8.2 Section 2:
Review of the Dividend Model
Intrinsic Value equals the present value
of future dividends discounted at the stock’s cost
of equity capital.
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Recall
the basic equation of stock valuation:
V0 = (d1 + V1)/(1 + ke) 1)
Here, V0 is the value of the stock, d1 is
next period’s (cash)
dividend, V1 is the value in one period and ke
is the discount rate, which a model like CAPM equates to the
stock’s cost of equity capital.
The equation says that the value must equal the present
value of next period’s dividend plus next period’s value,
discounted by the cost of equity capital.
We can
similarly write V1 in terms of d2 and V2:
V1
= (d2 + V2)/(1 + ke)
And
similarly for V2, V3¸and so on.
If we
substitute for V1 in equation 1), we get
V0
= d1/(1+ke) + (d2+V2)/(1+ke)2
By
substituting for V2, and then for V3, and
so on, we get the fundamental relationship that value of a stock
equals the present value of future dividends discounted at the
stock’s cost of equity capital.
This is the definition of the intrinsic value of a stock:
Intrinsic
value =V0 = d1/(1+ke) + d2/(1+ke)2
+ d3/(1+ke)3 + ….
2)