What type of preference shares offers shareholders dividends that accumulate if not paid in a given year?

Cumulative preference shares are designed to accumulate unpaid dividends. This means that if a company does not pay a dividend in a particular year, shareholders will still be entitled to receive that dividend in future years before any dividends can be distributed to ordinary shareholders. This feature provides an additional layer of security for investors as it ensures they will eventually receive any missed dividends, enhancing their overall returns on investment.

In contrast, non-cumulative shares do not provide this protection. If a dividend is not paid in a given year, the right to that dividend is lost permanently, and shareholders wait for an uncertain future payment without any guarantee of recovering missed distributions.

Convertible shares allow shareholders to convert their preference shares into a predetermined number of ordinary shares, which relates more to the structural rights associated with the shares rather than their dividend accumulation feature.

Redeemable shares involve the company's right to buy back the shares at a specific time or under certain conditions, which does not inherently relate to the accumulation of dividends.

Therefore, cumulative shares are distinct in their ability to accumulate unpaid dividends, providing a clear benefit to shareholders in terms of financial security and guaranteed returns if dividends are not paid timely.