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.

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)