(Reuters) - Activist investor Starboard Value LP on Monday called on Dollar Tree Inc to explore a sale of its underperforming Family Dollar business and nominated directors to replace a majority of its board after revealing a stake in the company.

"We believe Dollar Tree should explore all strategic alternatives for Family Dollar, including a sale of the business," Starboard Chief Executive Officer Jeffrey Smith said in a letter addressed to Dollar Tree CEO Gary Philbin.

The retailer bought Family Dollar in 2015 for about $8.5 billion in a bid to fend off growing competition from Walmart Inc and fellow discounter Dollar General Corp.

However, close proximity to certain Dollar General and Walmart stores as well as a growing shift to online shopping led to sluggish same-store sales growth and a nearly 15 percent decline in the company's stock price last year.

A sale of Family Dollar would likely fetch less than the price Dollar Tree paid for the business, Starboard said, but still urged investors and the management to back a sale for the struggling chain.

"The market is likely only ascribing approximately $1 billion - $3 billion of value to Family Dollar based on the current stock price," Smith said.

Starboard said it was also seeking to replace seven directors on the retailer's 12-member board, effectively giving it majority control.

Dollar Tree, however, said its board was equipped with the right "skills and perspectives" to make its business a success, especially after adding four new independent directors since May 2016.

The company also said that Starboard's nominations came out of the blue without any prior engagement or communication.

The activist investor also urged the company to explore and implement a multiple-price point strategy that would be above the $1.00 ceiling, which Dollar Tree has maintained since its founding thirty years ago.

Starboard said that Dollar Tree's existing price ceiling has restricted it from offering better quality products, while having multiple price points have worked in favor of rivals Dollar General and Canada's Dollarama Inc.

"We believe that Dollar Tree is deeply undervalued and significant opportunities exist to create value," Starboard said.

(Reporting by Aishwarya Venugopal in Bengaluru; Editing by Shinjini Ganguli)

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