Mathematics of the Financial Markets: Financial Instruments and Derivatives Modelling, Valuation and Risk Issues

4

Equities and stock indexes

4.1 STOCKS VALUATION

The fair (theoretical) value S of a stock can be computed in different ways, none of them being fully satisfactory, hence their results are often combined to get a final result; for example, in a prospectus for an initial public offering (IPO).

4.1.1 Discounted cash flows (DCF) method

This first method uses the same rationale as for a bond valuation: the fair price is the sum of discounted future cash flows that will be paid by the stock. But here we face a succession of n unknown future dividends instead of a fixed coupon, no final maturity, and of course no repayment of a principal. Calling di the dividend paid in year i, and zi the corresponding discounting rate, the result is equivalent to the one presented for a bond price (cf. Chapter 3, Eq. 3.1):

with two issues:

• n is an a priori undetermined number of years: we cannot know how long the corporation will survive (theoretically, n goes up to ∞). Fortunately, the longer the maturity is discounted, the lower the discounted amount. So above, say, 50 years, further cash flows can be neglected in present value.
• The future dividends di are not known in advance.

The calculation is therefore valid only if referring to a realistic assumption about the future dividends.

Example. Let us consider a stock distributing a constant dividend of $5, with a constant discount rate of 5%. The ...