Yes, I agree that a stock dividend is equivalent to a stock split. But you argued that a stock dividend is also equivalent to a cash dividend. In that case a cash dividend is equivalent to a stock split, which is clearly not the case.
A stock split leaves shareholders with exactly the same share of the company they had before, it's just divided into smaller increments. It also leaves the company's balance sheet exactly the same.
What's actually equivalent to a cash dividend is a stock buyback. That gives each shareholder a larger portion of the company, and removes cash from the balance sheet.
Companies will often do stock buybacks in place of cash dividends. They never do stock splits in place of cash dividends, because splits have no effect on shareholders' wealth.
If a company awards new shares to one specific person, that's different. And you're right, it has the same effect on all the other shareholders as if the company paid that person cash. That person gets more and it comes out of everybody else's pocket. But when everybody gets new shares it's just a split.
> But you argued that a stock dividend is also equivalent to a cash dividend.
They are not equivalent, no. That's what I was trying to emphasize with the difference in choice available to the investor.
> They never do stock splits in place of cash dividends, because splits have no effect on shareholders' wealth.
Neither do cash dividends. You own $100 of a company worth $1000. The company issues a 5% dividend. The company is now worth $950. You now own $95 of the company and got a $5 dividend. Wealth unimpacted (disregarding tax and future changes in the company's valuation of course).
A stock split leaves shareholders with exactly the same share of the company they had before, it's just divided into smaller increments. It also leaves the company's balance sheet exactly the same.
What's actually equivalent to a cash dividend is a stock buyback. That gives each shareholder a larger portion of the company, and removes cash from the balance sheet.
Companies will often do stock buybacks in place of cash dividends. They never do stock splits in place of cash dividends, because splits have no effect on shareholders' wealth.
If a company awards new shares to one specific person, that's different. And you're right, it has the same effect on all the other shareholders as if the company paid that person cash. That person gets more and it comes out of everybody else's pocket. But when everybody gets new shares it's just a split.