It's one of the more unusual marriages in American big business -- and it's ending in divorce. Starting next year, American Express (AXP 6.22%) will no longer be the exclusive credit card accepted at Costco Wholesale (COST -0.24%) stores.

Additionally, the AmEx and Costco co-branded TrueEarnings card will no longer be issued or accepted.

AmEx's tie-up with the mammoth retailer brings it a lot of business, so it's no wonder that the loss was taken hard by its investors. Here's a look at why this breakup occurred and the ramifications for both companies.

Mismatch
In retrospect, AmEx and Costco were always an odd couple.

The former has traditionally slanted its offerings to affluent shoppers, calling its cardholders "members" as if they've all joined some fancy club. The latter sells large quantities of items aimed at people who want to save money; its customer base is wide and typically not rich.

Yet apparently there was enough overlap to mutually benefit both parties. According to AmEx, around 20% of its worldwide loans and 10% of cards in use derived from the co-branding arrangement.

The partnership has been in force for 16 years (although it hasn't meant that rivals are entirely shut out -- Costco accepts debit cards from the other major card brands).

Lately, the relationship has been a bit shaky. Last year, Costco Canada dropped AmEx as the exclusive credit card at its stores and as its co-branding partner. These were replaced with, respectively, the MasterCard (MA 0.15%) network and co-branded MasterCards issued by Capital One Financial. Last week's decision can be seen as a follow-up to the Costco Canada move, albeit on a much larger scale.

Finding new mates
In this latest development, AmEx and Costco's arrangement was up for renewal, and apparently Costco's terms for extending were too burdensome for AmEx. So the partnership now has an end date: March 31, 2016, to be exact, for both AmEx credit card acceptance at the company's stores and the validity of TrueEarnings cards.

(MA 0.15%)

Meanwhile, Costco should gain handsomely from accepting cards that are much more prevalent (going into 2014, Visa had a total of around 285 million cards outstanding, MasterCard had 178 million, and AmEx had 53 million). And cheaper to process: AmEx charges merchant fees of around 3% per transaction, significantly higher than those charged by either Visa or MasterCard.

As for AmEx, some investors pushed the panic button when the Costco news hit the wire late last week and the firm's stock closed down by 6% that day. What didn't help was the subsequent media reports that suggested its co-branding deal with airline JetBlue would also come to an end (although, in contrast to the Costco arrangement, AmEx is not the carrier's exclusive co-brander).

This Fool's take
I think the fear is overblown. As MarketWatch commentator Jeff Reeves insightfully pointed out last Friday, if every single Costco purchase in 2014 had been made with one of AmEx's cards -- a serious hypothetical stretch -- it would have meant roughly $3.4 billion in revenue for the credit card purveyor.

That highly theoretical figure is less than 10% of what AmEx's top line was last year. Yes, it's a chunk of change, but hardly a catastrophe if it slips away. There are other retailers and potential co-branding partners out there to help make up for the loss, and plenty of would-be cardholders for AmEx to entice (particularly now that it's offering products targeted at the less affluent).

Besides, since TrueEarnings is a well-liked product judging by the reviews of its cardholders, it's very likely that many of them will switch to another AmEx card once the Costco plastic expires.

Lastly, the company has time to start making up for the loss; again, the partnership doesn't technically expire until the end of next March.

Meanwhile, AmEx stock was cheap on several yardsticks (P/E and dividend yield, to name two) compared to Visa and MasterCard even before the Costco news walloped the market. For value hunters, this latest dip might just be a fine opportunity to buy the shares at a bargain price.