The raising of new capital by allowing existing shareholders the privilege to buy shares at preferential rate is called?

The term you are looking for is "rights issue". A rights issue is a way for a company to raise new capital by offering existing shareholders the opportunity to buy additional shares at a preferential rate. This is done by giving shareholders the right, but not the obligation, to purchase new shares in proportion to their existing holdings. The purpose of a rights issue is to give current shareholders a chance to maintain their ownership percentage in the company, while also raising additional capital. It is different from a bonus issue, where existing shareholders are given free additional shares based on their current holdings, without having to pay for them.