That's a really good question. First, to clarify, capital appreciation refers to the increase of the price of a stock. Investors buy stocks for a different reasons. The primary reason is to receive a return on that investment. Return is an all-encompassing word. Investors earn a return if the stock price goes up or if the company pays dividends.
There are many companies that don't distribute dividends, either because (1) they may be in poor financial health or because (2) they prefer to reinvest that money in assets that will help generate more return. Even without the dividends, people do buy these companies. In the second case, a company's earnings are expected to rapidly increase, thereby generating more value and lifting the price of the stock. (These are called growth stocks.)
Analysts have developed a gazillion ways to determine a stock's value and potential return. Like many other things, the value of stock is in the eye of the beholder. You could be willing to purchase a share of Google for $2, while I may only be willing to spend $1 for a share. A market for Google develops when millions of people apply their own valuations of Google into buying and selling that stock. It's the market mechanism gives the a stock value (price).
It's likely that this answer won't satisfy you, because I'm essentially telling you that a market capitalization is in the eye of the beholder. Questioning a stock's value is an existential question that applies to everything that we buy, hold, or sell.
It's likely that this answer won't satisfy you, but it shouldn't. Nobody should ever feel that they "know" the value of a stock, that's preposterous.