Valuation of Stocks:
In practice, the value of a share is determined in the market through the
auction process, as exemplified by trading of shares on Wall Street.
In theory, the value of a share of stock (or the price per share, P) is the
present value of the cash flows related to owning that stock. Myron Gordon
developed a model that assumes that dividends are the cash flow that the stock
holder is entitled to, and that dividends will
grow at a constant rate (g) forever. When discounted at the "required rate
of return to the equity investor" (Ke), then the present value (P) of the
endless stream of constantly growing dividends, when discounted at Ke, equals D1/(Ke-g),
where D1 is the expected dividends for the following year.
There are four variations of Gordon's model - two for common stocks and two for preferred stocks. Preferred stocks differ from Common (in this context) in that preferred dividends are fixed. And the two variations (for each of the two types of stocks) differ only in the variable that is being solved for - in one case, the unknown variable is P (the theoretical price per share), and in the other K, either Ke or Kpr, the expected return to the stockholder.
1. Common: P = D1/(Ke-g)
2. "
Ke = (D1/P) + g
3. Preferred: P = D/Kpr
4. "
Kpr = D/P
Caveats:
* All variable are on an annualized basis.
* With Common, D1 is generally not a given. It is estimated by
taking the actual dividends over the past 4 quarters (Do), and increasing them
by the estimated growth rate. That is, D1 = Do (1 + g).
* With Preferred, because dividends are fixed, there is no growth (g) in
dividends, so that term is missing from the models.
* These models are valid in their mathematics, but they are forward looking
models as opposed to "historical", or backward looking models. Consequently some
of the variables are only best guess estimates, and the resulting prices or
returns cannot be guaranteed. Some analysts factor in that notion that
dividends follow earnings, and that earnings growth determines dividend growth.
Other analysts recognize that earnings are not real cash flows, and that real
cash flows are more relevant to value than earnings. Consequently, they
modify this model by regarding expected cash flows rather than expected
dividends.