

out of the left side,

Next, simplify by combining terms to

P

0

⫽

D

0

⫻ 11 ⫹ g2

k

e

⫺ g

⫽

D

1

k

e

⫺ g

P

0

⫻

11 ⫹ k

e

2 ⫺ 11 ⫹ g2

11 ⫹ g2

⫽ D

0

P

0

⫻ c

1

⫹ k

e

1

⫹ g

⫺ 1 d ⫽ D

0

P

0

⫻ 11 ⫹ k

e

2

11 ⫹ g2

⫺ P

0

⫽ D

0

⫺

D

0

⫻ 11 ⫹ g2

q

11 ⫹ k

e

2

q

11 ⫹ k

e

2>11 ⫹ g2

Find the current market price of Coca-Cola stock assuming dividends grow at a constant

rate of 10.95%, 

D

0

= $1.00, and the required return is 13%.

Solution

Coca-Cola stock should sell for $54.12 if the assumptions regarding the constant growth

rate and required return are correct.

P

0

⫽

$1.1095

0.0205

⫽ $54.12

P

0

⫽

$1.00

⫻ 11.10952

.13

⫺ .1095

P

0

⫽

D

0

⫻ 11 ⫹ g2

k

e

⫺ g

E X A M P L E   1 3 . 2 Stock Valuation: Gordon Growth Model

---

Chapter 13 The Stock Market

311

How the Market Sets Security Prices

Suppose you go to an auto auction. The cars are available for inspection before the

auction begins, and you find a little Mazda Miata that you like. You test-drive it in

the parking lot and notice that it makes a few strange noises, but you decide that you

would still like the car. You decide $5,000 would be a fair price that would allow you

to pay some repair bills should the noises turn out to be serious. You see that the auc-

tion is ready to begin, so you go in and wait for the Miata to enter.

The average industry PE ratio for restaurants similar to Applebee’s, a pub restaurant chain,

is 23. What is the current price of Applebee’s if earnings per share are projected to 

be $1.13?

Solution

Using Equation 6 and the data given we find:

The PE ratio approach is especially useful for valuing privately held firms and firms that

do not pay dividends. The weakness of the PE approach to valuation is that by using an

industry average PE ratio, firm-specific factors that might contribute to a long-term PE ratio

above or below the average are ignored in the analysis. A skilled analyst will adjust the

PE ratio up or down to reflect unique characteristics of a firm when estimating its stock price.

P

0

⫽ 23 ⫻ $1.13 ⫽ $26

P

0

⫽ P>E ⫻ E

E X A M P L E   1 3 . 3 Stock Valuation: PE Ratio Approach

Price Earnings Valuation Method

Theoretically, the best method of stock valuation is the dividend valuation approach.

Sometimes, however, it is difficult to apply. If a firm is not paying dividends or has a very

erratic growth rate, the results may not be satisfactory. Other approaches to stock val-

uation are sometimes applied. Among the more popular is the price/earnings multiple.

The price earnings ratio (PE) is a widely watched measure of how much the mar-

ket is willing to pay for $1 of earnings from a firm. A high PE has two interpretations.