The hedge fund run by Sears CEO Edward Lampert has sent the ailing retailer a proposal to buy its popular Kenmore appliance brand and a piece of its home services division.

Sears Holdings Corp. began formally exploring the sale of pieces of the business after Lampert’s ESL Investments expressed interest in acquiring them earlier this year.

ESL’s proposal valued Kenmore at $400 million, excluding the impact of cash or debt, according to a letter from ESL to a Sears board committee that was filed Tuesday with the Securities and Exchange Commission.

A separate proposal valued the Sears Home Services divisions’ home improvement business at $70 million, with a potential extra $10 million if the company met certain financial benchmarks.

In both cases, ESL proposed a cash acquisition and said the proposals are nonbinding.

ESL said it is “prepared to move as quickly as possible” and could enter into definitive agreements as soon as Aug. 24 and close on the acquisitions within 60 to 90 days.

Lampert’s fund’s initial letter offering to buy certain Sears assets and break up the company also included the Sears Home Services Parts Direct business and certain Sears real estate assets. According to the letter, ESL is still considering Parts Direct and plans to work with outside investors on a real estate deal, but wanted to move ahead with the proposal for Kenmore and the home improvement division.

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