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**Unformatted text preview: **t-growth model,
assumes that dividends will grow at a constant rate, but a rate that is less than the
required return. (The assumption that the constant rate of growth, g, is less than
the required return, ks, is a necessary mathematical condition for deriving this
model.5) By letting D0 represent the most recent dividend, we can rewrite Equation 7.2 as follows:
P0 D0 (1 g)1
(1 ks )1 D0 (1 g)2
(1 ks )2 ... D0 (1 g)∞
(1 ks )∞ (7.4) 5. Another assumption of the constant-growth model as presented is that earnings and dividends grow at the same
rate. This assumption is true only in cases in which a firm pays out a fixed percentage of its earnings each year (has
a fixed payout ratio). In the case of a declining industry, a negative growth rate ( g < 0%) might exist. In such a case,
the constant-growth model, as well as the variable-growth model presented in the next section, remains fully applicable to the valuation process. 326 PART 2 Important Financial Concepts If we simplify Equation 7.4, it can be rewritten as6
Gordon model
A common name for the
constant-growth model that is
widely cited in dividend
valuation. EXAMPLE D1
ks g P0 (7.5) The constant-growth model in Equation 7.5 is commonly called the Gordon
model. An example will show how it works.
Lamar Company, a small cosmetics company, from 1998 through 2003 paid the
following per-share dividends:
Year Dividend per share 2003 $1.40 2002 1.29 2001 1.20 2000 1.12 1999 1.05 1998 1.00 We assume that the historical compound annual growth rate of dividends is an
accurate estimate of the future constant annual rate of dividend growth, g. Using
Appendix Table A–2 or a financial calculator, we find that the historical compound annual growth rate of Lamar Company dividends equals 7%.7 The com- 6. For the interested reader, the calculations necessary to derive Equation 7.5 from Equation 7.4 follow. The first
step is to multiply each side of Equation 7.4 by (1 ks)/(1 g) and subtract Equation 7.4 from the resulting expression. This yields
P0 (1 ks )
1g D0 (1 g)∞
(1 ks)∞ D0 P0 (1) Because ks is assumed to be greater than g, the second term on the right side of Equation 1 should be zero. Thus
1 ks
1g P0 1 D0 (2) Equation 2 is simplified as follows:
P0 (1 ks ) (1
1g
P0 g) (ks D0 g)
P0 D0 (3)
(1 D1
ks g g) (4)
(5) Equation 5 equals Equation 7.5.
7. The technique involves solving the following equation for g:
D2003
Input
1.00 Function
PV 1.40 FV 5 N
CPT
I Solution
6.96 D1998
D2003 D1998
1
(1 g)5 (1 g)5
PVIFg,5 To do so, we can use financial tables or a financial calculator.
Two basic steps can be followed using the present value table. First, dividing the earliest dividend (D1998 $1.00)
by the most recent dividend (D2003 $1.40) yields a factor for the present value of one dollar, PVIF, of 0.714 ($1.00
$1.40). Although six dividends are shown, they reflect only 5 years of growth. (The number of years of growth can
also be found by subtracting the earliest year from the most recent year—that is, 2003 1998 5 years of growth.)
By looking across the Appendix Table A–2 at the PVIF for 5 years, we find that the factor closest to...

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