Under what conditions can a company purchase or redeem shares?

A company can purchase or redeem shares under specific conditions that primarily focus on legal compliance and financial stability. The correct understanding of these conditions is fundamental for ensuring that such actions do not compromise the company's financial integrity or violate corporate laws.

When option C states that the articles of the company must authorize the action and a solvency test must be met, it underscores two critical requirements. First, a company’s articles of incorporation or bylaws must explicitly permit the purchase or redemption of shares. This ensures that the decision aligns with the corporate governance framework established by the company itself. Second, the solvency test is a crucial aspect because it assesses whether the company can meet its liabilities after the shares are purchased or redeemed. This safeguards creditors and maintains financial stability, ensuring that the company does not act recklessly in reducing its equity base.

The other options touch upon concepts related to company shares but do not encompass the complete legal framework necessary for share transactions. The right of transfer is not directly relevant to the conditions for purchasing or redeeming shares. While the company’s authorization in its bylaws is part of the broader requirement, it is incomplete without considering the articles and solvency test. Finally, fully paid shares without a right of redemption do not address the company's ability or permission