After Whole Foods Market (NASDAQ: WFM) revealed its pending sale to Amazon (NASDAQ:AMZN) last Friday for $13.7 billion plus debt, CEO John Mackey told employees at a town hall meeting that a merger of the two companies had actually appeared to him in a dream about a year and a half ago.

Since the deal's announcement, investors have pushed Whole Foods' stock up nearly a dollar over Amazon's $42-per-share bid, indicating belief that a prominent grocery chain may try and nudge Whole Foods' management awake from its pleasant dream with a competing offer.

Few grocers have the moxie and the means to launch a disruptive sally. Let's take a look at the three largest and most likely of spoilers: Kroger Co (NYSE:KR), Costco Wholesale Corporation (NASDAQ:COST), and, of course, the retailer that's evolving into Amazon's arch-nemesis: Wal-Mart Stores Inc. (NYSE:WMT).  

Vector illustration of hands holding up signs labeled "Bid" as a gavel comes down.

Image source: Getty Images.

It's interesting that none of the three corporations holds enough ready money to compete with cash-rich Amazon on this deal. Kroger, Costco, and Wal-Mart each sport balance sheets that appear to belong to, well, grocers with razor-thin margins. Take a look at the numbers below:

Metric  Kroger Costco Wal-Mart
Cash and investments $0.4 $5.7 $6.5
Receivables $1.4 $1.5 $5.2
Inventory $6.4 $9.7 $43.4
Other $1.4 $0.4 $2.2
Total current assets $9.5 $17.3 $57.3
       
Payables $6.1 $9.4 $41.4
Current portion of short-term debt $1.9 $1.2 $2.6
Other $4.5 $10.8 $30.2
Total current liabilities $12.5 $21.4 $74.2
       
Working capital ($3.0) ($4.1) ($16.9)

All dollar figures in billions. Data sources: SEC 8-K filings, most recent quarter for each company.

Each grocery giant is perennially underwater in terms of working capital -- the excess of current assets over current obligations. Make no mistake, to present an attractive all-cash deal like Amazon's, each would end up financing 100% of a takeover of Whole Foods, regardless of how the respective management teams might spin it.

Let's say Costco presents an offer of, say, $14.5 billion and tells the market that it's using $3 billion of cash on hand, and borrowing the rest. In real terms, Costco would end up borrowing the entire amount; it's just that the company would increase long-term debt and/or tap credit lines post-deal closing to compensate for the $3 billion that's already in service to plug a hole in its working capital.

If debt-issuance is a given, how does each company stand on its ability to tap the public markets to raise funds for a buyout? Below is a comparison of the grocers' current debt-to-EBITDA ratio, a measure of total borrowings versus annual earnings:

 Metric Kroger Costco Wal-Mart
Long-term debt $13.4 $4.0 $39.7
EBITDA $5.2 $5.2 $33.1
Debt to EBITDA 2.6 0.8 1.2

All dollar figures in billions. Data sources: Ycharts, and SEC 8-K filings. Debt as of most recent quarter for each company, and EBITDA as of last trailing 12 months.

So far, so good. Costco and Wal-Mart each exhibit very low leverage, and Kroger's total leverage can be thought of as moderate.

Now let's assume a competitive bid will land at least 10% beyond Amazon's offer to be seriously entertained by Whole Foods' shareholders. This would bring the total cash deal price to $15 billion. We'll add this financing total to each company's current borrowings, as well as Whole Foods' $1 billion of debt, which must be assumed.

But we'll also add to each organization's earnings the $1.3 billion in annual EBITDA that Whole Foods will contribute (without considering any increased sales, cost-cutting, or synergies, for the sake of simplicity): 

  Kroger Costco Wal-Mart
Projected long-term debt $29.4 $20.0 $55.7
Projected EBITDA $6.5 $6.5 $34.4
Projected debt to EBITDA 4.5 3.1 1.6

All dollar figures in billions. Data sources: Ycharts, and SEC 8-K filings. Debt as of most recent quarter for each company, and EBITDA as of last trailing 12 months.

You can see right off that Kroger is in a bit of a red zone. Borrowings of nearly five times EBITDA isn't very comfortable leverage for a company with 1.7% annual profit margins.

Moreover, this acquisition isn't really a strategic fit for Kroger. The grocer has been able to win market share from Whole Foods over the last few years with its own natural and organics "Simple Truth" line. 

