The starting point of the analysis is the premise that the value of a security can be derived from the cash flows which an investor obtains from owning it. Let us assume that an investor holds a stock for one period which pays a dividend *D*_{1} at the end of the period. The cash flows to the stock holder in period 1 are the dividend payments *D*_{1} and the proceeds *P*_{1} from selling the stock at the end of period 1.^{1} In the case of certainty, the fair value *P*_{0} of the security today (*t* = 0) equals the sum of the cash flows *CF*_{t} to the stockholder discounted at the risk-free interest rate *i _{f}*.

As the present value *PV* of the stock price *P*_{1} at the end of period 1 equals the discounted dividend paid in year 2, *D*_{2}, and the discounted value of the price in period 2, *P*_{2}, we can write:^{2}

and thus

Using the same technique for *t* = 1,…, ∞ we can derive a general DCF formula under certainty. As the present value of the stock price approaches zero in infinity (*T* → ∞), we can stop discounting future prices at a period *T* in the distant future:^{3}

The general DCF formula under certainty states that the value of any security is the present ...

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