Ann: Quarterly Cashflow Report - June 2023, page-169

Livent certainly don't make it easy. The 5,000t figure you're referring to is just the 50% expansion of their Bessemer City Lithium Hydroxide Plant. For reference (and ignoring the forthcoming merger with AKE), Livent have the following operations:

Fenix Brine Operation at Hombre Muerto - Current production of 20 ktpa of lithium carbonate/chloride (mostly carbonate), expanding to 40 ktpa later this year, 70ktpa in 2025 and 100ktpa by 2030. Most of this lithium carbonate production acts as feedstock for their hydroxide conversion plants.

Nemaska Spodumene Mine and Hydroxide Plant (50% ownership) - 34 ktpa of lithium hydroxide production by 2025.

Bessemer City (USA) Lithium Hydroxide Plant - 15 ktpa lithium hydroxide production.

Zhejiang (China) Lithium Hydroxide Plant - 15 ktpa lithium hydroxide production.

The've also got the Guemes (Argentina) and Bromborough (UK) facilities, but these are small and focussed on specialty products (butyllithium, etc).

Even if we just boil it down to basic numbers to compare lithium carbonate operations and exclude all of the hydroxide conversion plants, and exclude the spodumene operation, Livent's production capacity from Fenix is 25 times greater than AGY's share of Rincon. By 2025, that production figure is 38 times higher than AGY.

AUD$6.25b (current Livent market cap) / 25 = AUD$250m
AUD$6.25b (current Livent market cap) / 38 = AUD$164m

Or we can just compare resource size (again excluding spodumene). At Fenix, Livent have 11.82Mt of LCE, whereas AGY have 0.245Mt.

AUD$6.25b (current Livent market cap) / 11.82Mt = AUD$528m per Mt LCE
AUD$0.428b (current AGY market cap) / 0.245Mt = AUD$1.74b per Mt LCE

Cutting a long story short, any comparison between the two won't be kind to AGY. Accordingly, we can't extrapolate "IP valuations" as you have done.