Final answer:
Nontaxable stock dividends result in no change to the total basis of the old and new stock, but the basis per share decreases.
Step-by-step explanation:
The statement is True. Nontaxable stock dividends indeed result in no change to the total basis of the old and new stock, but the basis per share decreases. This is because when a company issues stock dividends, it distributes additional shares to its shareholders without any tax implications. As a result, the total value of the shares held by the investor remains the same, but the basis per share decreases due to the increase in the number of shares.