To find the company's breakeven point, we need to determine the number of units it must sell for its income to equal its costs. Here's how we calculate the breakeven point in units:
1. Fixed Costs: These are costs that do not change with the level of production or sales, such as rent, salaries, and insurance. In this case, the fixed costs are [tex]$500,000.
2. Variable Costs per Unit: These are costs that vary directly with the level of production, such as direct materials and direct labor. We are given that the variable cost per unit is $[/tex]3.00.
3. Sales Price per Unit: This is the price at which the product is sold. We're told that the sales price per unit is [tex]$5.20.
Now, let's perform the calculation.
Breakeven Point Calculation:
The breakeven point occurs when total revenue equals total costs (i.e., total fixed costs plus total variable costs). The formula for the breakeven point in units is:
Breakeven Units = Fixed Costs / (Sales Price per Unit - Variable Cost per Unit)
Let's plug in our numbers:
Breakeven Units = $[/tex]500,000 / ([tex]$5.20 - $[/tex]3.00)
First, we calculate the contribution margin per unit, which is the sales price minus the variable cost per unit:
Contribution Margin per Unit = [tex]$5.20 - $[/tex]3.00 = [tex]$2.20
Now we divide the fixed costs by the contribution margin per unit to find the breakeven point:
Breakeven Units = $[/tex]500,000 / $2.20 ≈ 227,272.73 units
Since it's not possible to sell a fraction of a unit, and the company needs to cover all its costs, we need to round up to the next whole unit:
Breakeven Units ≈ 227,273 units
The breakeven point for the company is therefore 227,273 units. Looking at the options provided in the question (A: 500,000 units, B: 600,000 units, C: 700,000 units, D: 800,000 units), none of these correspond exactly to the calculated breakeven point. However, since multiple choice questions typically require picking the closest correct answer, and all of the options are much higher than our calculated value, there seems to be some degree of mistake in the provided options. Please double-check the options to ensure that the correct one is selected.
