Conventional wisdom suggests that running retail stores is more expensive than selling the same merchandise online. Conventional wisdom is wrong. It may also seem that using existing retail stores as mini-distribution centers to fulfill online orders for shoppers is a less expensive option than full-fledged distribution centers. But in actuality, it's typically the most expensive option. As more and more shopping shifts online, retailers are working hard to capture the sale, no matter the cost. But when it comes to profitability, an online sale is not an equivalent replacement for that same item purchased in store. Retail consultancy AlixPartners built models for CNBC to illustrate an approximation of the financial differences an apparel retailer might see when selling $100 worth of goods in-store and the same $100 worth of goods online. Buy in-store The AlixPartners models begin with a typical $100 clothing purchase made by a shopper in a physical store, with a typical cost of goods sold — or what the retailer paid to have that clothing manufactured — of about $40. Then, there is the cost of running stores, but because those costs are considered "legacy" costs — and have been in place for many years — there's a maturity and scale to them, making them more efficient, and less "expensive" relatively, than the cost of running online operations. In a physical retail store, a shopper, effectively, picks out her own merchandise, and gets it home herself, so there's no additional "picking, packing, shipping" cost paid by a retailer with this model. Thus the $100 outfit has associated operating costs, like rent, overhead and labor of about $28. So a $100 purchase, minus the $40 cost of the goods, minus the $28 operating costs associated with that unit of clothing, leaves a profit margin of 32 percent. Buy online, ship from distribution center Now, consider a shopper instead goes to a retailer's website to search for and buy that same $100 outfit, with the same $40 cost. The model assumes that the $100 purchase comes with free shipping, which is fairly typical for a purchase of that value. There are costs associated with processing an online order. In this case, it has to be picked, packed and shipped to the shopper from a distribution center. It's much more expensive on a per item basis, for a retailer to ship individual orders, one at a time, from fulfillment centers to consumers' homes, than it is to send a truckload of inventory from a distribution center to a store. So, for the retailer, the clothing shipped from a distribution center would have associated operating costs of $30, slightly more than the in-store operating costs.

The higher operating costs in this model result from distribution costs that can be four times higher, and overhead and infrastructure costs that can be three times more than an in-store model. "Overhead and infrastructure cost is where strategy comes into play," explained Pete Madden, a director at AlixPartners. "A retailer has to make decisions. Do I own my [distribution center]? Do I pay a third party to do it for me? The cost for certain corporate functions, associated with running distribution centers like IT and marketing, can be in the tens of millions of dollars in terms of investment." There's also the investment to build and manage websites, apps, distribution centers, and establish shipping networks or partnerships to fulfill those orders. Online operations also have other incremental costs when it comes to acquiring and then taking care of customers, Madden said. A retailer needs systems to help shoppers with order management and tracking, and to show them where inventory may be available (i.e., online only, or available in certain stores). Plus there's a cost to manage the complexity of the "endless aisle" online, logistics and IT coordination with shipping vendors like FedEx and UPS, and increased marketing spending for search engine optimization to drive shoppers to their websites. "All these costs," said Madden, "until they slow and until online grows into a larger share of business, will continue to outpace any similar costs for legacy stores." Which means, all of it together makes a retailer's online business much more like a start-up, with less scale leading to higher costs and lower profitability, compared to its legacy store networks. Put it altogether, and AlixPartners models that the same outfit purchase made online and shipped to a consumer has a profitability breakdown as follows: $100 purchase price, minus the $40 cost of the goods, minus the $30 operating costs associated with that unit of clothing, leaving a profit margin of 30 percent. Buy online, pick-up in store Now that many retailers can serve shoppers both in-store and online, there are increasing instances of consumers looking for the convenience of ordering merchandise online, but picking it up in-store. In some cases, it may be faster or even more convenient for shoppers to pick-up in store, than waiting for home package delivery. But, offering a "buy online pickup in store" option, means a retailer is paying to operate both channels. So when breaking down the operating cost to fulfill that order, you have to account for all the aforementioned operating costs of running both channels. So that same $100 outfit that cost the retailer $40 to buy, now comes with associated operating costs of $37 dollars spread over both the store and web operations, leaving an operating a profit margin of 23 percent. Buy online, ship from store Leveraging stores as distribution centers sounds like an efficient, lower cost option. But it's not. It's true that in many cases, stores are considerably closer, geographically, to shoppers than distribution centers, which are often located in less populated areas. But, using stores as distribution centers is the least profitable model. The main reason for the compressed profitability is the cost of double-shipping merchandise. But the retailer would do this if it means keeping a shopper happy by getting that shopper merchandise faster. As a retailer, you are operating two channels, and shipping that merchandise twice, to fulfill an order placed online but shipped to a consumer from a store. Generally, store merchandise gets there by the semi-truckload, so a retailer has paid for that distribution cost once.

A mom, right, shopping with her daughters at a JC Penney store in Aurora, Colorado. Matthew Staver | Bloomberg | Getty Images