a product sells for $200.00 p/unit and its variable cost p/unit are $130 the fixed cost are $420,000. if the firm wants to earn $35,000 pretax income, how many units must be sold?
To calculate the number of units that must be sold to earn a pretax income of $35,000, we first need to determine the contribution margin per unit. The contribution margin is the price per unit minus the variable cost per unit.
Contribution Margin per Unit = Selling Price per Unit - Variable Cost per Unit
Contribution Margin per Unit = $200.00 - $130.00
Contribution Margin per Unit = $70.00
Next, we can calculate the number of units needed to cover the fixed costs and earn the desired pretax income. The formula to calculate the required number of units is:
(Number of Units × Contribution Margin per Unit) - Fixed Costs = Pretax Income
Let's substitute the known values:
(Number of Units × $70.00) - $420,000 = $35,000
Simplifying the equation:
(Number of Units × $70.00) = $35,000 + $420,000
(Number of Units × $70.00) = $455,000
Now, divide both sides of the equation by $70.00 to solve for the number of units:
Number of Units = $455,000 ÷ $70.00
Number of Units ≈ 6,500
Therefore, approximately 6,500 units must be sold to earn a pretax income of $35,000.
To determine the number of units that must be sold in order to earn a specific pretax income, we need to understand the concept of contribution margin.
The contribution margin is the difference between the selling price and the variable cost per unit. It represents the amount that contributes towards covering fixed costs and generating profit. In this case, the contribution margin is calculated as follows:
Contribution Margin per Unit = Selling Price per Unit - Variable Cost per Unit
Contribution Margin per Unit = $200 - $130 = $70
To calculate the number of units that must be sold, we can use the following formula:
Number of Units Sold = (Fixed Costs + Target Pretax Income) / Contribution Margin per Unit
Given that the fixed costs are $420,000 and the target pretax income is $35,000, we can substitute these values into the formula:
Number of Units Sold = ($420,000 + $35,000) / $70
Number of Units Sold = $455,000 / $70
Number of Units Sold ≈ 6,500
Therefore, approximately 6,500 units must be sold in order to earn a pretax income of $35,000.