Last month, activist investor fund Starboard Value LP revealed that it had acquired a 5.1% stake in Staples (NASDAQ:SPLS). Considering that Starboard also owns a large stake in Staples' main rival -- Office Depot (NASDAQ:ODP) -- it was immediately clear that Starboard planned to push for a merger of the two office supply retailers.

On Tuesday, Starboard finally made its merger demands public in a letter to Staples Chairman and CEO Ron Sargent that was also released to the media. However, while a merger-focused strategy might be good from Starboard's perspective, it wouldn't necessarily benefit all Staples investors.

Making the case for a merger

In its letter, Starboard cites several Wall Street analyst notes estimating the synergies from a Staples-Office Depot merger at anywhere from $500 million to $1.7 billion. The letter also highlights Staples' poor stock performance over the past few years and warns that it could fall further if the company fails to pursue a merger with Office Depot.

Starboard Value LP wants Staples to merge with top rival Office Depot. 

Based on the massive synergies and Staples' lack of a compelling stand-alone plan, Starboard Value CEO Jeffrey Smith claims that the prospect of a merger "makes too much sense to ignore." He makes it clear that if Staples doesn't willingly explore a merger, Starboard will apply more pressure.

Staples responded later on Tuesday with a generic press release stating that its representatives have already spoken to Starboard Value on several occasions, and that the Staples board is always interested in ways to maximize shareholder value.

The elephant in the room

Nobody really disputes that a merged Staples-Office Depot would produce much better earnings than the two could achieve separately. Merging the two companies would create opportunities for additional overhead reductions and store closures. Gross margin would probably improve, too, thanks to lower competition.

However, even if Staples and Office Depot both wanted to merge, there's no guarantee that they would actually be able to do so. The real question is not whether a Staples-Office Depot merger would be good for shareholders, but whether regulators would permit a merger in the first place.

The FTC allowed Office Depot and OfficeMax to merge, but it might oppose a merger with Staples.

In this regard, the FTC's 2013 decision to permit Office Depot and OfficeMax to merge has gotten a lot of attention. Whereas the FTC had blocked a proposed Staples-Office Depot merger in 1997, it allowed Office Depot and OfficeMax to merge based on evidence that office supply superstores now faced competition from other sources.

Merger advocates may be reading too much into the decision, though. In 2013, Office Depot and OfficeMax were each less than half the size of Staples and struggling to stay profitable. Without a merger, one or both may have eventually folded. Allowing the two to merge to become a more viable competitor to Staples was a no-brainer.

By contrast, merging Staples and Office Depot would turn two viable competitors into a $38 billion office supply giant. Even though people can also get office supplies from Wal-Mart or various e-commerce outlets, the FTC still might balk at letting the two remaining national office supply superstores merge.

A potentially costly distraction

This is why pursuing a merger is a dicey proposition for Staples. First, Staples would have to offer a significant premium over Office Depot's current stock price to entice its management, board, and shareholders to support the merger.

Second, Office Depot would probably demand a break-up fee amounting to hundreds of millions of dollars. This would compensate it for the likely disruption to its current merger integration process that would be caused by planning for a merger with Staples. If federal regulators were to block a proposed merger, Staples would have to pay this fee.

Neither of these things are problems for Starboard, as it owns 10% of Office Depot. That stake will allow it to profit from any merger premium that Staples might offer. Even in a failed merger scenario, where Staples had to pay a break-up fee, Starboard would come out ahead because it owns a larger percentage of Office Depot than of Staples.

However, for Staples investors who don't own Office Depot stock, the calculus is different. If regulators were to block a proposed merger, forcing Staples to pay a big break-up fee, Staples would be back to square one in terms of turnaround planning and would have strengthened its main rival.

Starboard Value can profit from an attempted Staples-Office Depot merger, regardless of whether it ultimately gains regulatory approval. For most shareholders, that's not true. Staples needs to carefully weigh the risk of having a merger attempt blocked against the potential reward of becoming the only major office-supply chain in the U.S.