This analysis suggests the most likely outcome is that, if Alibaba IPOs this year (which seems likely), it will be valued at $80 billion.
Yahoo’s 20% stake will be worth $16 billion pre-tax and $11 billion after tax. Using the current share count (which is going to go down with buybacks), it suggests Alibaba alone is worth $10 / share.
Yahoo’s 35% stake in Yahoo Japan is currently worth $8.34 billion at current exchange rates. (However, Yahoo announced on their last earnings call that they had hedged their Japanese yen exposure in December.) That’s $5.15 / share in value.
And then Yahoo still has $6.5 billion in cash, which is another $5.91/share.
Put it all together and you have a little over $21 a share, suggesting the core business is worth zero.