market a new product for 2.00 a unit. fixed costs to manufacture this product are 100,000. the contribution margin is 40 percent. how many units must be sold to realize net income of 100,00 from this product?
To determine the number of units that must be sold to achieve a net income of $100,000, we will use the contribution margin ratio. The contribution margin ratio is the percentage of each unit's selling price that contributes to covering fixed costs and generating profit.
First, let's calculate the contribution margin per unit:
Contribution margin per unit = Selling price per unit × Contribution margin ratio
Contribution margin per unit = $2.00 × 40% = $0.80
Then, we can calculate the total contribution margin:
Total contribution margin = Contribution margin per unit × Number of units sold
Since we want the net income to be $100,000, we need to subtract this amount from the total contribution margin to determine the total fixed costs:
Total fixed costs = Total contribution margin − Net income
Finally, we can calculate the number of units required to achieve the desired net income:
Number of units sold = Total fixed costs / Contribution margin per unit
Let's put the numbers into these formulas:
Contribution margin per unit = $0.80
Net income = $100,000
Fixed costs = $100,000
Total contribution margin = Contribution margin per unit × Number of units sold
Total fixed costs = Total contribution margin − Net income
Number of units sold = Total fixed costs / Contribution margin per unit
Using substitution method:
Total contribution margin = $0.80 × Number of units sold
Total fixed costs = $0.80 × Number of units sold − $100,000
Number of units sold = $100,000 / $0.80
Therefore, the number of units that must be sold to realize a net income of $100,000 from this product is:
Number of units sold = $100,000 / $0.80 = 125,000 units