Question

Raile Gear Works sells a single gear for a price of $55.00 per unit. The variable costs of the gear are $23.00 per gear and annual fixed costs are $448,000.

Required:
What is the break-even level of annual sales for Braile Gear Works?

Answer 1

To find the break-even level of annual sales for Raile Gear Works, divide the annual fixed costs ($448,000) by the contribution margin per unit ($55 - $23), resulting in 14,000 units. This is the number of units that need to be sold annually to cover all costs without making a profit or incurring a loss.

Step-by-step explanation:

To calculate the break-even level of annual sales for Raile Gear Works, we need to consider both the fixed and variable costs and the selling price per unit. The break-even point is where the total revenue equals the total costs, meaning no profit or loss is incurred.

We start by understanding that the variable cost per gear is $23.00, and the gear is sold for $55.00. The fixed costs annually are $448,000.

The formula to calculate the break-even point in units is:

Break-even point (units) = Fixed Costs / (Selling Price per Unit - Variable Cost per Unit)

This gives us:

Break-even point (units) = $448,000 / ($55 - $23)

Break-even point (units) = $448,000 / $32

Break-even point (units) = 14,000 units

So, Raile Gear Works needs to sell 14,000 gears annually to break even.