No, Aeropostale (NYSE: ARO) hasn't been bought out yet.

Less than two weeks ago, I suggested that the clothier would make a great buyout candidate. In fact, I argued that it would be one of three great buyouts by private equity. Almost as if in response to that article, on Thursday a source at the teen retailer stated that its management wants the company to stay public, according to a New York Post report.

Whew! I'm glad the company got that settled. Except that it really doesn't settle anything.

When a company starts saying that it doesn't want to be bought, well, that's the kiss of death. Aeropostale has even hired Barclays Capital to bolster its takeover defenses, according to the New York Post. But to be honest, a lot of buyouts begin with the acquired company playing coy as a bargaining position.

So let's review why the teen retailer and two other picks would make great pickups in this environment.

1. Aeropostale
Aeropostale is like recent buyout J Crew, but cheaper. The retailer's perched atop a pile of cash that would make Scrooge McDuck envious, with zero debt. Its stock trades for just 10 times earnings, and the company practically gushes cash, with operating cash flow at 2.8 times its capital investment in the year ending in October. The company has been ramping up investment to support further growth. While same-store sales have been flat in the last quarter, Aeropostale's performance has been stellar throughout the recession. Laggards such as Abercrombie & Fitch (NYSE: ANF) have finally started to post gains in same-store sales, while Aeropostale is facing tough comparisons from a year ago. And last month, the company announced a $300 million increase in its buyback authorization. What more could you want?

2. Gap (NYSE: GPS)
Gap has many of the same traits as Aeropostale -- great cash flow, pristine balance sheet, and a good price. While Gap has been written off by many as a has-been retailer, the company still has a lot of life in it.

Over the past year, Gap generated more than three times as much cash as it put into its business. And it's already taken steps to make that business efficient, closing underperforming stores and reducing inventory. Better still, the company has invested in its fast-growing online and international operations. As evidence, the company's operating margin sits at its highest level in a decade.

The stock trades at less than 12 times trailing earnings, with a quickly growing yield that's up almost 20% annually over the last five years. The one argument against a private-equity buyout here is Gap's market cap of $13.5 billion -- much bigger than the sweet spot of $3 billion-$5 billion for most private equity deals.

3. NeuStar (NYSE: NSR)
This is a small-cap monopoly that mints money. And it's undiscovered. You may not be familiar with this company, but you've almost certainly used its services, especially if you've ever kept your phone number while changing mobile phones or dialed into a TV show to vote for a contestant. NeuStar connects telecoms of all types, from traditional wireline providers such as Frontier Communications to wireless providers such as Sprint and Verizon. Sitting at the nexus of these telecoms with its registry database, it's been able to generate 20% net profit margins consistently. Incredible!

NeuStar has a P/E of less than 18, and nearly 19% of its market cap is net cash. It is a cash machine, churning out six times as much cash as it's invested in its capital-light business.

Foolish takeaway
Will Aeropostale or any other company mentioned here be a buyout? Time will tell, but I'll be looking for all the protests from management saying that they want to remain public as a good indicator of what's happening behind the scenes.

Jim Royal, Ph.D., owns shares in Frontier. Netflix is a Motley Fool Stock Advisor pick. The Fool owns shares of Aeropostale. Try any of our Foolish newsletter services free for 30 days

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