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**Unformatted text preview: **dividends
during initial
growth period (1 1
ks )N DN 1
ks g2 (7.6) Present value of
price of stock
at end of initial
growth period The following example illustrates the application of these steps to a variablegrowth situation with only one change in growth rate.
EXAMPLE The most recent (2003) annual dividend payment of Warren Industries, a rapidly
growing boat manufacturer, was $1.50 per share. The firm’s financial manager
expects that these dividends will increase at a 10% annual rate, g1, over the next
3 years (2004, 2005, and 2006) because the introduction of a hot new boat. At
the end of the 3 years (the end of 2006), the firm’s mature product line is
expected to result in a slowing of the dividend growth rate to 5% per year, g2, for
the foreseeable future. The firm’s required return, ks, is 15%. To estimate the current (end-of-2003) value of Warren’s common stock, P0 P2003, the four-step
procedure must be applied to these data.
Step 1 The value of the cash dividends in each of the next 3 years is calculated
in columns 1, 2, and 3 of Table 7.3. The 2004, 2005, and 2006 dividends are $1.65, $1.82, and $2.00, respectively.
Step 2 The present value of the three dividends expected during the 2004–2006
initial growth period is calculated in columns 3, 4, and 5 of Table 7.3.
The sum of the present values of the three dividends is $4.14.
Step 3 The value of the stock at the end of the initial growth period (N
can be found by first calculating DN 1 D2007:
D2007 D2006 (1 0.05) $2.00 (1.05) 2006) $2.10 T A B L E 7 . 3 Calculation of Present Value of Warren Industries
Dividends (2004–2006)
Dt
t End of
year 1 2004 2 2005 3 2006 D0 D2003
(1) PVIF15%, t
(4) Present value
of dividends
[(3) (4)]
(5) FVIF10%, t
(2) [(1) (2)]
(3) $1.50 1.100 $1.65 0.870 $1.44 1.50 1.210 1.82 0.756 1.38 1.50 1.331 2.00 0.658 1.32 3 Sum of present value of dividends
t1 D0 (1 g1)t
(1 ks )t $4.14 CHAPTER 7 Stock Valuation 329 By using D2007 $2.10, a 15% required return, and a 5% dividend
growth rate, we can calculate the value of the stock at the end of 2006 as
follows:
P2006 D2007
ks g2 $2.10
0.15 0.05 $2.10
0.10 $21.00 Finally, in Step 3, the share value of $21 at the end of 2006 must be converted into a present (end-of-2003) value. Using the 15% required return,
we get
PVIFks ,N PN PVIF15%,3 P2006 0.658 $21.00 $13.82 Step 4 Adding the present value of the initial dividend stream (found in Step 2)
to the present value of the stock at the end of the initial growth period
(found in Step 3) as specified in Equation 7.6, we get the current (end-of2003) value of Warren Industries stock:
P2003 $4.14 $13.82 $17.96 per share The stock is currently worth $17.96 per share. The calculation of this
value is depicted graphically on the following time line.
Time line for finding
Warren Industries
current (end-of-2003)
value with variable
growth 2003 2004 D2004 = $1.65
Present Value
of Dividends
During Initial
Period = $4.14
Present Value
of Stock Price
at End of
Initial Period End of Ye...

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