Introduction to Corporate Finance

Ross et al.: Fundamentals

of Corporate Finance, Sixth

Edition, Alternate Edition

III. Valuation of Future

Cash Flows

(^276) 8. Stock Valuation © The McGraw−Hill
Companies, 2002
From Chapter 6 (Example 6.7), we know that the dividend on a share of preferred stock
has zero growth and thus is constant through time. For a zero growth share of common
stock, this implies that:
D 1 D 2 D 3 Dconstant
So, the value of the stock is:

P 0 ...

Because the dividend is always the same, the stock can be viewed as an ordinary perpe-

tuity with a cash flow equal to Devery period. The per-share value is thus given by:

P 0 D/R [8.2]

where Ris the required return.

For example, suppose the Paradise Prototyping Company has a policy of paying a

$10 per share dividend every year. If this policy is to be continued indefinitely, what is

the value of a share of stock if the required return is 20 percent? The stock in this case

amounts to an ordinary perpetuity, so the stock is worth $10/.20 $50 per share.

Constant Growth Suppose we know that the dividend for some company always

grows at a steady rate. Call this growth rate g. If we let D 0 be the dividend just paid, then

the next dividend, D 1 , is:

D 1 D 0 (1 g)

The dividend in two periods is:

D 2 D 1 (1 g)

[D 0 (1 g)] (1 g)

D 0 (1 g)^2

We could repeat this process to come up with the dividend at any point in the future. In

general, from our discussion of compound growth in Chapter 6, we know that the divi-

dend tperiods into the future, Dt, is given by:

DtD 0 (1 g)t

An asset with cash flows that grow at a constant rate forever is called a growing perpe-

tuity.As we will see momentarily, there is a simple expression for determining the value

of such an asset.

The assumption of steady dividend growth might strike you as peculiar. Why would

the dividend grow at a constant rate? The reason is that, for many companies, steady

growth in dividends is an explicit goal. For example, in 2000, Procter and Gamble, the

Cincinnati-based maker of personal care and household products, increased its dividend

by 12 percent to $1.28 per share; this increase was notable because it was the 44th in a

row. The subject of dividend growth falls under the general heading of dividend policy,

so we will defer further discussion of it to a later chapter.

D

(1 R)^5

D

(1 R)^4

D

(1 R)^3

D

(1 R)^2

D

(1 R)^1

246 PART THREE Valuation of Future Cash Flows

Students who are
interested in equity
valuation techniques
should check out the
“Investment Models”
section within the
“Business” category at
http://www.yahoo.com.

Dividend Growth

The Hedless Corporation has just paid a dividend of $3 per share. The dividend of this com-

pany grows at a steady rate of 8 percent per year. Based on this information, what will the div-

idend be in five years?

EXAMPLE 8.2