Final answer:
The assertion that a firm's decrease in leverage by issuing stock and paying down debt will result in an increase in share price is false. In a perfect capital market as described by Modigliani and Miller, the total firm value and thus share price are independent of its capital structure.
Step-by-step explanation:
When analyzing capital structure decisions in a perfect capital market without frictions, such as taxes or bankruptcy costs, a firm's decision to decrease its leverage ratio by issuing shares and using the proceeds to pay down debt should, in theory, cause the firm's equity to become less risky. This is because there is now less debt in the capital structure, which generally means that equity holders face less risk from potential financial distress. However, the assertion that this will necessarily lead to an increase in the price per share is false. According to Modigliani and Miller's capital structure irrelevance proposition, in a perfect capital market, the total value of the firm should be independent of its capital structure. Therefore, while the risk profile of the remaining shares would decrease, the market price per share would not necessarily increase simply due to a change in the capital structure.