What does it mean that the shares are issued at a discount to the share price?
There is a difference between how you structure a rights offering with pre-emptive rights for existing shareholders and an equity offering without pre-emptive rights. In a rights offering, the discount is irrelevant to existing shareholders. The deeper the discount, the higher the rights value will be, and a shareholder’s net worth is the same, assuming they take up their rights in full. There is no economic dilution as long as you either subscribe for new shares or sell your subscription rights.