Dollar Tree (NASDAQ:DLTR) hasn't been the same deep-discount leader since it acquired Family Dollar in 2015. Where it was once the industry's pure-play option, selling everything in its stores for $1 or less, the addition of Family Dollar -- with its variety of price points -- has left Dollar Tree struggling.

Sales rose 4.6% in the second quarter to $5.5 billion, but it was the Dollar Tree chain that led the way with same-store sales rising 3.7% for the period, while Family Dollar comps were flat. Year-to-date comps are up almost 4% at the former, and down 0.5% at the latter.

Shopping cart filled with coins

Image source: Getty Images.

Now billionaire investor Carl Icahn has reportedly taken a large stake in Dollar Tree, and though it's unknown what plans (if any) he has in mind, speculation is that he might seek to have Dollar Tree undo its Family Dollar acquisition. That would be an ironic twist, since it was Icahn who pushed Family Dollar to sell itself at the time. While he preferred Dollar General (NYSE:DG) be the acquirer, once the two chains got into a bidding war, Icahn bailed on Family Dollar and sold his entire stake, reportedly making a $200 million profit.

Ruining a good thing

As I saw it, it was never a good idea for Dollar Tree to buy Family Dollar. Although the acquisition tripled the number of stores Dollar Tree operated, putting it ahead of Dollar General, it also made Family Dollar's multiple-price-point business model the dominant one, since Family Dollar was bringing in more stores than what Dollar Tree owned. That upended what until then was a very sleek business model, one which consumers responded to because it more effectively allowed them to budget their trips to the store.

Of the three chains, Dollar Tree also had by far the best operating margins. But now the weight of carrying Family Dollar has dragged margins down to where they're comparable with Dollar General.

Since Dollar Tree is the best-run store, its stock also exceeded the performance of its rivals by nearly two-to-one. But since the acquisition closed, Dollar General stock has outpaced Dollar Tree about tenfold.

DLTR Chart

DLTR data by YCharts.

Preparing for change to come

Family Dollar was a broken business at the time of the acquisition, and though Dollar Tree has helped shore up some of the problems the chain had, the effect has not really been to boost Family Dollar, but to drag Dollar Tree down. And shedding Family Dollar could once again provide a spark for Dollar Tree's business and its stock.

Although dollar stores are not Amazon-proof, they are decidedly resistant. The dollar stores have remained resilient even in the face of e-commerce threats because of the fill-in nature of the customer visits they generate. Even with the addition of refrigerators and freezers, it hasn't changed the treasure hunt environment they're known for.

Yet Dollar Tree is bracing for a battle, as it just updated a change-of-control agreement with CEO Gary Philbin. Instead of giving him 1.5 times his salary and a bonus in the event there's a change in control at the company, he'll get 2.5 times his salary and bonus. Total compensation for Philbin is currently over $7.7 million.

Notably, it hasn't adopted a poison-pill defense to prevent someone from taking over the company. Dollar Tree seems to be ensuring that if it does happen, and Icahn uses his leverage to oust management, it will be well compensated. 

Dollar Tree shouldn't have bought Family Dollar to begin with, and Icahn -- having put in motion Family Dollar's sale in the first place -- -- can use this opportunity to fix the damage done to Dollar Tree as a result, while profiting from the experience once again.

This article represents the opinion of the writer, who may disagree with the “official” recommendation position of a Motley Fool premium advisory service. We’re motley! Questioning an investing thesis -- even one of our own -- helps us all think critically about investing and make decisions that help us become smarter, happier, and richer.