D C F M Dpu E 2 - 1 D N - 0 4 - 0 3 5 - 4 2: Iscounted ASH LOW Odel Xhibit Ocket O
D C F M Dpu E 2 - 1 D N - 0 4 - 0 3 5 - 4 2: Iscounted ASH LOW Odel Xhibit Ocket O
D C F M Dpu E 2 - 1 D N - 0 4 - 0 3 5 - 4 2: Iscounted ASH LOW Odel Xhibit Ocket O
P0 =
D 1 + D 2 + D 3 + . . .+ D
( 1 + k ) ( 1 + k )2 ( 1 + k ) 3
( 1 + k )
where P0 is the stocks current price, D i is the expected dividend to be paid in the future period i,
and k is the discount rate. The discount rate k is also the investors opportunity cost of investing
in the stock and, thus, is the investors required rate of return on equity. The key to estimating the
required return is to solve equation (1), under various assumptions, for k. To solve for k, define Pn
as,
Pn =
D 1 + D 2 + D 3 + . . .+ D n
( 1 + k ) ( 1 + k ) 2 ( 1 + k )3
( 1 + k )n
We note that equation (1) and equation (2) are equivalent as n approaches infinity. Equation (2)
will serve as the basis for the following derivations.
CONSTANT GROWTH DCF MODEL
If dividends grow at a constant rate, g, then equation (2) can be rewritten as,
Pn =
n -1
D 1 + ( 1 + g ) D 1 + ( 1 + g ) D 1 + . . .+ ( 1 + g ) D 1
( 1 + k ) ( 1 + k )2
( 1 + k )3
( 1 + k )n
P n +1 =
n -1
( 1+ g ) D1 ( 1+ g ) D1
( 1+ g ) D1 ( 1+ g ) D 1
+
+ . . .+
+
2
3
( 1+ k )
( 1+ k )
( 1 + k )n
( 1 + k ) n +1
Thus,
P n - P n +1 =
n
( k-g )
D1 - ( 1+ g ) D1
=
Pn
( 1+ k )
( 1 + k ) ( 1 + k ) n +1