Fundamentals of Financial Management (Concise 6th Edition)

Chapter 9 Stocks and Their Valuation 281

equals 10.0%, so its expected earnings for the coming year are (0.10)$1,000,000 "
$100,000. You could take out the entire $100,000 of earnings in dividends, or you
could reinvest some or all of the $100,000 in the business. If you pay out all the
earnings, you will have $100,000 of dividend income this year, but dividends will
not grow because assets and therefore earnings will not grow.
However, suppose you decide to have the! rm pay out 40% and retain 60%.
Now your dividend income in Year 1 will be $40,000; but assets will rise by $60,000,
and earnings and dividends will likewise increase:

Next year’s earnings! Prior earnings " ROE(Retained earnings)

! $100,000 " 0.1($60,000)

! $106,000

Next year’s dividends! 0.4($106,000)! $42,400

Moreover, your dividend income will continue to grow by 6% per year thereafter:

Growth rate! (1 $ Payout ratio)ROE 9-4

= (1 – 0.4)10.0%

= 0.6(10.0%) = 6.0%

This demonstrates that in the long run, growth in dividends depends primarily on
the! rm’s payout ratio and its ROE.

Present Values of Dividends of a Constant Growth Stock where

F I G U R E 9! 2 D 0 " $1.15, g " 8.3%, rs " 13.7%

Dividend

($)

1.15

PV D 1 = 1.10

0 5 10 15 20

PV of Each Dividend =D^0 (1 + g)

t

(1 + rs)t

= Area under PV Curve

= $23.06

Dollar Amount of Each Dividend

= D 0 (1 + g)t

Years

P 0 = ΣPV Dt

8

t = 1

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