Source: Apple.

Many investors are worried that the deal between motion-tracking sensor designer InvenSense (INVN) and Apple (AAPL 0.27%) came with some unfavorable terms for the former. Indeed, InvenSense's management has always been forthright in telling investors that its biggest customers receive better pricing than the average customer.

That said, the average customer pays about $1 for a chip like the six-axis sensor found in both the iPhone 6 and iPhone 6 Plus, according to InvenSense CEO Behrooz Abdi. When InvenSense won the design in the new iPhone models, I said that InvenSense made a good deal with Apple even if it only receives about $0.85 per unit because of the high demand for the iPhone 6 and iPhone 6 Plus.

With that in mind, I thought it would be fun to use some inexact science to see how good or bad the deal with Apple really is for InvenSense.

How many new iPhones did Apple sell?
In the calendar fourth quarter, Apple reported selling 74.5 million iPhones. That includes both of the new models as well as the iPhone 5s and iPhone 5c. Additionally, Apple continues to sell the iPhone 4s in some developing markets as an entry-level phone.

CIRP estimates that 75% of iPhone sales in the U.S. during the fourth quarter were either the iPhone 6 or iPhone 6 Plus. Management noted that the product mix is different in all its geographic markets, with some geos skewing toward the big-screen iPhone 6 Plus. Its second-largest iPhone market, China, is expected to be one of those markets that skewed toward the iPhone 6 Plus.

With the two biggest markets having a similar affinity for the new models, 75% of iPhone sales seems like a fair estimate for global sales of the new model iPhones. That would mean Apple sold 55.9 million units with InvenSense chips inside.

What did InvenSense sell each unit for?
Last quarter, Apple accounted for about 45% of InvenSense's $115.9 million in revenue, or about $52.1 million. That would imply InvenSense is receiving about $0.93 per unit. That's well above my previous expectations and implies InvenSense is maintaining some pricing power despite Apple's demand.

Let's see if we can back into a different number.

In InvenSense's fiscal first quarter -- the quarter before the Apple contract went into effect -- the company achieved a gross margin of 50%. That's the same quarter Mr. Abdi mentioned that the ASP for the six-axis sensors is about $1. That implies a $0.50 cost of revenue for six-axis sensors.

Last quarter, the company reported a gross margin of 46%. If we assume the non-Apple revenue still achieved a gross margin of 50%, then we can determine that Apple's revenue generated a gross margin of about 41%. With a $0.50 cost per chip, that implies an $0.85 selling price for Apple. That's more in line with expectations, but vastly different from the $0.93 per unit calculated earlier.

Why the big difference?
There are several explanations for the discrepancy. The estimates for units sold could be wrong. CIRP's estimate could be wrong, or it might not apply to the global market (with the rest of the world buying a higher percentage of the new iPhone models). Apple also could have ordered more units in the quarter than it sold, inflating InvenSense's sales for the quarter.

Neither of those explanations seem particularly likely. Apple reported a decrease in iPhone inventory of 200,000 units last quarter. And while the iPhone 6 Plus model was particularly popular in China and other markets, there's only so much upside to 75% of unit sales.

More likely, the six-axis sensors carry a lower gross margin than InvenSense's other products. If the cost to make a six-axis chip is actually $0.55 instead of $0.50, the price per unit at a 41% gross margin suddenly rises to $0.93 -- the same as the other estimate. As such, an $0.85 price per unit for Apple is very conservative, with the price likely being closer to $0.90 per unit.

What's an investor to make of it?
There are a couple key takeaways from this analysis. The first is that despite Apple's immense buying power, InvenSense was able to maintain some pricing power, keeping prices within 10% to 15% of its average selling price for six-axis sensors.

That speaks to the quality of the designs InvenSense is producing compared to its peers like STMicroelectronics and Bosch. With best-in-class designs, InvenSense is poised to take a large share of the sensor market as it expands into not only smartphones, tablets, and wearables, but all sorts of Internet-of-things devices.

The second is an immediate revenue and gross margin impact from Apple. Goldman Sachs' analyst estimates that Apple will ship 54.75 million iPhone units this quarter. BlueFin Research estimates iPhone shipments of 57 million to 58 million, with 46 million to 47 million of the units being the new models.

Typically, just 50% to 60% of iPhone shipments in Apple's second quarter are the new model. However, Apple reported it was below its inventory target at the end of December, suggesting the iPhone 6 and iPhone 6 Plus will account for a higher than normal percentage of production. Still, BlueFin's prediction of an 81% new-model mix seems quite high. 

If 60% to 65% of the iPhones sold are models with InvenSense chips inside, the revenue opportunity is likely between $30 million and $35 million, or 31% to 37% of InvenSense's revenue guidance of $95 million to $98 million. Apple also reportedly pre-ordered 6 million Apple Watch units, which could add another $5 million to $5.5 million in revenue for InvenSense.

Still, Apple is likely to make up a smaller percentage of revenue in the current quarter than last quarter. Unless Samsung makes up significantly more revenue (and it could with the upcoming release of the Galaxy S6), we could see gross margin improve in InvenSense's fourth quarter.