Some publicly traded firms do stock splits. Many stock holders as well as some analysts believe that a stock split would definitely benefit current shareholders by raising the firms stock price. For example, Apple, Inc. (AAPL) announced a 4 to 1 stock split in August 2020, following its 7-for-1 stock split in 2013. You read in chapter 14 that, in theory, a 4:1 stock split would increase the number of outstanding shares four fold and cut down the post-split stock price to 1/4 of pre-split price, thus leaving the wealth of Apple's shareholders unchanged. Unlike Apple, many other successful firms such as Amazon, Google, and Berkshire Hathaway with per share stock prices much higher than Apple's have not done stock splits. Also, many brokerage firms have recently cut down the stock trading commission to zero and allowed investors to buy fractional shares of firms (i.e., less than one share). So you are puzzled why some shareholders, traders, and analysts adamantly believe that stock splits benefit shareholders. Please explain whether or not stock splits in general would benefit a firm's current shareholders with at least a 5-year investment (holding) horizon. You would want to use your understanding of chapter 14 stock split material, especially the signaling aspects of stock splits, optimal stock price range theory, and past empirical evidence in your explanation.