Question

Hudson Co. reports the contribution margin income statement for 2017 below. Using this information, compute Hudson Co.’s (1) break-even point in units and (2) break-even point in sales dollars.

HUDSON CO.
Contribution margin income statement
For the year ended December 31, 2017
Sales (9,600 units @ \(225 each)	\)2,160,000
Less: Variable cost (9,600 units @ \(180 each)	1,728,000
Contribution margin	432,000
Less: Fixed cost	324,000
Pre-tax income	\)108,000

Short answer

1. Break-even point in units:7,200 units.
2. Break-even point in dollars:$1,620,000.

Step-by-step solution

Definition of Break-Even Units

The number of units that a business entity must sell to achieve the situation of no-profit, no-loss is known as break-even units. It is calculated using the fixed cost and the contribution margin per unit.

Break-even point in units

$\begin{array}{rcl}\mathrm{Break}-\mathrm{even}\mathrm{point}\mathrm{in}\mathrm{units}& =& \frac{\mathrm{Fixed}\mathrm{cost}}{\mathrm{Sales}\mathrm{price}\mathrm{per}\mathrm{unit}-\mathrm{Variable}\mathrm{cost}\mathrm{per}\mathrm{unit}}\\ & =& \frac{\$324,000}{\$225-\$180}\\ & =& 7,200\mathrm{units}\end{array}$

Break-even point in dollars

$\begin{array}{rcl}\mathrm{Contribution}\mathrm{margin}\mathrm{ratio}& =& \frac{\mathrm{Sales}-\mathrm{Variable}\mathrm{cost}}{\mathrm{Sales}}\\ & =& \frac{\$2,160,000-\$1,728,000}{\$2,160,000}\\ & =& 0.20\\ & & \\ \mathrm{Break}-\mathrm{even}\mathrm{point}\mathrm{in}\mathrm{dollars}& =& \frac{\mathrm{Fixed}\mathrm{cost}}{\mathrm{Contribution}\mathrm{margin}\mathrm{ratio}}\\ & =& \frac{\$324,000}{0.20}\\ & =& \$1,620,000\end{array}$