An offer of new shares made to existing shareholders at a preferential price is called?

An offer of new shares made to existing shareholders at a preferential price is called a "rights issue". This allows existing shareholders to purchase additional shares in the company at a discount, giving them the opportunity to increase their ownership stake without having to compete with outside investors. The company may issue rights to raise capital, pay down debt, or finance an expansion. Rights issues are a common way for companies to raise capital while also rewarding their existing shareholders.