Principles of Managerial Finance

478 PART 4 Long-Term Financial Decisions

model,also known as theGordon model.The key expression derived for this

model was presented as Equation 7.5 and is restated here:

P 0  (11.4)

where

P 0 value of common stock

D 1 per-share dividend expectedat the end of year 1

ksrequired return on common stock

gconstant rate of growth in dividends

Solving Equation 11.4 for ksresults in the following expression for the cost

of common stock equity:

ksg (11.5)

Equation 11.5 indicates that the cost of common stock equity can be found by

dividing the dividend expected at the end of year 1 by the current price of the

stock and adding the expected growth rate. Because common stock dividends are

paid from after-taxincome, no tax adjustment is required.

EXAMPLE Duchess Corporation wishes to determine its cost of common stock equity, ks.

The market price, P 0 , of its common stock is $50 per share. The firm expects to

pay a dividend, D 1 , of $4 at the end of the coming year, 2004. The dividends paid

on the outstanding stock over the past 6 years (1998–2003) were as follows:

Using the table for the present value interest factors, PVIF(Table A–2), or a

financial calculator in conjunction with the technique described for finding

growth rates in Chapter 4, we can calculate the annual growth rate of dividends,

g. It turns out to be approximately 5% (more precisely, it is 5.05%). Substituting

D 1 $4, P 0 $50, and g5% into Equation 11.5 yields the cost of common

stock equity:

ks 0.050.080.050.130, or 1



3



.



0



%

The 13.0% cost of common stock equity represents the return required by exist-

ingshareholders on their investment. If the actual return is less than that, share-

holders are likely to begin selling their stock.

$4



$50

Year Dividend

2003 $3.80

2002 3.62

2001 3.47

2000 3.33

1999 3.12

1998 2.97

D 1



P 0

D 1



ksg