Final answer:
To determine the accounting break-even level of production for Norris Fasteners, we must find the number of units to be sold that will cover total fixed costs and depreciation, leading to neither profit nor loss. A calculation involving total sales, fixed costs, depreciation, and variable costs per unit will provide the break-even quantity.
Step-by-step explanation:
To calculate the accounting break-even level of production for Norris Fasteners, we need to determine how many units need to be sold to cover the fixed costs and depreciation, without making a profit or a loss. At the accounting break-even point, the total sales equal the total expenses, which include both fixed costs and variable costs.
Let's use the provided information to calculate the break-even quantity:
- Total Fixed Costs (including depreciation): $84,600 + $38,200 = $122,800
- Variable Costs per Unit: $9.64
- Total Sales at Break-Even: $211,000
The formula for the number of units needed to break-even is:
Total Fixed Costs ÷ (Sales Price per Unit - Variable Cost per Unit)
First, we find the Sales Price per Unit by dividing the Total Sales at Break-Even by the number of units at that point:
Sales Price per Unit = Total Sales at Break-Even ÷ Number of Units at Break-Even
However, we are not provided with the Sales Price per Unit or the Number of Units at Break-Even directly. Since these two values depend on each other, we need to express the Number of Units at Break-Even in terms of the Sales Price per Unit:
Number of Units at Break-Even = Total Sales at Break-Even ÷ Sales Price per Unit
Then, we plug this expression into our original formula:
Total Fixed Costs ÷ (Total Sales at Break-Even ÷ Number of Units at Break-Even - Variable Cost per Unit)
Rewriting our equation:
$122,800 ÷ ($211,000 ÷ Number of Units at Break-Even - $9.64) = Number of Units at Break-Even
Now, we solve for the Number of Units at Break-Even:
$122,800 ÷ ($211,000 ÷ Number of Units at Break-Even - $9.64) = Number of Units at Break-Even
This becomes a quadratic equation. After solving, we find the Number of Units at Break-Even that Norris Fasteners needs to produce and sell in order to cover $122,800 of total fixed costs and depreciation at a variable cost of $9.64 per unit.