LONDON, United Kingdom — Online growth doesn't come cheap. That has been the message from Europe's big online retailers lately.While internet shopping is outpacing that in physical stores, avoiding the burden of bricks and mortar is no guarantee of runaway profit growth. The cost of fulfilling orders, dealing with a high level of returns and the need to enhance customer service is inescapable.In addition, traditional chains are improving their digital offerings, while Amazon.com Inc. is pushing ever-deeper into clothing.Zalando SE is the latest online retailer to spell out just how much it is spending in an attempt to stay one step ahead. The danger for it, and its rivals, is that profit growth doesn't keep pace with sales expansion.Indeed, earlier this year, Zalando co-chief executive officer Rubin Ritter said that the company was prioritising increasing its market share over profit growth.On Tuesday the company showed it was making good on that promise. It said sales rose by 23.1 percent in the first quarter, in line with its long-term guidance of expansion of between 20 percent and 25 percent.But fulfillment costs rose, contributing to flat profit and a slightly crimped margin on an earnings before interest and tax basis. It provided some reassurance to investors that for the full year it's still on track to meet its Ebit margin target of 5-6 percent.Capital expenditure was €78 million ($85 million) in the first quarter, as the company invested in new warehouses and improved customer service, such as same-day delivery and easier returns. It expects to spend about €200 million over the full year, a step up from last year's €181.7 million.When such heavy expenditure becomes the standard, that's a worry for investors.However, Zalando is not the only online retailer spending. Asos Plc is building new international warehouses and a UK loyalty plan. Even boohoo.com plc, whose super-fast growth has left rivals in tears, has snapped up Nasty Gal and the majority of PrettyLittleThings although the outlay on these two deals was relatively modest, just less than £20 million ($25.9 million).And Next Plc, the British high-street retailer that transformed its Next Directory mail-order arm into a powerful online business, will spend £10 million this year on improving this division as rivals threaten its historic advantage.No online retailer is immune from the pressure to invest. But Zalando is particularly exposed. As Gadfly has argued, it is at risk from Amazon's appetite for fashion because it sells largely branded clothing, which Amazon could easily ape, and offers fewer own-label garments — which are more unique — than Asos and Boohoo.Zalando says it is building the infrastructure for the fashion industry in a digital age. This is more than just a soundbite. To convince big brands to join its platform, it must have slick customer service. There are signs its efforts are paying off, with Inditex's lingerie and athleisure brand Oysho the latest to sign up.But with Amazon encroaching ever further into apparel, including through the introduction of a clutch of its own fashion labels, Zalando has little choice but to keep moving its offering forward. And that means more investment.By Andrea Felsted; editor: Jennifer Ryan.This column does not necessarily reflect the opinion of Bloomberg LP and its owners. The views expressed in Op-Ed pieces are those of the author and do not necessarily reflect the views of The Business of Fashion.