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That was easy? Not really. The familiar slogan that Staples Inc. used until last year can hardly be applied to its attempt this year to buy rival Office Depot for $6.3-billion (all currency in U.S. dollars). The companies have received blessings from regulators in Australia, New Zealand and China, but they're still working with authorities in the United States, the European Union and Canada. The U.S. Federal Trade Commission said that it would decide by Dec. 8.

Activist investor Starboard Value LP pushed the two companies to the altar last February. It bought stakes in both companies and sold its vision of the deal to both boards. It also warned Staples's management that if they didn't pursue the transaction, "it would be a clear sign that significant leadership change is needed."

As the FTC deadline approaches, it creates a classic dilemma for investors looking to make quick profits on a controversial deal. Staples announced a stock-and-cash offer in February that valued Office Depot at about $11 per share. But reports about the FTC review pushed down the stock prices of both companies. Office Depot's share price sank below $8 this past summer, and Staples's share price has declined from close to $17 to less than $13. If U.S. regulators bless the takeover, investors could win big, but if they disallow it, there could be much more downside.

For the math, we turned to analyst Brian Nagel of Oppenheimer & Co. Inc. He says that predicting what U.S. regulators will do is " inherently challenging." Given the failure of the Sysco-U.S. Foods merger in June, and reports that the FTC "intensified" its review of Staples-Office Depot in September, Nagel concludes that the deal has just a 20 per cent chance of going though.

This leads to what's known as a probability-weighted stock price analysis. If the deal is approved, Nagel assumes the merged company will earn $1.35 per share in 2018, and the market will give it a price-to-earnings (P/E) ratio of 15 to 18, a range consistent with similar healthy retailers. The result is a share price of $20 to $24 for Staples, nearly double its recent price.

But if you plug in the 80 per cent probability of the merger failing, Nagel sees a stand-alone Staples making 85 cents in 2016, with the market awarding it a P/E multiple of 10 to 12, in a range with other "disadvantaged retailers." That's a share price range of $8.50 to $10.50.

Blend the two scenarios at those weightings, and you get a range of $10 to $14 for Staples–about where it's traded lately as the prospects for the deal darkened. The same exercise yields a range of $6.75 to $8.15 for Office Depot–again, similar to recent trades.

In short, both companies are fairly valued, and there's no more upside. But this is where probability theory ends and the reality of the FTC's decision begins. It's an either-or bet. Are you feeling lucky?

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