A small Michigan insurer that the parent company of Steak n Shake unsuccessfully tried to buy twice has been acquired by another insurer.

The outstanding shares of Fremont Michigan Insuracorp Inc. will be purchased by Dearborn, Mich.-based Auto Club Insurance Association, the companies announced on Monday.

ACIA will pay $36.15 per share in cash, valuing the property and casualty insurer at $67.7 million.

Steak n Shake parent Biglari Holdings Inc. owns 9.7 percent of Fremont’s stock, and will still turn a big profit on the deal.

“I have enjoyed working with Fremont’s chairman of the Special Committee in our effort to realize the full value of Fremont’s shares,” Biglari Holdings CEO Sardar Biglari said in a written release. “The merger with ACIA represents a victory for all Fremont stockholders.”

The $36.15 per-share purchase price represents a premium of about 35 percent above the $26.75 per-share closing price of Fremont on April 15, the last trading day prior to the announcement of the deal.

Biglari Holdings twice made offers to buy the insurer over the past two years but was rebuffed both times.

Fremont rejected a bid for $24.50 per share in 2009, a premium of just 11.3 percent over the stock price, and described the offer as a “hostile takeover attempt.”

Biglari Holdings raised its bid In October 2010, offering $29 per share in cash, a 41-percent premium.

Investment advisers say Sardar Biglari wanted to use the insurer’s $60 million investment portfolio to fund more acquisitions, following in the footsteps of his investing hero, Warren Buffet.

In October 2009, Steak n Shake disclosed that it had purchased a roughly 10-percent stake in Fremont shortly after Biglari said he intended to transform Steak n Shake into a holding company to pursue purchases “either related or unrelated to its ongoing business activities.” Steak n Shake bought about 172,000 shares of the company for about $3.5 million, a per-share price of about $20.35.

Biglari took over Indianapolis-based Steak n Shake Co. in a 2007 proxy fight and renamed the company, moving its headquarters to San Antonio.