"So if Apple doesn't pay out dividends, what's to justify their high share price?"
The high share price does. It makes up for the lack of dividends. Depending on the market sector a company is in will determine what if any dividends they pay.
The short version, essentially Apple (AAPL) makes stuff so they need cash on hand to pay for inventory. The larger the pile of cash, the easier it is to rapidly increase their inventory. The high price reflects this value position. If they pay dividends, they are less fluid, slower to react and if pinched they need to sell stocks to raise cash. More stock means a lower stock price for the same corporate value.
Compare this to a service company like Teekay Tankers (TNK) who only need money to purchase capital goods and pay salaries. The current earnings per share are 1.28 and their dividends are 1.03 for a current annual yield of 8.5%. They recently purchased new tankers and sold stock to cover the purchase because they aren't sitting on a pile of cash. The stock price took a hit but seems to be slowly recovering a bit.
Now then, 8.5% puts a doubling time at nearly 8.5 years where AAPL stock has a doubling time of either 1 or 3 years depending on market volatility. Also the 8.5% dividend yield of TNK isn't fixed either and when short of cash they can and will withhold the dividend. The downside to not having a dividend is you need to sell the stock to realize the profit. Note that BRK-A doesn't pay dividends either but at ~$120K/share does it really matter?
In the interest of full disclosure, I have financial stakes in both AAPL and TNK and really wish I had a stake in BRK-A but at ~$120K/share... Boy, so much for the short version.