The dividend expected in Year 2 grows to $1.242(1.08)$1.341, but the present
value of this dividend falls to $1.043. Continuing, D 3 $1.449 and PV(D 3 )
$0.993, and so on. Thus, the expected dividends are growing, but the present value
of each successive dividend is declining, because the dividend growth rate (8%) is
less than the rate used for discounting the dividends to the present (13.4%).
If we summed the present values of each future dividend, this summation would
be the value of the stock,Pˆ 0. When g is a constant, this summation is equal to
D 1 /(rsg), as shown in Equation 5-2. Therefore, if we extended the lower step func-
tion curve in Figure 5-1 on out to infinity and added up the present values of each
future dividend, the summation would be identical to the value given by Equation
5-2, $23.00.
Although Equation 5-2 assumes that dividends grow to infinity, most of the value is
based on dividends during a relatively short time period. In our example, 70 percent of
the value is attributed to the first 25 years, 91 percent to the first 50 years, and 99.4 per-
cent to the first 100 years. So, companies don’t have to live forever for the Gordon
growth model to be used.
Dividend and Earnings Growth
Growth in dividends occurs primarily as a result of growth in earnings per share (EPS).
Earnings growth, in turn, results from a number of factors, including (1) inflation, (2)
the amount of earnings the company retains and reinvests, and (3) the rate of return the
company earns on its equity (ROE). Regarding inflation, if output (in units) is stable,
but both sales prices and input costs rise at the inflation rate, then EPS will also grow at
198 CHAPTER 5 Stocks and Their Valuation
Dividend
($)
1.15
PV D = 1.10
0 5 10 15 20
PV of Each Dividend =D (1 + g)
(1 + r )
= Area under PV Curve
= $23.00
Dollar Amount of Each Dividend
= D (1 + g)
t
t
1
0
0 t
s
Years
P =∑PV Dt
8
t = 1
ˆ 0
FIGURE 5-1 Present Values of Dividends of a Constant Growth Stock
where D 0 $1.15, g 8%, rs13.4%
194 Stocks and Their Valuation
