Problem: Two-stage dividend growth
A stock currently pays a dividend of $2 for the year. Expected
dividend growth is 20% for the next three years and then growth
is expected to revert to 7% thereafter for an indefinite amount of
time. The appropriate required rate of return is 15%. What is this
stock’s intrinsic value?
Solution:
P0 =
D1
D2
D3
P3
+
+
+
(1 + r)1 (1 + r)2 (1 + r)3 (1 + r)3
where P3 =
D0 (1 + g0 ) D0 (1 + g1)2 D0 (1 + g1)3
P0 =
+
+
+
3
2
1
(1 + r)
(1 + r)
(1 + r)
P0 =
$2.40
$2.88
$3.456
P0 = $2.086957 + 2.177694 + $2.272376 +
D0 (1 + g1)3 (1 + g2 )
(r − g2 )
(1 + r)3
$3.69792
+
+
+
1
2
3
(1 + 0.15) (1 + 0.15)
(1 + 0.15)
( 0.15 − 0.07 )
(1 + 0.15)3
$46.224
1.520875
P0 = $2.086957 + 2.177694 + $2.272376 + $30.39303
P0 = $36.930057
D4
(r − g2 )