Why Stock Prices Are What They Are
This is the second installment in a series that explains why stocks are priced as they are (or for those who prefer a more precise view, why supply and demand trends for a stock are such as to cause the two to converge at one point as opposed to any number of others). Part 1 introduced the penultimate explanation, to wit, that the price of a stock is the present value of future dividends. That content introduced the core theory that explains stock pricing in terms of the present value of dividends. Relating theory to observable reality can, however, be a challenge. We started by exploring two important realties relating to the assumed rate of return and to the stream of dividends. Now, we'll make a big jump and explore additional manners in which reality intersects with theory leading, ultimately, to EPS-based valuation.
Recapping the Core Theory
We concluded Part 1 with the Gordon Dividend Growth Model, a simple equation that looks like this:
- D is the Dividend
- k is required rate of annual return which can be derived with reference to the factors introduced in the Capital Asset Pricing Model; returns available on risk-free treasury securities, a premium (a bonus) offered to incentivize investors to assume equity market risk, and the degree of risk inherent in an individual company
- g is the expected dividend growth rate
For reasons mentioned in Part 1, you cannot simply plug in numbers and be good to go. A theory is not the same thing as an instruction manual. It's value is in the way it sensitizes us to the important determinants of stock pricing; dividends, market rates of return, company-specific risk, and growth.
Let's now stretch our consideration to the real world.
Reinvestment of profits
Perhaps the first frustration typically experienced with the Dividend Discount Model is that many companies do not pay dividends, and many more pay dividends that are so meager as to be almost equivalent to no dividends at all.
For better or worse, many companies today prefer to retain all or most of the profit they earn. In some instances, this can be motivated by a desire to preserve a cushion for a rainy day. That's certainly commendable. But realistically, the amount retained is usually far in excess of what's needed to enhance survival prospects. Typically, profits retained are reinvested for future growth. Either way, profits not given to shareholders as dividends are known as retained earnings.
Earnings retention and reinvestment are more desirable than dividend payments if the corporation can earn a higher return on the money than shareholders could get (by reinvesting dividends on their own). If all goes well, the reinvestment will enable the corporation to pay a higher dividend in the future than would otherwise have been the case.
Let's consider an example. Suppose the long-term infinite dividend growth rate we assume for mature companies is five percent and that the market required rate of return is seven percent. If Company A's initial dividend is $1.00, according the dividend discount model, the fair price for such a stock would be $50; based on $1.00 divided by .02, which is k (*.07) minus g (.05).
Suppose, instead, that Company A pays no dividends. But because it productively uses funds that it reinvests in the business, in year three it is able to introduce a dividend of $1.75, which will then grow five percent per year forever. Assuming k stays at seven percent, the Dividend Discount Model can be used to compute a three-years-from-now fair price of $87.50; based on $1.75 divided by .02, which is k (*.07) minus g (.05). But that's three years into the future. What's the fair price today? That's easy (in theory). We compute the present value of $87.50 three years hence assuming a five percent discount rate. It works out to $75.59 ($87.50 divided by 1.05 to the third power).
