Principles of Managerial Finance

CHAPTER 7 Stock Valuation 327

variable-growth model
A dividend valuation approach
that allows for a change in the
dividend growth rate.

8. More than one change in the growth rate can be incorporated into the model, but to simplify the discussion we will
   consider only a single growth-rate change. The number of variable-growth valuation models is technically unlimited,
   but concern over all possible shifts in growth is unlikely to yield much more accuracy than a simpler model.

pany estimates that its dividend in 2004, D 1 , will equal $1.50. The required

return, ks, is assumed to be 15%. By substituting these values into Equation 7.5,

we find the value of the stock to be

P 0 $



1



8



.



7



5



per share

Assuming that the values of D 1 , ks, and gare accurately estimated, Lamar Com-

pany’s stock value is $18.75 per share.

Variable-Growth Model

The zero- and constant-growth common stock models do not allow for any shift

in expected growth rates. Because future growth rates might shift up or down

because of changing expectations, it is useful to consider a variable-growth model

that allows for a change in the dividend growth rate.^8 We will assume that a sin-

gle shift in growth rates occurs at the end of year N,and we will use g 1 to repre-

sent the initial growth rate and g 2 for the growth rate after the shift. To determine

the value of a share of stock in the case of variable growth, we use a four-step

procedure.

Step 1 Find the value of the cash dividends at the end ofeach year, Dt, during the

initial growth period, years 1 throughN.This step may require adjusting

the most recent dividend,D 0 , using the initial growth rate,g 1 , to calculate

the dividend amount for each year. Therefore, for the firstNyears,

DtD 0

 (1g 1 )tD 0

 FVIFg 1 ,t

Step 2 Find the present value of the dividends expected during the initial growth

period. Using the notation presented earlier, we can give this value as



N

t 1



N

t 1



N

t 1

(Dt PVIFks,t)

Step 3 Find the value of the stock at the end of the initial growth period,

PN(DN 1 )/(ksg 2 ), which is the present value of all dividends ex-

pected from year N1 to infinity, assuming a constant dividend growth

rate, g 2. This value is found by applying the constant-growth model

(Equation 7.5) to the dividends expected from year N1 to infinity. The

present value of PNwould represent the value todayof all dividends that

are expected to be received from year N1 to infinity. This value can be

represented by

PVIFks,N PN

DN 1



ksg 2

^1

(1ks)N

Dt

(1ks)t

D^0 (1g^1 )t

(1ks)t

$1.50



0.08

$1.50



0.150.07