Shares of Broadcom (NASDAQ: BRCM) have been powering higher ever since the company announced that it would divest itself of its cellular baseband program. One concern that continues to loom over the company is considerable risk to its low-end connectivity business. However, if we work through the math here, it's pretty clear that Broadcom is making the "right" trade-off here.

Cellular savings against the revenue being defended
According to Broadcom management, $500 million to $800 million of revenue within its connectivity business is now "at risk" as a result of getting rid of cellular via means such a sale or a simple shutdown. This business is at risk simply due to the fact that at the low end and midrange of the smartphone market, device vendors typically like to buy "complete" solutions -- apps processor, modem, and connectivity. With Broadcom only participating in connectivity, it becomes tougher to take share in that market.

Let's assume that in an extreme scenario this business is indeed worth about $800 million to Broadcom today and that its operating margin is roughly 15%-17%. If this business simply disappeared, it would mean a reduction of $800 million on the top line and about $120 million-$136 million in operating income. Note that Broadcom expects to save about $700 million in annualized research and development and selling, general, and administrative expenses as a result of its cellular divestiture. This implies a worst-case net win of $564 million. Not bad, right?

The biggest problem is the lack of upside
If Broadcom had been able to really "win" in cellular, it could have seen pretty substantial upside. At a $700 million operating expense run rate, and at 40% gross margin, Broadcom would have needed about $1.75 billion in cellular revenue to break even. This wasn't unrealistic, particularly given that the mobile apps processor/baseband market is worth in the tens of billions. But as it turns out, the low end of the market is a low-margin bloodbath and the high end is dominated by in-house solutions and Qualcomm (NASDAQ:QCOM).

The bad news for Broadcom is that it will lose what is probably the company's biggest revenue growth opportunity, but the good news is that the money saved can be reallocated to more profitable businesses and returning capital to shareholders. If there had been a reasonable and fairly timely path to Broadcom succeeding in this market, it would have made sense to take the near-term pain for long-term gains. But from Broadcom's perspective, that was unrealistic.

Foolish takeaway
The interesting thing now will be to whom this business gets sold, if it is sold at all, and what the industry is going to look like going forward. Qualcomm has earned its place as it is quite profitable in this market, but it will be interesting to see if a company the likes of Apple (NASDAQ:AAPL) would pick this business up in order to build in-house baseband efforts, or if that rumor that MediaTek is interested ultimately proves true.