They say it's not over until the fat lady sings. In the month-long bid by Pfizer (PFE 0.55%) for AstraZeneca (AZN 0.19%), it appears she's not only finished singing, but left the building all together.

At least until the next performance.

Pfizer said on Monday that its final bid on May 18 really was its absolutely last bid. Since AstraZeneca rejected the offer, under U.K. law, the companies are now at a standstill for three months. After that, AstraZeneca could reopen talks. Pfizer technically has to wait six months to make a new bid under the law, but according to ISI analyst Mark Schoenebaum, the takeover panel usually makes an exception allowing for a private offer after just three months.

What AstraZeneca should do
Let's start with what it shouldn't do: sit around waiting for another bidder.

One of the main appeals of buying AstraZeneca is the potential to move Pfizer's headquarters to the U.K. and lower its tax rate. Merck (MRK 0.37%) is the second largest U.S. pharmaceutical company, but Merck only has about $20 million in cash, compared with Pfizer's nearly $34 billion. And Merck's market cap is 88% of Pfizer's, making it harder to use its shares to get the deal done.

AstraZeneca could accept Pfizer's current bid of around $117 billion if Pfizer reoffers it in six to 12 months. With the stock trading at $90 billion right now, it's not hard to see shareholders pushing for this option. Of course, we'll have to see where AstraZeneca is when the cooling off period ends.

The other option is for AstraZeneca to hold out for a higher price. AstraZeneca was reportedly only asking for a takeout about 7% higher than Pfizer's final offer, but considering Pfizer has already come up 18% from its initial offer, it may not be willing to raise its bid anymore.

Remaining independent wouldn't be that bad of an option. Bolstered by a strong pipeline of oncology drugs, AstraZeneca has predicted that its 2023 revenue will be at least $45 billion, up from $25.7 billion last year. If the share price can follow suit, investors would be sitting on a 75% increase in value over the next decade. And there's potential for further gains if earnings can outpace revenue growth if AstraZeneca can expand its operating margins by cutting expenses.

What Pfizer should do
If it's hell-bent on buying a U.K. company, GlaxoSmithKline (GSK 0.49%) is another option, but it's not nearly as good of a fit for Pfizer as AstraZeneca is. GlaxoSmithKline recently sent its oncology portfolio to Novartis, so Pfizer wouldn't get any oncology drugs in the deal, one of the main attractions to AstraZeneca. GlaxoSmithKline is also nearly 50% larger than AstraZeneca, making it harder to get a deal done.

Pfizer could take my advice and buy 30 or so smaller biotechs rather than make one large purchase, but I wouldn't count on seeing the drugmaker go on a buying spree. Pfizer sat on a substantial nest egg for years before buying Wyeth. Pfizer will do some deals to augment the pipeline, but unless the culture changes, you're more likely to see the company buying back shares with its extra cash than substantially increasing its rate of acquisitions.

Pfizer is in the process of figuring out whether it can increase shareholder value by breaking itself up into different segments. While adding drugs through an acquisition would seem to be the opposite of a breakup, Pfizer may be bulking up the segments to make them more profitable. In theory, higher revenue in each segment will allow them to have better operating margins after the breakup.

If that's the plan, Pfizer could split first and then fill in the gaps, but that won't look nearly as attractive as buying first and then splitting up.

My guess is that if it can't get AstraZeneca, Pfizer will buy some other large drugmaker that fits well. Bristol-Myers Squibb, for instance, is about the same size as AstraZeneca. Pfizer wouldn't get the tax benefit, but Bristol has a nice pipeline of oncology drugs that Pfizer seems to be after.