A company can manufacture a product using hand tools. Tools will cost $1,000, and the manufacturing cost per unit will be $1.50. As an alternative, an automated system will cost $15,000 with a manufacturing cost per unit of $0.50. With an anticipated annual volume of 5,000 units and neglecting interest, the breakeven point (years) is most nearly:

2.8 years

Explanation:

Assume that the number of years it will take for both alternatives to be equal is "t". The breakeven point can be found by equating the fixed cost formulas of both alternatives.

First alternative:

= 1,000 + (1.50 * 5,000 units) * t

Second alternative:

= 15,000 + (0.5 * 5,000) * t

1,000 + 7,500t = 15,000 + 2,500t

7,500t - 2,500t = 15,000 - 1,000

5,000t = 14,000

t = 14,000 / 5,000

t = 2.8 years

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