Helen of Troy has already suggested that it would return money to investors, but it wasn’t interested in selling itself, despite calls from an activist investor.

Then on Monday, the consumer products company unveiled a doozy of a shareholder-payout program.

Helen of Troy said that it would buy back $550 million worth of its shares over the next three years, to be financed by cash on hand and loans. It will begin with a $300 million tender offer starting immediately.

The buyback is huge, representing nearly 29 percent of the company’s outstanding stock. But it isn’t clear whether Sachem Head Capital Management, the hedge fund looking to shake up the consumer products maker, will find it enough.

In a letter sent last week, Sachem Head argued that the company — which owns the housewares maker Oxo International and produces products for brands like Revlon and Dr. Scholl’s — should consider selling itself, given what the hedge fund said was interest from a number of potential suitors.

Helen of Troy responded that it believed its shares were undervalued, and that its board had already taken steps that addressed Sachem Head’s complaints on matters including executive compensation and a succession plan for chief executive.

But Sachem Head also suggested that if the company wouldn’t sell itself, it should consider taking on debt to finance buybacks or special dividends.

What Helen of Troy announced on Monday hews pretty closely to that alternative, though the company noted that it said last year that it would return capital not earmarked for strategic acquisitions to shareholders.

“Utilizing our strong balance sheet to fund a significant share repurchase provides immediate and continuing benefits to shareholders and underscores our confidence in the company’s current strategy and future growth potential,” Timothy F. Meeker, the company’s chairman, said in a statement.

It isn’t clear whether Sachem Head, whose founder is a protégé of the veteran activist investor William A. Ackman, will be appeased by the plan. A spokesman for the hedge fund declined to comment.

Other investors seemed pleased, however. Shares in Helen of Troy traded near highs on Monday afternoon at $63.56, up 7 percent for the day.