Paying a premium to acquire Whole Foods would find Kroger purchasing natural and organic foods market share at a lower rate of return than it can create by simply competing in the open market. The cash return to a buyer of Whole Foods at the current share price of $43 is around 9%.

(According to Whole Foods and Amazon in a regulatory filing, the Enterprise Value (EV) to EBITDA ratio of this deal is approximately 10.6 times, based on the last 12 months' earnings and a $42 share price offer. Now trading at $43 per share in anticipation of bid competition, Whole Foods's EV to EBITDA ratio is closer to 11.0. Inverting the EV to EBITDA ratio approximates the cash return of an investment to the acquirer. At the present ratio of 11.0, Whole Foods will generate a cash return of just 9% to a potential buyer.)

This is less than Kroger's trailing-12-month return on invested capital (ROIC) of nearly 12%.

As for post-merger optimization, Kroger wouldn't likely be able to squeeze out much more than the $300 million in annual cost savings Whole Foods' management team will capture by 2020, on top of a previous $300 million productivity goal, which is nearly complete. And Kroger doesn't have the tools at its disposal that Amazon does to immediately boost revenue. 

The situation isn't much different for Costco, which has also taken some of Whole Foods' market share while producing a ROIC in the mid-teens over the last several years. By some estimates, Costco boasts a higher dollar volume of organic sales than Whole Foods, having crossed the $4 billion mark in organic foods revenue in 2015. However, its business model is vastly different than the organic grocer's.

With an emphasis on value and the absence of frills, and a distaste for the sort of experiential retailing that characterizes a grocery trip to Whole Foods, there's not a discernible cultural mesh between the two companies.

We should note that when Amazon purchased the socially conscious online shoe retailer Zappos in 2009, it largely left the company to operate within its own cultural moorings, while enormously expanding the reach of its products.

In short, tipping into moderate or slightly high leverage -- for an imperfect strategic fit -- would be a defensive rather than a logical action on Costco's part. 

A bid that might make sense

In contrast to its two market-leading peers, Wal-Mart could easily step in and raise the stakes on Amazon. The organization's balance sheet is so huge that borrowing a measly $15 billion would only raise its financial leverage to a reading of 1.6.

And, its tremendous earnings power enables Wal-Mart to add whatever additional debt might be required to outlast Amazon in successive bidding rounds. Remember that number of $13.7 billion that Amazon is paying for Whole Foods? Wal-Mart earned $13.6 billion over the last four business quarters.

While it's hard to imagine that Wal-Mart can optimize Whole Foods' processes, technology, distribution, and online marketing to the extent that Amazon can, it's still a more strategic buyer than other competitors.

Wal-Mart already has years of experience in one of the evolving fronts of the grocery battleground that is crucial to Whole Foods: smaller-format stores. Supply chain and operational efficiencies developed through Wal-Mart's "Neighborhood Market" locations can potentially assist Whole Foods as it scales its "365 By Whole Foods" value concept. And Whole Foods very much needs to ramp up 365 units to better compete with Trader Joe's, Aldi, and the latest European competitor to enter the U.S., German deep discounter Lidl

Should any of these heavyweights actually follow through?

I'm not sure it's in the best interest of any of these three companies to attempt to thwart Amazon. Whole Foods is a complicated business at a crossroads. It generates superior margins through a loyal customer base, which is willing to pay for the company's higher product standards. Yet there isn't a clear and quick solution to improving its declining same-store sales, hurt by non-core customers who have been peeled away by competitive pricing from grocers of every stripe as of late. 

Thus, interrupting Amazon's bid wouldn't constitute a strategic action that yields huge synergies to the winner of a bidding war. In the hands of Kroger, for example, it would be an act of desperation simply intended to stem the pace of Amazon's disruption to the industry.

Guess what? Amazon is going to disrupt the grocery business no matter what. It makes more sense for competitors to pour the equivalent amount of acquisition money into their own operations, improve technology, get leaner, and compete.

John Mackey, CEO of Whole Foods Market, is a member of The Motley Fool's board of directors. Asit Sharma has no position in any stocks mentioned. The Motley Fool owns shares of and recommends Amazon, Costco Wholesale, and Whole Foods Market. The Motley Fool has a disclosure policy.