Value-oriented retailer Dollar Tree (DLTR -0.16%) will soon have a new chief executive. Rick Dreiling, who is currently the chain's executive chairman, will officially take the day-to-day helm from Mike Witynski on Jan. 29.

There's no denying he's got the chops. The 69-year-old Dreiling has more than 50 years' worth of retail experience under his belt, including a seven-year stint as CEO of Dollar Tree's chief rival Dollar General (DG -0.59%). The question is, however, can Drieling do something Witynski was unable to do for the subpar-performing discounter? If he can, it's pretty clear where he'll need to start.

Dollar Tree's surprising sore spot

On the off chance you're not aware, Dollar Tree isn't just Dollar Tree anymore. The company acquired Family Dollar back in 2015, combining two distinctly different operations. Family Dollar is a chain of value-oriented stores selling goods at a variety of price points, while Dollar Tree's shtick from its onset was selling everything it offers at the singular price point of $1.

Inflation has since forced that figure up to $1.25. Indeed, in an effort to keep Dollar Tree's assortment compelling enough to keep shoppers coming back as well as combat the impact of inflation, many Dollar Tree stores now sell a small selection of goods for well over $1.25 apiece (although these items are still good overall values). Nevertheless, the Dollar Tree brand has seemingly struggled to find a sustainable balance between its rising inventory costs and customers' long-standing pricing expectations.

Curiously though, it's not the Dollar Tree arm that's weighing on the parent company's profits. It's Family Dollar, and that's despite the chain's pricing flexibility.

The image below tells the tale, comparing the two units' similar top lines and the two chains' oddly disparate bottom lines.

Dollar Tree is a much more profitable business than Family Dollar.

Data source: Dollar Tree. Chart by Author. All dollar figures are in millions.

Here's perhaps the more relevant comparison of each chain's gross margin rates and operating margin rates.

Family Dollar's profit margin rates are markedly lower than Dollar Tree's.

Data source: Dollar Tree. Chart by author.

For perspective, Dollar General's gross margin rates are usually on the order of 31%, while its net operating margins hover around 9%.

There's an explanation for the surprisingly different results being produced by Dollar Tree and Family Dollar: The different mix of merchandise the two business segments sell. Roughly half of Dollar Tree's top line comes from the sale of consumables like food, while the other half is driven by sales of miscellaneous non-consumable goods. Roughly three-fourths of Family Dollar's revenue stems from the sale of consumables, however, where profit margins tend to be thin. The remainder is evenly mixed between home goods, apparel, seasonal, and electronics. These categories tend to be more profitable than food and other items used up on a regular basis. Family Dollar just doesn't sell a lot of this other merchandise.

Worth watching, but not worth the risk of buying

The question remains: Can Dreiling actually do anything about Family Dollar's sales mix that will prevent its already-thin margins from slumping even further? Probably not anytime soon.

To the company's credit, it at least recognizes the problem. During the third-quarter earnings call held in November, CFO Jeff Davis said, "Family Dollar's gross margin declined 100 basis points, largely due to a product mix shift and product cost inflation."

He went on to say, however, "We expect to see continued pressure across both segments related to the inflationary cost environment and merchandise mix as our consumable sales are expected to continue outpacing discretionary." Neither Davis nor Witynski articulated a specific plan to combat pressured margins, other than to say they hope to sell relatively more non-consumable goods going forward.

And given the current circumstances, Dreiling may not have an immediate answer either despite decades of retailing experience. As Davis also noted during the call, "the economy continues to pressure middle- and low-household-income customers, resulting in needs-based purchasing [of consumables]" rather than the purchase of higher-margin discretionary goods.

Bottom line? While investors should give incoming Dollar Tree CEO Rick Dreiling the benefit of the doubt, that doesn't necessarily mean they should buy the stock just yet. He'll need to prove he can do what's not been done yet, which is altering the mix of what Family Dollar frequently sells. Until then, investors looking for a value-oriented retailer with the right merchandise mix at the right price being sold using the right business model will want to stick with Dollar General.