In CFA level 1 Reading 38, it says
Stock dividends are a non-cash form of dividends. With a stock dividend (also known as a bonus issue of shares), the company distributes additional shares (typically 2–10 percent of the shares then outstanding) of its common stock to shareholders instead of cash. Although the shareholder’s total cost basis remains the same, the cost per share held is reduced. For example, if a shareholder owns 100 shares with a purchase price of $10 per share, the total cost basis would be $1,000. After a 5 percent stock dividend, the shareholder would own 105 shares of stock at a total cost of $1,000. However, the cost per share would decline to $9.52 ($1,000/105).
Superficially, the stock dividend might seem an improvement on the cash dividend from both the shareholders’ and the company’s point of view. Each shareholder ends up with more shares, which did not have to be paid for, and the company did not have to spend any actual money issuing a dividend. Furthermore, stock dividends are generally not taxable to shareholders because a stock dividend merely divides the “pie” (the market value of shareholders’ equity) into smaller pieces. The stock dividend, however, does not affect the shareholder’s proportionate ownership in the company (because other shareholders receive the same proportionate increase in shares); nor does it change the value of each shareholder’s ownership position (because the increase in the number of shares held is accompanied by an offsetting decrease in earnings per share, and other measures of value per share, resulting from the greater number of shares outstanding).
When the company pays the same dividend rate on the new shares as it did on the old shares, a shareholder’s dividend income increases, but the company could have accomplished the same result by increasing the cash dividend.
In the last paragraph, did CFA meant to say "same dividend amount" and not "same dividend rate"? Because if it was at the same dividend rate, then the dividend amount would reduce proportionally since the new share price after stock dividend would be lower than before the stock dividend.
For example, using the example from paragraph one, the original share price was $10, say I own 100 shares, and if the payout ratio is say 5%, I get $50 of dividend.
After stock dividend, the share price is now $9.52, and I have 105 shares, at 5% dividend rate I would still get $5.
There is no increase in dividend since the "pie" slice is the same for everyone after stock dividend.