AUBURN HILLS, Mich. — Chrysler plans to revamp its struggling Dodge car brand under a new turnaround plan and says the company’s cash has grown by nearly $2 billion since it exited bankruptcy protection in June.

Under the plan, the automaker aims to introduce four new Dodges by 2013 and put new exteriors, interiors and engines on most of its current lineup. The new Dodges include a mid-size sedan for the North American market designed by Fiat SpA, the Italian automaker that now owns 35 percent of Chrysler.

That sedan is a key component of Chrysler LLC’s five-year overhaul, which is being outlined here. Chrysler lacks a competitive product in the segment, the largest in the U.S. car market.

The automaker’s sales are down sharply this year as a weak U.S. economy curbs overall demand for autos and buyers flee to other brands.

The 84-year-old Chrysler lost upward of $8 billion last year and would have run out of cash had the U.S. government not stepped in with $15.5 billion in aid. Chrysler was forced into bankruptcy protection earlier this year.

Chrysler CEO Sergio Marchionne said Wednesday the automaker’s cash has grown by $1.7 billion since it exited Chapter 11 this summer and totaled $5.7 billion at the end of September. He also said Chrysler was breaking even in that month.

Chairman C. Robert Kidder said the company intends to go public and repay its loans “with all deliberate speed.”

Another key to Chrysler’s revival is whether it can tackle quality problems. Doug Betts, senior vice president of quality, said work is under way.

He said the company has been restructured so the 14 teams focusing on specific areas act quickly to resolve problems.

When he arrived late in 2007, it took 71 days for someone to begin working on a problem, so Chrysler’s ability to raise its quality fell behind rivals.

“Seventy-one days goes to zero days,” Betts said.

Fiat has plans to replace most of Chrysler’s engines with its own. Paolo Ferrero, senior vice president of powertrain, said the number of Chrysler-designed engines will drop to 12 percent by 2014 from 84 percent currently, with many larger engines replaced by smaller, four-cylinder ones.