Asked by Esmeralda Pimentel on May 19, 2024
Verified
Johnson Plumbing's fixed costs are $700,000 and the unit contribution margin is $17. What amount of units (rounded to a whole number) must be sold in order to realize an operating income of $100,000?
A) 5,000
B) 41,176
C) 47,059
D) 58,882
Unit Contribution Margin
The difference between the selling price per unit and the variable cost per unit, showing how much each unit contributes to covering fixed costs and earning profit.
Operating Income
The profit earned from a firm's normal core business operations, excluding deductions of interest and taxes.
Fixed Costs
Expenses that do not change in proportion to the volume of goods or services a company produces.
- Facilitate a cost-volume-profit (CVP) analysis and pinpoint the break-even point.
- Calculate the required sales volume to achieve a specified operating income.
Verified Answer
Contribution margin per unit = Selling price - Variable costs per unit
In this case, we are not given the selling price or the variable costs per unit, but we are given the unit contribution margin, which is $17.
Next, we can use the formula to calculate the break-even point in units:
Break-even point (in units) = Fixed costs / Contribution margin per unit
Substituting the given values:
Break-even point = $700,000 / $17 = 41,176 units (rounded to the nearest whole number)
To calculate the units needed to achieve an operating income of $100,000, we can use the formula:
Operating income = (Unit contribution margin x Units sold) - Fixed costs
Substituting the given values:
$100,000 = ($17 x Units sold) - $700,000
$800,000 = $17 x Units sold
Units sold = $800,000 / $17 = 47,058.82 (rounded to the nearest whole number)
Therefore, the best choice is (C) 47,059 units.
Learning Objectives
- Facilitate a cost-volume-profit (CVP) analysis and pinpoint the break-even point.
- Calculate the required sales volume to achieve a specified operating income.
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