There are so many things that needs to happen before AGY would...

There are so many things that needs to happen before AGY would start paying dividends, which means the time horizon makes answering the question almost impossible... might as well ask an 8 ball.

This is a growth stock.... they will only start paying dividends when they cannot deploy the capital in a more effective way.
And I hope that won't happen any time soon.

Plus, why do you even want dividends?
Income streams are taxed. ( dividends, cgt, interest ) they are all normal tax ( assuming you are an Austrlian tax resident ) and taxed all the same rate.
The difference is that with CGT if you are an investor you can get 50% discount AND decided when you will realise the benefit.... so that is the one you want.
Dividends has NO benefit in Australia.... please don't even mention the poorly understood "franking credits" - there are no benefits to a franked dividend, if fact I'd rather get unfranked and not have the ATO hang on to my money untill tax time with the withholding credit a frank div creates.
Much better to NOT get a dividend and then sell some shares if you need the cash.... there is a reason Buffet don't pay dividends.

Here is a post going through the possible earnings @ 10,000tpa produciton and US15,500 price. AGY valution/profit
This calculation does NOT include any consideration of HOW the additional 8ktpa production was funded by capital raise or debt.
If CR then profit is distriubuted to more holders and goes down per share.
if debt then there are debt repayments which reduces the profit.... maybe both will work out to be the same impact.

It does take into account 25% tax and AGY 90% ownership of PUNA and other liabilities and costs as supplied by PEA.

Also.
Companies will only pay out a percentage of profits..... not 100%
If indeed the EPS is A$0.0762 ( A$95,290,460 profit for AGY ) then a typical payout may be 30%-50%.

The above does not take into account the profit from any byproducts that Puna could sell but maybe that just offsets any other overhead or costs not accounted for.

So it could be in the range of A$0.023 - A$0.038.... but not anytime soon.