Valuation in Theory: The Valuation of a Single Asset
43.1 CERTAIN CASH FLOWS
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 D1 at the end of the period. The cash flows to the stock holder in period 1 are the dividend payments D1 and the proceeds P1 from selling the stock at the end of period 1.1 In the case of certainty, the fair value P0 of the security today (t = 0) equals the sum of the cash flows CFt to the stockholder discounted at the risk-free interest rate if.
As the present value PV of the stock price P1 at the end of period 1 equals the discounted dividend paid in year 2, D2, and the discounted value of the price in period 2, P2, we can write:2
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 ...