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Does saying “no” pay off in the long run when it comes to hostile bids?

A hostile takeover often goes, well, rather hostile. A company is usually put on the spot for resisting what is usually an unwanted, yet temptingly high, buyout offer.

The shareholders of the Botox maker Allergan may be wondering whether management’s vigorous opposition to a long-running hostile offer from Valeant Pharmaceuticals, which has teamed up with the hedge fund Pershing Square Capital Management, is worth it. A new report from the proxy advisory firm Institutional Shareholder Services tries to answer that question.

Allergan’s resistance has been stiff. Allergan has tried to prevent its suitors from nominating directors to replace the Allergan board, and sued the two bidders in federal court in California.

Allergan’s justification for resistance is that the Valeant and Pershing Square offer “grossly undervalues” it and seeks to buy the company on the cheap. If Allergan’s investors stick with management in saying no, the company says, shareholders will reap much more financial gains in the long term. On Monday, Allergan’s management got some support after it reported third-quarter earnings that beat expectations.

Over the coming weeks, Allergan shareholders will probably get a formal say in this contest, if a friendly deal is not reached before a special meeting scheduled for Dec. 18. The question is whether saying no will pay off over the long term.

In a report issued last week, I.S.S., which advises large shareholders like mutual funds and pension funds on how to cast their shareholder votes, tried to give an answer. I.S.S. examined all hostile takeovers in the last five years in which shareholders actually got to vote on some or all of the target’s directors.

I.S.S. found only seven hostile bids that went to a vote by shareholders through a proxy contest. That’s not a lot. Even in this small sample, however, was one good sign for Allergan: Only one of the companies was acquired by its hostile bidder.

That was Terra Industries, in which shareholders granted three board seats to CF Industries, a fertilizer company that spent months in pursuit of a deal. That only came after a long dance in which Terra agreed to be acquired by a Norwegian company, Yara International, leading CF to submit a higher bid that won approval. (The M.&A. game never ends; CF Industries was recently in merger talks with Yara, but those talks seem to have ended.)

In the other six cases, the companies stayed independent. I.S.S. then examined the returns of those six. Though a small sample, anecdotally at least, it could show whether the companies were able to deliver on their promise to give more value to shareholders than the hostile offer could.

I.S.S. found that on an absolute return basis, the six companies returned, on average, 50.4 percent from the time of the vote rejecting each company’s hostile bid through Oct. 20.

But when compared to what shareholders could have earned had they taken their money and invested it elsewhere, the “no” companies performed poorly. These companies lagged the Standard & Poor’s 500-stock index by 25 percentage points and their peers by an even greater 78.4 percentage points from the time of the vote through Oct. 20.

Two companies did do well. The “home run” of the group was Illumina, which rejected Roche’s $6.7 billion offer in 2012 and went on to beat its peers by 247 percentage points in the study’s time frame.

Another winner was Airgas, which resisted a $5.8 billion advance from Air Products & Chemicals. Airgas lagged the S.&P. 500 by 5.2 percentage points, but beat its peers by 20.8 percentage points and Air Products by even more. This was a mea culpa moment for I.S.S., because it had endorsed Air Products’ hostile offer. But this report acknowledged that the Air Products bid had “no meaningful premium for the change of control.”

I.S.S. attributed the success of these two companies to their dominance in their corners of their markets. In the case of Illumina, its DNA gene sequencing business was “closer to viability” than Roche acknowledged, and its proprietary products gave it a “scarce asset” to outperform the market. I.S.S. asserted that Airgas also held control of a “scarce asset” because it was one of the few players in the “U.S. packaged gas market.”

I.S.S. argued that the other companies that stayed independent relied on less successful “self-help” strategies. The independent strategy didn’t work for Pulse Electronics, Casey’s General Stores, NRG Energy or Onvia, all of which have lagged the market significantly. For those counting, that means that four out of the six companies should have accepted their takeover offers.

There are issues with I.S.S.’s report. It looked at only seven deals, which is hardly a good universe from which to judge. Yet, if you look back over time, you can find even greater disasters such as Time Inc.‘s rejection of Paramount’s bid at $200 a share bid in 1989. (It took Time almost a decade to make it back to that level in market value.)

The report also includes two smaller companies, Onvia and Pulse, which are more thinly traded and not as widely followed. The law firm Wachtell Lipton Rosen & Katz, which represents Allergan in its defense, attacked I.S.S.’s report for these deficits, saying they “completely undermine” the study’s “conclusions.”

But the law firm misses the point. Even if we took its criticism into account and eliminated the two contentious analyses, the fact is that saying “no” carries consequences.

For shareholders, trying to figure out when a board is right to say no is an inherently difficult task. The I.S.S. report says perhaps we are better off looking at the plan that a would-be buyer has when evaluating hostile deals.

Either way, outperforming the market is almost impossible in the long term. When a buyer is offering top dollar in a hostile offer, it is going to be exceedingly hard for a company’s management to contend that it could do better unless it has a unique product that no one else can replicate.

So what does this mean for Allergan? Allergan is offering a two-pronged defense. The first is to assert that Valeant lacks the business plan and the management to run Allergan effectively. The second is to argue that more money will be made if Allergan’s current plans are put in place, such as its plan of management “efficiencies,” which includes a 13 percent reduction in the work force. The company has also set a goal of reaching $12 billion in revenue by 2019, and it recently raised its earnings outlook. To reach that, Allergan would have to have five years of double-digit revenue growth, which would probably require it to make an acquisition itself.

It’s not surprising that Valeant challenges Allergan’s plans and has asserted that its offer is higher on a “stand-alone basis.”

In the weeks before the special shareholder meeting, Valeant may again raise its offer. A number of analysts put Allergan’s value above $200 a share, or higher than Valeant’s latest informal bid made on Monday.

This is where shareholders should look, rather than at the highly charged war of words and ensuing legal battles. The question for shareholders is: Who will create the most value, and how can it be created? The I.S.S. report is simply stating that if you are expecting value to be created in the future by existing management and choose that over an immediate cash offer by a hostile bidder, you may be sorely disappointed.

The IRR of No by I.S.S.