The parent company of Steak n Shake has raised its offer for a small Michigan insurer that spurned its advances late last year.

Biglari Holdings Inc. has offered to acquire the outstanding shares of Fremont Michigan Insuracorp Inc. for $29 per share in cash, a 41-percent premium to Monday's closing price. The deal values the property and casualty insurer at $51 million.

Biglari Holdings plans to take its offer to Fremont's board, which rejected a lower offer from Biglari in December 2009. A statement from the San Antonio-based company led by activist-investor-turned-CEO Sardar Biglari implores the board to come to the table to fulfill its "fiduciary duties" to shareholders and "reach a mutually satisfactory transaction."

The company has not revealed its plans for Fremont, but investment advisers say Biglari wants to use the firm's $60 million investment portfolio to fund more acquisitions, following in the footsteps of his investing hero, Warren Buffett. Buffett's Berkshire Hathaway acquired its first insurer in the 1960s and now funds billions of dollars in investments through the portfolios of its insurance companies.

Fremont rejected a bid for $24.50 per share last year, a premium of just 11.3 percent, describing the offer as a "hostile takeover attempt." At the time, the company said its own strategy represented "a better long-term value for shareholders."

The shares have steadily fallen since Fremont rejected the original offer, closing at $20.50 each on Monday. Fremont soared more than 36 percent in early trading Tuesday, with volume more than 85 times the stock's average. Biglari shares were trading down slightly, at $388 each.

Fremont, which provides insurance to individuals, farms and small businesses in Michigan, has not responded to the latest offer.

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.”

Fremont has 1.77 million outstanding shares. Biglari would have to pay about $46 million for the shares it doesn't already own, by IBJ's calculation.

Biglari took over Indianapolis-based Steak n Shake Co. in a 2007 proxy fight, helped return its restaurants to profitability, then transformed it into a holding company for a diverse range of investments.

The renamed company, which relocated its headquarters to San Antonio, has moved aggressively to invest or take over other firms, including Advance Auto Parts and Sonic Corp. The Steak n Shake restaurant operations remain in Indianapolis.