My fellow Foolish colleague Timothy Green recently penned an interesting piece asking, "When will NVIDIA's (NVDA -10.01%) Tegra [business] turn profitable?"

In the article, he concludes that the company's Tegra business unit will "probably keep losing money for at least a couple more years as it grows." He does, however, think that as sales of chips in the automotive market become a larger part of the business unit's revenues, those losses will continue to narrow.

In this article, I'd like to expand on this analysis by trying to figure out at what revenue run rate this business can hit breakeven and start moving into profitability.

Where is the business today?
According to NVIDIA's most recent form 10-Q filing, its Tegra processor business took in $128 million in revenue last quarter and posted an operating loss of $41 million.

If we assume that the gross profit margins in the Tegra business are about 35% (I think this is a reasonable estimate, but there is certainly a wide margin of error), this would imply quarterly operating expenses in the range of $81 million. Assuming these expenses don't vary much quarter to quarter, this would suggest an annual operating expense run rate of $324 million.

At 35% gross profit margins, it would seem that "breakeven" for the Tegra processor business should be around $926 million in annual revenue.

NVIDIA will probably want to bring this down
The company's automotive business is growing at a healthy clip, but it's important to keep in mind that the Tegra business brought in $579 million in its last fiscal year, seemingly a long way from breakeven.

Though the business may eventually get to breakeven through revenue growth, I think that the company will also try to lower the bar for breakeven.

NVIDIA has two ways that it can lower that proverbial bar: It can either lower its operating expenses or it can improve the gross profit margin profile of the business. I believe that the company is trying to do both. NVIDIA has made it quite clear that it is trying to improve the gross margin profile of its automotive business by adding more value to its platforms, particularly through software.

As far as operating expenses go, we have seen the company take steps to rationalize its spending here, too. NVIDIA recently wound down its Icera cellular modem business, which should lead to some cost savings, and as it has deemphasized phones/tablets, there's probably some additional fat to trim as far as operating expenses go.

It's going to take some time, but the business can afford the wait
I concur with Green that the Tegra business will probably continue to lose money for the next couple of years. However, over the long term, there seems to be a good chance that NVIDIA's automotive business will reach the revenue scale needed to drive (no pun intended) a business that's both growing and profitable.

Fortunately for NVIDIA and its shareholders, it already has a healthy and profitable core graphics processing unit business. As long as its core graphics processing unit business remains healthy, NVIDIA should be able to absorb the operating losses that its Tegra business generates.