What does it mean in general, and what does it mean for a shareholder like me?
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A non-renounceable offer is a mechanism that many Australian companies use to raise capital/funds for operations. The "non-renouncable" part means you cannot sell your right to the capital raising. If it was renouncable then you'd see the rights trading under CTMR.
These sorts of offers are very popular in bull markets but in subdued conditions often cost the company almost as much in administrative/legal fees as the capital raised.
Any such offer will dilute your shareholding in the company unless you take up the offer. How do you know how many people will take up the offer? You don't until it has closed. You could always call the company secretary to ask.
For speculative mining companies, such offers are common and are used to fund exploration efforts.
Typically they are offered near the current market price or at a discount to the market price and sometimes have further characteristics such as an attaching option. When stock prices are volatile this dramatically affects how many people take up the offer.