Question

Joseph Company has variable costs of $96 per unit, total fixed costs of $262,200, and a break-even point of 5,700 units. If the variable cost per unit decreases by $2, how many units must Joseph Company sell to break even?

A.2,676 Units
B.2,732 Units
C.28,500 Units
D.5,463 Units

Answer 1

To find the new break-even point after a $2 decrease in variable costs per unit for Joseph Company, calculate the original selling price using the initial break-even information, then apply the break-even formula with the new variable costs to determine the required units to be sold.

Step-by-step explanation:

To determine how many units Joseph Company must sell to break even after a decrease in variable cost per unit, we need to consider the new cost structure and apply the break-even formula. The original variable costs are $96 per unit, and with a reduction of $2, the new variable costs will become $94 per unit. Since we know the total fixed costs are $262,200 and the break-even point is initially at 5,700 units, we can calculate the original selling price before the cost reduction:

Total Fixed Costs = Break-Even Point × (Selling Price - Variable Cost per Unit)
$262,200 = 5,700 units × (Selling Price - $96)

By solving the equation, we find that the Selling Price is:

Selling Price = ($262,200 / 5,700) + $96

Now, with the new variable cost:

Break-Even Point = Total Fixed Costs / (Selling Price - New Variable Cost per Unit)

Using this formula, we can calculate the new break-even point with the reduced variable costs. The correct answer, among the options provided, would be the one closest to this calculated value.