At first glance, Elliott Investment Management appears to have an insurmountable disadvantage in its campaign to block the business group behind Toyota Motor from buying out a key unit in one of Japan¡¯s largest take-private deals of all time.

After all, the group already owns about 48% of Toyota Industries, and holds deep ties with many of the buyout target¡¯s top minority shareholders. Meanwhile, the U.S. activist fund only has a 6.7% stake ¡ª a far cry from what¡¯s needed to scuttle what it describes as a lowball offer before the tender period closes on Feb. 12.

So Toyota may look closer to the two-thirds majority required to push through the deal than the 33% of eligible shares Elliott needs to block it, but a closer look indicates billionaire Paul Singer¡¯s fund may not be so far from pulling it off.