When it became public that Amazon (NASDAQ:AMZN) planned to buy Whole Foods (NASDAQ:WFM), the share prices for a number of supermarket chains fell. Costco (NASDAQ:COST) saw a big drop as well because the prevailing wisdom says that the online giant obtaining a physical presence somehow dooms the warehouse club.

It's an argument I buy when it comes to traditional grocers. Consumers, in most cases, have no special attachment to their supermarket chain. In general, they pick a store based on geographic convenience and price. Perhaps someone will drive a little out of their way to visit a chain that has some favored items, but in most cases, convenience rules the day.

When it comes to Costco, though, that's not the case. The chain's stores are a destination in themselves, which has so far made them Amazon-proof. That's not likely to change just because the online retailer now owns Whole Foods. And even if customers visit less often because Amazon's newly purchased chain lowers prices and adds same-day delivery, that shouldn't dent the warehouse club's bottom line.

IMAGE SOURCE: YCHARTS.

Why won't Costco be hurt?

As you can see in the chart above, Costco shares dipped strongly after the Amazon/Whole Foods deal became public before the market opened on June 16. Shares actually closed at $180.06 on June 15, then dropped to $167.11 at the end of June 16, falling further to $162.90 at market close on June 20. That's a nearly 10% drop driven by the idea that Amazon's move would somehow be devastating to the warehouse club.

That thinking makes sense when you apply it to most supermarket chains. Those retailers make their money from selling items at a markup. If Whole Foods becomes more competitive on price and can serve a larger geographic area due to Amazon's delivery logistics experience and technology, then those retailers will lose share.

Costco, however, does not make most of its money from selling stuff. Instead, the chain makes about 75% of its money from selling memberships. For the warehouse club to suffer because of the Amazon/Whole Foods marriage, it would need to lose members.

AMAZON BUYING WHOLE FOODS IS NOT AN AUTOMATIC DISASTER FOR COSTCO. IMAGE SOURCE: WHOLE FOODS.

Why won't Costco lose members?

Costco and Amazon have a lot of overlap when it comes to members. In fact, in October, Morgan Stanley published a paper where it estimated that nearly half (45%) of Costco members also had an Amazon Prime membership. That report, which was first covered by The Seattle Times, found that "Members of both Costco and Prime have not and generally do not intend to spend more with one retailer/e-tailer at the expense of the other," according to the report, which noted brand loyalty being a boon to both.

It's possible that a cheaper Whole Foods with same-day delivery eventually entices a small percentage of Costco members forgo their membership to the warehouse club. However, that day is far off as Amazon has to implement those changes.

Because it sells annual memberships, Costco will have time to adjust to any big moves Amazon makes. That makes it very premature to assume that Amazon owning Whole Foods means bad news for Costco.