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**Unformatted text preview: **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 either the PV or FV value 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%. CHAPTER 7 Stock Valuation 327 pany estimates that its dividend in 2004, D1, 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
P0 $1.50
0.08 $1.50
0.15 0.07 $18.75 per share Assuming that the values of D1, ks, and g are accurately estimated, Lamar Company’s stock value is $18.75 per share. Variable-Growth Model variable-growth model
A dividend valuation approach
that allows for a change in the
dividend growth rate. 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 single shift in growth rates occurs at the end of year N, and we will use g1 to represent the initial growth rate and g2 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 of each year, Dt, during the
initial growth period, years 1 through N. This step may require adjusting
the most recent dividend, D0, using the initial growth rate, g1, to calculate
the dividend amount for each year. Therefore, for the first N years,
Dt D0 (1 g1)t D0 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 D0 (1 g1)t
(1 ks )t N t 1 Dt
(1 ks )t N (Dt
t 1 PVIFks ,t) Step 3 Find the value of the stock at the end of the initial growth period,
PN (DN 1)/(ks g2), which is the present value of all dividends expected from year N 1 to infinity, assuming a constant dividend growth
rate, g2. This value is found by applying the constant-growth model
(Equation 7.5) to the dividends expected from year N 1 to infinity. The
present value of PN would represent the value today of all dividends that
are expected to be received from year N 1 to infinity. This value can be
represented by
(1 1
ks )N DN 1
ks g2 PVIFks ,N PN 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. 328 PART 2 Important Financial Concepts Step 4 Add the present value components found in Steps 2 and 3 to find the
value of the stock, P0, given in Equation 7.6:
D0 (1 g1)t
(1 ks )t
1 N P0
t Present value of...

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