Final answer:
To calculate the new operating income after an increase in units sold, we find the per-unit variable cost and per-unit contribution margin, then use these values to determine the new total variable costs and contribution margin. Subtracting the fixed costs from the new total contribution margin gives us the new operating income, which is $21,280.
Step-by-step explanation:
To determine the new operating income if the student's business sold 9,230 units instead of 8,855 units, we must first calculate the variable cost per unit and the contribution margin per unit based on the information provided. We are given that sales are $80,000, variable costs are $50,000, and the contribution margin is $30,000 for 8,855 units sold.
First, we calculate the variable cost per unit:
Variable Cost per Unit = Total Variable Costs / Number of Units = $50,000 / 8,855 = $5.6477 (rounded to four decimal places)
Second, we calculate the contribution margin per unit:
Contribution Margin per Unit = Total Contribution Margin / Number of Units = $30,000 / 8,855 = $3.3883 (rounded to four decimal places)
Using these unit costs, we can now calculate the new operating income for 9,230 units:
- New Total Variable Costs = Variable Cost per Unit * New Quantity = $5.6477 * 9,230 = $52,128 (rounded to the nearest dollar)
- New Total Contribution Margin = Contribution Margin per Unit * New Quantity = $3.3883 * 9,230 = $31,280 (rounded to the nearest dollar)
Finally, the new operating income is calculated by subtracting the fixed costs from the new total contribution margin:
New Operating Income = New Total Contribution Margin - Fixed Costs = $31,280 - $10,000 = $21,280 (rounded to the nearest dollar)
Therefore, the new operating income would be $21,280.