Final answer:
An increase in prepaid expenses will not cause a change in the stockholders' equity of a business because it's an intra-asset exchange that does not affect equity.
Step-by-step explanation:
The option that will not cause a change in the stockholders' equity of a business is A) An increase in prepaid expenses. When a company increases its prepaid expenses, this is merely an exchange within the assets on the balance sheet—specifically between cash (or equivalents) and prepaid expenses, and thus does not affect the stockholders' equity. In contrast, B) an increase in retained earnings, C) the sale of common stock, and D) the declaration and payment of dividends all directly affect the stockholders' equity. Retained earnings increase with profits and decrease with losses and dividend payments. Selling common stock increases stockholders' equity by the amount raised, whereas paying dividends decreases retained earnings, which is a component of stockholders' equity.