During the past year a company had total fixed costs of $700,000. Its product sold for $93 per unit. Variable costs during this time equaled $45 per unit. Next year the company is anticipating a 10% increase in total fixed costs and a $3 per unit decrease in variable costs, but would like to maintain its current selling price per unit. How many units must the company sell next year to earn $1,000,000? (Round answer to complete units.)

Question

Quizplus · Accepted Answer

First, we need to find the contribution margin per unit:

Contribution Margin = Selling Price - Variable Cost
Contribution Margin = $93 - $45
Contribution Margin = $48 per unit

To earn $1,000,000, the company needs to have a profit of $1,000,000.

Profit = Revenue - Total Cost
Profit = (Selling Price x Quantity) - (Variable Cost x Quantity) - Total Fixed Cost

Since we want to maintain the selling price per unit, we need to solve for the quantity:

Profit = (Selling Price x Quantity) - (Variable Cost x Quantity) - Total Fixed Cost
$1,000,000 = ($93 x Q) - ($42 x Q) - $770,000 (total fixed cost + 10% increase in total fixed cost)
$1,000,000 = $51 x Q - $770,000
$1,770,000 = $51 x Q
Q = 34,706 units (rounded up to the nearest whole unit)

Therefore, the company needs to sell 34,706 units next year to earn $1,000,000. The best choice is B.

During the Past Year a Company Had Total Fixed Costs