Iphone
Source: Apple.

After selling a record 74.5 million iPhones during the first quarter of its 2015 fiscal year, Apple (NASDAQ:AAPL) faces a huge challenge to top that number in Q1 of FY 2016, the current quarter. CEO Tim Cook acknowledged that Apple's comparable quarter will be tough to beat, but he remained optimistic. In the Q4 conference call, he noted that 30% of iPhone sales in the previous quarter came from customers who previously used an Android phone.

He also pointed out that just 30% of the iPhone user base owns an iPhone 6 or iPhone 6s model, which represents about 350 million devices that could upgrade at some point over the next year or two. Couple that with the faster-than-ever Android switcher rates, and Apple could be in store for even more unit growth from the iPhone.

Beating 231 million iPhones
Apple shipped 231 million iPhones in fiscal 2015 -- 37% more than in fiscal 2014. A significant portion of that growth came as a result of the larger screen sizes of the iPhone 6 and iPhone 6 Plus.

The larger screens appeal to emerging markets such as China, where smartphones are often used as a person's primary computing device. Indeed, sales in Greater China grew 84% year over year in 2015. The economic impact of China's currency devaluation didn't slow down sales, either, as sales grew 99% in the region last quarter.

The question is: Now that Chinese consumers have their large-screen iPhones, will sales fall back to earth?

Let's crunch some numbers
Those 350 million or so iPhone owners with a 5s or older are certainly prime candidates to upgrade. If Apple can convince 40% of them -- 140 million -- it would already be more than halfway toward beating last year's stellar results. I think that's a conservative estimate for upgrades, considering the typical two-year upgrade cycle for most iPhone owners.

Let's also factor in iPhone 6 and iPhone 6 Plus owners who may be interested in upgrading earlier than most. Approximately 135 million of iPhone users had an iPhone 6s or iPhone 6 at the end of last quarter. If just 30% of those users upgrade to the new iPhone this year, that's another 40 million iPhones sold. Roughly 45% of Americans replace their smartphone at least once a year, according to Recon analytics, so that estimate is also rather conservative to account for factoring in the global reach of the iPhone.

The global smartphone market is expected to grow by around 100 million units next year. Apple typically takes around 15% of smartphone shipments, but new smartphone purchasers are typically attracted to lower-end smartphones, so 5% is a more conservative estimate for new smartphone owners buying an iPhone. That brings the total up to 185 million.

If Apple can match its Android switcher rate of 30% of new iPhones throughout the next year, it could sell about 80 million iPhones to users who previously owned an Android device. That would bring total iPhone sales up to 265 million -- 15% unit growth year over year. If just 25% of new iPhone buyers are Android switchers, it would sell only 247 million units -- 7% growth.

Factors that could affect results
I tried to err on the conservative side of estimates, but there are some factors that could affect upgrades.

First of all, carriers are dropping the phone subsidy model in the U.S. and having customers pay for the phone in installments. This approach provides a financial incentive for users to hold on to their phones longer, since the phone payments stop once the device is paid off. On the flip side, the lack of a contract enables users to upgrade their phones more often, even though it's often a financially poor decision to do so. Many people take advantage of that option, so the factor seems to be neutral, possibly even positive.

The second factor is that Android switching may slow down. A big draw of the iPhone 6 and iPhone 6 Plus was the large screen, previously only available with Android phones. As a result, Apple probably saw a higher-than-average share of iPhone purchases made up of Android switchers. Apple continues to make it easy for Android users to switch with an app and a trade-in program, but the draw of the large-screen device may have already run its course. As a result, it's probably better to use a more conservative estimate than the 30% share Android switchers accounted for last quarter.

Overall, Apple investors should expect iPhone unit sales to come in with mid- to high-single-digit growth. But with the year-old iPhone 6 Plus model in the mix, average selling price may increase as well, leading to iPhone revenue growth in the low double digits.

Adam Levy owns shares of Apple. The Motley Fool owns shares of and recommends Apple. Try any of our Foolish newsletter services free for 30 days. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.