Question

Shawn Pen & Pencil Sets Inc. has fixed costs of \(80,000. Its product currently sells for \)5 per unit and has variable costs of \(2.50 per unit. Mr. Bic, the head of manufacturing, proposes to buy new equipment that will cost \)400,000 and drive up fixed costs to \(120,000. Although the price will remain at \)5 per unit, the increased automation will reduce costs per unit to $2.00. As a result of Bic’s suggestion, will the break-even point go up or down? Compute the necessary numbers.

Short answer

Break-even point before buying the new equipment is 32,000 unit and after buying new equipment is 40,000 units.

The break even point is gone up due to new equipment.

Step-by-step solution

Break-even point before buying the new equipment

$\begin{array}{rcl}\mathrm{Break}\mathrm{even}\mathrm{point}& =& \frac{\mathrm{Fixed}\mathrm{cost}}{\left(\mathrm{Revenue}\mathrm{per}\mathrm{unit}-\mathrm{Variable}\mathrm{cost}\mathrm{per}\mathrm{unit}\right)}\\ & =& \frac{\$80,000}{\left(\$5-\$2.50\right)}\\ & =& 32,000\mathrm{units}\end{array}$

Break-even point after buying the new equipment

$\begin{array}{rcl}\mathrm{Break}\mathrm{even}\mathrm{point}& =& \frac{\mathrm{Fixed}\mathrm{cost}}{\left(\mathrm{Revenue}\mathrm{per}\mathrm{unit}-\mathrm{Variable}\mathrm{cost}\mathrm{per}\mathrm{unit}\right)}\\ & =& \frac{\$120,000}{\left(\$5-\$2\right)}\\ & =& 40,000\mathrm{units}\end{array}$

The break-even point of the company is increased after buying the new equipment.