NEW YORK (The Deal) -- Though activist investor Jana Partners said in a regulatory filing this week it believes the best option is for pet retailer PetSmart (PETM) to sell itself -- preferably to a financial sponsor -- industry experts are trying to figure out how that math would work.

One of the reasons for that is the perceived success rate of the activist. When Jana revealed it had a 9.9% activist stake at the start of the month, the stock predictably spiked. That, and other financial metrics, led news outlets to suggest a deal might be a stretch for PE.

A review of the numbers suggests otherwise.

Ebitda at the company is projected to grow, though, at a slower pace, according to analysts' estimates compiled by Bloomberg. For the fiscal year ended Feb. 3, PetSmart had almost $930 million in Ebitda as compared to $890 million for the prior year. And Ebitda is expected to grow to about $940 million for the curent fiscal year ending Jan. 31, 2015 while the fiscal year after that Ebitda is projected to grow to roughly $960 million.

On July 2, the day before Jana revealed its stake, PetSmart's unaffected stock price closed at nearly $60 a share, giving the company a market cap of about $5.95 billion. Adding debt of nearly $520 million and subtracting cash of about $230 million to that amount (per Bloomberg data), would equate to an enterprise value of $6.24 billion or a valuation multiple of 6.7 times Ebitda (using the $930 million Ebitda figure for its current fiscal year).

That's under the unaffected 7 times multiple PE firms look for when considering potential buyout targets.

But since Jana revealed its stake on July 3, the stock has jumped, now trading at around $68 per share, giving it a market cap of almost $6.75 billion and an enterprise value of roughly $7 billion, or close to 7.6 times Ebitda.

A industry source said at that price, PetSmart is becoming rich in price for PE.

But PE usually assumes around a 20% premium to the unaffected stock price, if the enterprise value is below 7 times Ebitda. That would mean PE might be willing to pony up around $72 a share for a company with stable but solid Ebitda and cash flow, even if the company has issues, with the idea that it can bring in new management and cut costs.

A $72 per share offer would equate to a market cap of about $7.14 billion, based on about 99.2 million shares outstanding, and an enterprise value of $7.43 billion, or a multiple of nearly 8 times Ebitda -- within the range of what PE firms have been willing to pay for retailers.

And PetSmart sells products in a sector that has been very active for M&A, as consumers are willing to spend increasingly more on products for their pets.

Yet at a price tag of over $7 billion, a deal has its hurdles, the industry source said. At that size, it would mean the deal would have to be syndicated, involving more than one PE firm. Assuming that in a leveraged buyout, debt financing of 7 times Ebitda can be obtained, would still mean that the acquirers would have to sink around $900 million of equity or cash into a deal­ - a hefty check.

But what also has to be figured in is PetSmart's real estate and equipment. According to filings with the Securities and Exchange Commission, those assets are valued at almost $950 million and can be monetized through a sale leaseback, for example.

Plus, Jana has received backing from asset manager Longview Asset Management LLC, which not only supported the sale idea, but said that in some situations it might even consider rolling its 9% stake in the purveyor of pet products into a leveraged buyout. That would mean less leverage for a deal.

Jana said in the letter to the PetSmart board attached to Tuesday's filing it fears that the company is attempting a leveraged recapitalization of the company without a firm turnaround plan in place. Jana said that it could push for change at the board level at its next annual meeting if its suggestions, such as conducting a strategic review that could include a sale, aren't explored.

A source familiar with the situation said PetSmart already has been approached by PE firms interested in doing due diligence, but have been rebuffed, which, in turn galvanized Jana into going activist. Firms such as or similar to Apollo Global Management LLC and Apax Partners LLP, would be likely candidates, though these were examples and there is no indication that they had actually approached the company.

Another option would be for PetCo Animal Supplies Inc., backed by PE firms Leonard Green & Partners LP and TPG, to merge with PetSmart, with the two PE firms either buying out PetSmart and taking it private, or having PetSmart acquire PetCo, with the two firms taking shares in the listed entity, allowing the two firms to exit the long-held portfolio company.

The private equity firms have already profited, taking out almost $1.2 billion dividends through recaps in 2010 and 2012. When the two firms took PetCo private in 2006, the companies invested about $775 million in equity with $350 million from Leonard Green and $415 million from TPG.

It also demonstrates how lucrative a deal in a pet retailer can potentially be. According to a source, PetCo is leveraged at 6.5 times Ebitda.

An industry source said that with the intense competition from big box players and e-commerce, a merger of the two top pet retailers would likely not be blocked by regulators, and is a trend in general that will continue, leaving only one category killer standing as legacy brick-and-mortar players contend with the internet.

PetSmart declined comment, as did Jana and Longview. TPG also declined comment while Leonard Green did not respond to a request for comment.