Of course, the sure way to overcome both obstacles is for BHP to offer a price that is too generous to refuse.

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But how far is BHP prepared to go?

Its revised offer represents a premium of around 30 per cent to the price at which Anglo was trading before news of the offer leaked – which in financial parlance is called the “undisturbed price”. (Because BHP is offering its shares as payment to Anglo shareholders, the value of its offer fluctuates a bit.)

This isn’t a knockout price, but it’s within the scope of a normal takeover premium. There would be some Anglo shareholders happy enough with this, but Anglo has a duty to shareholders to walk the fine line of pushing BHP to pay more but not pushing it away.

BHP’s shareholders don’t want to see the company overpay, and need to trust that chief executive Mike Henry will be disciplined enough to walk away and avoid sticker shock.

Anglo has one further line of defence. It can convince its shareholders that it can grow the company itself and improve earnings organically.

In rejecting BHP’s revised offer this week, Anglo said its shareholders “are well positioned to benefit from increasing demand from future enabling products while the increasing capital intensity to bring greenfield supply online makes proven assets with world-class resource endowments ever more attractive. The Anglo American team is focused on delivering against its strategic priorities of operational excellence, portfolio simplification and growth and is set to accelerate delivery in order to unlock this inherent value.”

It’s a pretty motherhood statement that lacks any detail on how this could be achieved.

So the pressure will be on the Anglo board to put some meat around those lofty aspirations and make them credible enough to convince shareholders that they can create the same kind of value (in the short to medium term) as BHP is offering today.

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Anglo could also rustle up some alternative offers and there has been talk of others, such as Rio Tinto and Glencore keeping a watchful eye on proceedings, but nothing concrete.

BHP will argue that its track record demonstrates it would be a more able steward of Anglo’s assets.

Sure BHP has made some poor acquisitions over the past couple of decades, but Henry and his most recent predecessor, Andrew Mackenzie, haven’t fallen into that trap.

So let’s compare the pair (of companies).

In 2001, BHP and Anglo had roughly equivalent market capitalisations – $US21 billion and $US22 billion, respectively. Today, BHP has a market capitalisation that is 3½ times that of Anglo.

And over the past three years, BHP has delivered a total shareholder return (measuring share price growth plus dividends) of 54 per cent versus Anglo, where total shareholder return has fallen by 18 per cent.

It is now a question of third time lucky for BHP, who are considered likely to make one more attempt to lure Anglo over the line with another upwardly revised offer.

Mark III would be difficult for the Anglo board to refuse.