Dollar General Corporation (DG -1.72%) reported its Q2 financial results last month -- profits up 14% on a 6% revenue rise, with same-store sales growing 0.7%. Rival Five Below (FIVE -1.62%) reported 38% profit growth on a 21% gain in sales, with same-store sales shooting up 3.1%. But best of all were the results at Dollar Tree (DLTR 0.73%), where profits turned positive as sales soared 65.9% (boosted by sales from the acquired Family Dollar), with same-store sales up 1.2%.

And if you ask Goldman Sachs, that makes Dollar Tree the best dollar stock to buy -- while Dollar General and Five Below get relegated to the ranks of also-rans.

Here's what you need to know about the series of dollar-store stocks that Goldman rerated this morning.

A weak economy creates strong prospects for dollar stores. Image source: Getty Images.

1. It's a great time to go dollar-store shopping

As explained in a write-up on this morning, Goldman Sachs is generally bullish on the dollar-store sector as a whole. "Premised on value and convenience," says Goldman, dollar stores are especially attractive to "low-income households" suffering from "sluggish wages lagging inflation in the cost of living," and working longer hours, "driving the appeal of convenience." All things considered, says Goldman, what's bad news for the American economy is "a good cycle for the dollar stores."

2. Why Dollar Tree is best

Within the sector, Goldman likes Dollar Tree best, and has rated the stock a "conviction buy" with a price target of $101 per share -- implying 22% upside from today's prices. Although it's true that at a valuation of nearly 28 times earnings, Dollar Tree stock looks expensive today, Goldman believes that it's "benefiting from secular shifts toward value and convenience," and at the same time enjoys "the added benefit of synergies" from its Family Dollar acquisition.

According to Goldman, although analysts quoted on S&P Global Market Intelligence believe that Dollar Tree will experience a steep post-merger earnings decline this year, Dollar Tree stock will rebound quickly, and could "nearly double" its 2015 earnings by 2018.

3. Why Dollar General and Five Below are not

At the same time, the seemingly cheaper Dollar General stock, which costs less than 17 times earnings today, has less growth potential in Goldman's view. Priced at $72 and change today, Goldman sees Dollar General stock rising only to $84 -- a 16% rise, but only good enough for a neutral rating, according to the analyst.

Conversely, the analyst calls Five Below "priced to perfection" at a price-to-earnings ratio of more than 38. Analysts quoted on S&P Global see Five Below growing faster than its competitors, with an expected growth rate of 24% annually over the next five years. But given the sector-high P/E ratio, Goldman has decided to sit on the sidelines and wait for better prices. The analyst rates this one, too, as only neutral.

The most important thing: Valuation

Setting the three stocks side by side, Five Below sports a PEG ratio (its P/E, divided by its growth rate) of 1.4, while Five Below is even pricier at 1.6. That being the case, I'm inclined to agree with Goldman's decision to refrain from recommending either of those stocks.

That said, the consensus on Wall Street is that Dollar Tree itself is no great bargain. Indeed, its 28 P/E, when divided by consensus growth rates of only 18%, suggests that at a PEG ratio of 1.6, Dollar Tree is fully as overvalued at Five Below, and even more expensive, valuation-wise, than Dollar General.

In order for Goldman Sachs to be proven right about recommending Dollar Tree over its rivals, therefore, it's essential that Dollar Tree grow much faster than most analysts on Wall Street currently believe possible -- probably something on the order of mid- to upper-20s percentile growth -- and moreover, it needs to grow quick to hit Goldman's targeted doubling of earnings by 2018.

Can Dollar Tree fulfill the promises that Goldman is making on its behalf? We'll find out in just a few months. Dollar Tree reports its Q3 earnings on Nov. 22.