March 11 (Reuters) - Activist investor Starboard Value on Wednesday urged CarMax ( KMX ) to revamp its digital car-buying and selling platform and tighten costs, arguing the used-car retailer has "fallen well short of its underlying potential".

In a letter to incoming CEO Keith Barr, Starboard said simplifying CarMax's ( KMX ) online trade-in process and improving conversion rates could help the company regain market share as more consumers compare offers digitally.

Starboard, which holds a stake worth about $350 million in the company, also called on CarMax ( KMX ) to target selling, general and administrative expenses at 70%-75% of gross profit, arguing tighter cost discipline would help the company price vehicles more competitively and restore growth.

"We believe modest price reductions of approximately $100 to $300 per vehicle and combined with a more responsive, data-driven pricing system that adjusts in real time to local market conditions can restore competitiveness," Starboard said.

The investor also nominated Bill Cobb, chief executive of Frontdoor, along with Jeffrey Smith, Starboard's founder and CEO, to join CarMax's ( KMX ) board of directors.

Starboard added that advances in artificial intelligence could help CarMax ( KMX ) streamline workflows, cut manual processes, improve customer interactions and move away from legacy management systems.