Apple (NASDAQ:AAPL) stock is hitting a new all-time high again today, likely thanks to recent bullish comments from analysts. The latest analyst note is perhaps one of the most notable, coming from KGI Securities' well-connected Ming-Chi Kuo. His estimate for iPhone 6 and 6 Plus sales for this quarter is downright monstrous.

iPhone 6. Image source: Apple.

Will iPhone sales soar?
Apple's fiscal 2015 first quarter, which falls during the fourth calendar of 2014, is likely to shape up to be a record breaker for the tech giant on many fronts. The iPhone, in particular, looks poised to be a big winner following the recent rollout of the new iPhone 6 and 6 Plus -- the company's first foray into smartphones with displays larger than 4 inches.

Kuo predicted (via AppleInsider) that Apple's iPhone sales will hit 71.5 million in the quarter, up 40% year over year. This growth would easily trump Apple's year-over-year first-quarter iPhone sales growth of just 6.7% in fiscal 2014. 

Since Apple's first quarter is typically the company's first full quarter of sales of the latest iPhone, the three-month period usually helps the company achieve new record revenue and earnings from new customers and customers upgrading their devices.

Sales during the quarter are usually limited by supply, and this time has been no exception. For most of the quarter, there have been shortages of new iPhone 6 and 6 Plus models in retail stores. Online sales have also been, and remain, constrained. The 64GB space gray iPhone 6 and 6 Plus, for instance, currently show shipping times of seven to 10 business days and two to three weeks, respectively. In general, however, shipping times have improved for most models as the quarter dragged on.

As supply slowly catches up with demand, investors should not expect the same robustness in iPhone sales in the second quarter of fiscal 2015. Indeed, Kuo predicted a 31% sequential slowdown to 49.4 million units. This figure, though, would still be up 13% from Apple's year-ago sales.

Massive sales and earnings growth
Such substantial growth in Apple's first-quarter iPhone sales would have a significant impact on growth of the company's top and bottom lines. Assuming an average selling price of $650, 71.5 million units could mean that Apple's iPhone business alone brings in about $46.5 billion in revenue. That would amount to 81% of Apple's total revenue in the year-ago quarter and 110% of Apple's total revenue last quarter.

Apple CEO Tim Cook told The Wall Street Journal that he believed the new iPhone 6 models would trigger the "mother of all upgrades." iPhone 6. Image source: Apple.

This sort of revenue in Apple's iPhone segment would also likely have a meaningful impact on the company's earnings growth. While management does not share gross profit margin numbers for each product segment, Apple has emphasized on multiple occasions that the iPhone is its most profitable business. When iPhone sales soar, Apple's earnings should benefit substantially.

The current consensus analyst estimates for Apple's revenue and earnings-per-share year-over-year growth in the first quarter are 15% and 21.7%, respectively. The outsized growth in EPS reflects both the high expectations for Apple's iPhone sales and the company's reduction in share count through an aggressive repurchase program.

While any analysts' estimates, including Ming-Chi Kuo's, should be taken with a grain of salt, there is good reason to believe Apple's first quarter will shape up quite nicely for the company. It's no secret that Apple's new, larger iPhones have been a tremendous success. The likely big jump in Apple's iPhone sales in this quarter is another reminder that the tech giant deserves its all-time high share price. On the flip side, a rising price that seems to be largely driven by increasingly bullish analysts is eliminating potential upside in Apple stock from here.

This article represents the opinion of the writer, who may disagree with the “official” recommendation position of a Motley Fool premium advisory service. We’re motley! Questioning an investing thesis -- even one of our own -- helps us all think critically about investing and make decisions that help us become smarter, happier, and richer.