Principles of Managerial Finance

326 PART 2 Important Financial Concepts

6.96

1.00 PV

FV

CPT

I

N

1.40

5

Solution

Input Function

Gordon model
A common name for the
constant-growth modelthat is
widely cited in dividend
valuation.

If we simplify Equation 7.4, it can be rewritten as^6

P 0  (7.5)

The constant-growth model in Equation 7.5 is commonly called the Gordon

model.An example will show how it works.

EXAMPLE Lamar Company, a small cosmetics company, from 1998 through 2003 paid the

following per-share dividends:

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 com-

pound annual growth rate of Lamar Company dividends equals 7%.^7 The com-

Year Dividend per share

2003 $1.40

2002 1.29

2001 1.20

2000 1.12

1999 1.05

1998 1.00

D 1



ksg

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 (1ks)/(1g) and subtract Equation 7.4 from the resulting expres-
   sion. This yields
   P 0 D 0  (1)
   Because ksis assumed to be greater than g, the second term on the right side of Equation 1 should be zero. Thus

P (^0)   (^1) D 0 (2)
Equation 2 is simplified as follows:
P (^0) D 0 (3)
P 0 (ksg)D 0
(1g)(4)
P 0  (5)
Equation 5 equals Equation 7.5.

7. The technique involves solving the following equation for g:
   D 2003 D 1998
   (1g)^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 (D 1998 $1.00)
   by the most recent dividend (D 2003 $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 thePVIFfor 5 years, we find that the factor closest to 0.714 occurs at
   7% (0.713). Therefore, the growth rate of the dividends, rounded to the nearest whole percent, is 7%.
   Alternatively, a financial calculator can be used. (Note:Most calculators require eitherthe PVor FVvalue to
   be input as a negative number to calculate an unknown interest or growth rate. That approach is used here.) Using
   the inputs shown at the left, you should find the growth rate to be 6.96%, which we round to 7%.

^1

(1g)^5

D^1998

D 2003

D^1

ksg

(1ks)(1g)

1 g

^1 ks

1 g

D^0 (1g)∞

(1ks)∞

P^0 (1ks)

1 g