Chip giant Broadcom (AVGO 0.61%) recently tried to buy fellow chipmaker Qualcomm (QCOM 1.41%) -- a move that probably would've succeeded had President Trump not issued an executive order blocking the deal on national security grounds

Broadcom likely wanted to add Qualcomm's business to its own because the two companies' product lines are hugely complementary: Broadcom is a leading vendor of Wi-Fi and radio frequency (RF) chips into smartphones, while Qualcomm is the leading manufacturer of smartphone applications processors and other related components.

A Qualcomm mobile chip.

Image source: Qualcomm.

The combination of the two companies would've undoubtedly created a mobile chip powerhouse. 

After this deal fell through, my fellow Foolish colleague Leo Sun suggested that Broadcom could, as an alternative, buy Qualcomm's main rival in the mobile applications processor market, MediaTek. 

Here's why I respectfully disagree that MediaTek would be a potential target for Broadcom.

Broadcom buys leaders

Broadcom generally likes to buy companies that lead in their respective fields, something that's readily apparent in Broadcom's acquisition history. Broadcom wants to have a portfolio of already great businesses. It's not really interested in having businesses that aren't the best today but could be the best with some additional investment.

MediaTek is a distant second to Qualcomm in the mobile applications processor market. According to Strategy Analytics, MediaTek captured 18% revenue share of the overall mobile applications processor market during the first half of 2017 -- less than half of Qualcomm's whopping 42% share. 

As MediaTek isn't either the leader in its field or within spitting distance of being the leader in its field (Broadcom would probably be interested in buying a very close second with the ambition of trying to become first), it doesn't seem to be a good fit for Broadcom's product portfolio.

This isn't to say that MediaTek is a bad business -- it's not -- but that it just doesn't meet a key criteria that Broadcom would require for a potential acquisition target.

MediaTek's financials don't fit with Broadcom's goals

During fiscal year 2017, Broadcom reported a gross profit margin of 63%, representing a 250-basis-point improvement from the year before. Even more impressively, Broadcom's operating margin grew from an already solid 40% during fiscal year 2016 to a whopping 45.3% in fiscal year 2017. 

During the first quarter of Broadcom's fiscal year 2018, operating income hit an eye-popping 48.2%. 

Broadcom has made it clear that it aims to maintain its current very high gross profit and operating margin in the years ahead -- something that it's able to do because its business portfolio is replete with leadership franchises. 

By contrast, MediaTek's gross profit margin during 2017 was just 35.6% and its operating margin was a scant 4.12%. Adding MediaTek to Broadcom's business portfolio would likely lead to a significant dilution in the latter's consolidated financial results -- something that Broadcom investors probably wouldn't be too thrilled with.

Broadcom shareholders might think that a better use of Broadcom's cash would be to return that cash to stockholders in the form of a dividend or share repurchases.

And, given that Broadcom just announced that it has authorized a share repurchase program good for $12 billion, I think that Broadcom's board of directors agrees.