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To determine the new basis per share after a stock dividend, the appropriate method is to take the old total cost and divide it by the new number of shares. This process reflects the dilution of the basis per share that occurs when shares are issued as a dividend.

When a company issues a stock dividend, shareholders receive additional shares, which increases the total number of shares they own. However, because the overall value of their investment remains the same (assuming no market price changes directly from the dividend), the basis per share decreases. By dividing the original total cost of the investment by the new total number of shares, you accurately reflect the reduction in the basis attributable to the additional shares received from the stock dividend.

This method is essential for investors to maintain a correct record of their investment's basis for tax reporting purposes, especially when the time comes to calculate gains or losses upon selling shares. The adjusted share basis accurately represents the investor's cost per share after the dividend has been issued.