Check out the latest Dollar Tree earnings call transcript.

Dollar Tree (DLTR 2.47%) has been struggling for years, weighed down by its 2015 acquisition of Family Dollar. That deal vastly expanded the number of stores it operated, but also changed the company's business model from selling all goods for $1 or less to one with a sliding scale of prices.

Activist investor Starboard Value thinks it's time to undo the mistake Dollar Tree made. First, it wants the company to sell the Family Dollar chain. But the hedge fund also suggests that it's time for Dollar Tree to break the dollar barrier and begin selling goods for higher prices. While there's some sense to the proposals, there is also a risk that they could do much more harm than good.

Shopping cart filled with coins

Image source: Getty Images.

Cutting loose

The easier point to agree with is selling Family Dollar. The chain was ailing before Dollar Tree bought it, and because the deep discounter had to take on so much debt to finance the transaction, it has become distracted by trying to get Family Dollar back on track. In the process, its own performance has suffered.

Whereas Dollar Tree had been the most profitable dollar-store chain -- generating much fatter operating margins than either Family Dollar or the similarly-positioned Dollar General (DG 0.87%) -- Starboard Value points out that it is now suffering from margin compression.

Dollar Tree's stock had also outperformed its rivals, quadrupling in value over the five-year period before the acquisition, while Dollar General and Family Dollar had much lower gains.

Dollar Tree has two choices: either it can invest more time and money in Family Dollar and hope for a turnaround (which hasn't happened in four years of ownership), or it can sell the chain and start fresh. Dollar Tree might not get all that much for Family Dollar because it remains damaged goods. Still, by cutting its losses on Family Dollar, Dollar Tree would be able to focus on its core business going forward.

A dollar and change

Starboard Value's second proposal is much more controversial because it runs counter to Dollar Tree's image for selling everything for $1 or less. Raising prices could potentially lead to customer backlash. Arguably, the one-price model is what made Dollar Tree a superior business in the first place.

Starboard Value does make a compelling case that when Canada's Dollarama raised prices to as high as $2, it saw same-store sales growth double as average ticket size and store traffic rose. That's likely because it was able to bring new and better products into its stores.

As the hedge fund points out, Dollar Tree has maintained the $1 threshold for 30 years. Because of inflation, Dollar Tree's products are now smaller or of lesser quality than they once were.

A different animal altogether

Dollar Tree had flirted with the dollar-and-above model even before buying Family Dollar, without much success. For nearly a decade prior to the acquisition, it operated a small dollar-and-above chain called Deal$, which it shut down in 2016. Raising prices at the core Dollar Tree chain might simply make it a new version of Family Dollar that would compete directly with Dollar General. It would also have to contend with European grocery giants Aldi and Lidl, which have made a big push into the deep-discount market and are expanding rapidly in the U.S.

Aldi and Lidl are different animals, targeting supermarket consumers, much the way Five Below goes after the wallets of teens and tweens. But if Dollar Tree expands the universe of goods it sells, it will have to compete against a broader set of competitors.

Starboard Value does want to limit how high Dollar Tree raises its prices, suggesting that $2 could be the maximum, with most goods still selling for a buck. But if Dollar Tree were to move away from being the dollar-store pure-play it is now, it would be difficult to reverse course. The change could make it a much worse business than it is today.