A company's sales have increased from $100 million to $105 million over the past year.

To match the profit increase resulting from a sales increase of $5 million (from $100 million to $105 million) with a 10% profit margin, the profit increase is $0.5 million. Given that 50% of product costs are spent on materials, the material cost reduction needed to achieve the same profit increase can be calculated as follows:

Current materials cost = 50% of $100 million = $50 million.

Desired profit increase = $0.5 million.

Required material cost reduction = ($0.5 million / $50 million) x 100 = 1%. Therefore, a 1% reduction in material costs is needed to match the profit increase. References: Financial management textbooks and principles, cost reduction strategies, and profit margin analysis.