Just two years ago, investors had seemingly written off FedEx (NYSE:FDX). Earnings had stagnated, and as a result, the stock price was no higher than it had been in 2005.

FDX Chart

FedEx 10-Year Stock Chart, data by YCharts.

On Wednesday morning, the package delivery giant made another big step in its comeback. FedEx reported that EPS soared 37% year over year to $2.10 for the first quarter of fiscal year 2015, while revenue increased 6% to $11.7 billion. This puts the company on track to meet -- and possibly even exceed -- its guidance for 26% to 33% EPS growth this year.

Revenue growth picks up

One of FedEx's biggest problems in recent years has been sluggish global growth. The recovery from the Great Recession has been very slow. Moreover, cost-conscious customers have been trading down from FedEx's signature high-margin Express service in favor of cheaper "deferred" or "economy" shipping methods.

FedEx began to see an acceleration in demand growth last quarter.

Now, shipping demand is finally starting to pick up, which is great news for FedEx investors. In the 2014 fiscal year, which ended in May, FedEx's revenue grew just 3% year over year. By contrast, revenue growth accelerated to 6% last quarter.

Revenue growth was well-distributed across FedEx's three main operating units. Year-over-year revenue growth totaled 6% at the Express division, 8% at the Ground division, and 13% at the Freight division.

FedEx's management appears to be confident that demand will remain strong going forward. On Tuesday, the company announced it will increase shipping rates by an average of 4.9% next January. For comparison, FedEx raised Ground shipping rates by 4.9% for 2014, but only increased Express rates by 3.9%.

Earnings growth also accelerates

FedEx was able to leverage expenses due to higher demand.

FedEx's solid revenue growth last quarter -- along with an ongoing cost-cutting program -- allowed the company to leverage its expenses. The Express, Ground, and Freight segments all posted improved operating margins.

The company's EPS of $2.10 easily topped the average analyst estimate of $1.96. FedEx's multibillion-dollar share repurchase program, which concluded last quarter, helped turbocharge EPS growth, as the diluted share count fell from 319 million to 289 million. The impact of buybacks on FedEx's EPS growth will peak next quarter before moderating later this fiscal year.

Looking ahead

FedEx should continue to post rapid earnings growth during the next few quarters, and it may even have a chance to exceed the high end of its $8.50-$9.00 full-year EPS guidance range.

For example, oil prices have fallen significantly in the past few months, which should lead to lower fuel costs across all three main FedEx operating segments. The impact is most critical in the FedEx Express division, which spends about $1 billion per quarter on fuel.

There is a lag of roughly two months between when fuel prices fall and when those savings are passed on to customers. As a result, FedEx is likely to post particularly strong earnings growth in the current falling fuel price environment.

FedEx is gradually replacing all of its fuel-guzzling three-engine planes.

FedEx's fuel costs will also be helped by the company's efforts to replace old planes with more fuel-efficient models. In the next three quarters, FedEx will replace 17 MD-10s with smaller Boeing 757s and 767s. The Boeing aircraft will better match capacity with demand. They are also much more fuel efficient because they have two engines, whereas the MD-10s each have three engines.

Still on a roll

FedEx shares increased 3% in pre-market trading Wednesday morning. While FedEx shares have surged in the past two years, there could still be upside left in light of the company's strong earnings growth.

FedEx's $1.7 billion profit-improvement program will wrap up near the end of FY 16. That alone should support another year of double-digit earnings growth beyond this year's projected 26%-33% rise in EPS.

Most important, the recent increase in demand is great news for FedEx investors. A return to faster global economic growth will allow FedEx to leverage its fixed costs and deliver long-term double-digit earnings growth.

Adam Levine-Weinberg has no position in any stocks mentioned. The Motley Fool recommends FedEx. 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.