328 PART 2 Important Financial Concepts
TABLE 7.3 Calculation of Present Value of Warren Industries
Dividends (2004–2006)Present value
Dt of dividends
End of D 0 D 2003 FVIF10%,t [(1)(2)] PVIF15%,t [(3)(4)]
t year (1) (2) (3) (4) (5)1 2004 $1.50 1.100 $1.65 0.870 $1.44
2 2005 1.50 1.210 1.82 0.756 1.383 2006 1.50 1.331 2.00 0.658 (^1) . (^3) (^2)
Sum of present value of dividends
3
t 1
$
4
.
1
4
D^0 (1g^1 )t
(1ks)t
Step 4 Add the present value components found in Steps 2 and 3 to find the
value of the stock, P 0 , given in Equation 7.6:
P 0
N
t 1
(^) (7.6)
Present value of Present value of
dividends price of stock
during initial at end of initial
growth period growth period
The following example illustrates the application of these steps to a variable-
growth 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, g 1 , 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, g 2 ,for
the foreseeable future. The firm’s required return, ks,is 15%. To estimate the cur-
rent (end-of-2003) value of Warren’s common stock, P 0 P 2003 , 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 divi-
dends 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 (N2006)
can be found by first calculating DN 1 D 2007 :
D 2007 D 2006
(1 0.05) $2.00 (1.05) $2.10
DN 1
ksg 2
1
(1ks)N
D 0
(1g 1 )t
(1ks)t