The offer of 30p per share comes after 12 years of often acrimonious relations between Mr Sugar, who founded the consumer electronics company, and the City.
Although Mr Sugar was feted by investors as one of Britain's most dynamic entrepreneurs at the height of the consumer boom of the late 1980s, the company's share price has been in steady decline for several years.
Mr Sugar is understood to be disappointed with Amstrad's performance in the harsh trading climate of the 1990s and believes that the stock market is undervaluing the company. Fierce competition in the personal computer market and weak consumer spending have pushed the company into a deep loss. Next month it is expected to report a pounds 75m pre-tax loss for the year ended 30 June. There are also fears that it will pass the dividend.
But the company has built up a cash pile of more than pounds 100m by unloading its computer stocks at little or no profit.
Amstrad shares, which peaked at 220p in 1988, closed at 28p yesterday, 3p higher on the day.
The company rose to prominence by selling word processors and personal computers at sharply lower prices than its rivals. But fierce competition led to a savage price-cutting war.
Amstrad, an acronym for Alan Michael Sugar Trading, was floated in 1980, when it was valued at pounds 8m. At its peak the company was valued at more than pounds 1.3bn.
But a move into the computer market for corporate users has failed, initially because of delays in bringing new high-performance personal computers to the market.
In July, Amstrad's group finance director and corporate finance director both resigned suddenly. There are no non-executive directors on the board.
Mr Sugar is set to join a number of entrepreneurs, including Richard Branson and Andrew Lloyd Webber, the composer, who have returned to the private domain by buying out their companies.
He fell out of favour 18 months ago after he sold a 7.5 per cent stake in the company at 79p a share for a profit of pounds 34m, which he invested in private ventures, including a controlling stake in Tottenham Hotspur Football Club. Since then Amstrad's performance has declined steadily.
Yesterday's proposed buyout terms drew a sharp response from some analysts. 'I think the price is very low and will be viewed in the City as a final insult,' one said.
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