Equity Valuation: Models from Leading Investment Banks

43

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 CF_t to the stockholder discounted at the risk-free interest rate i_f.

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

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 ...