Final answer:
To earn a post-tax income of $35,000 with a 30% tax rate, the firm must first calculate the required pre-tax income and the total profit needed. After calculating the contribution margin per unit, the firm must sell 5,875 units to reach the desired post-tax income.
Step-by-step explanation:
Calculating Required Unit Sales to Achieve Desired Profit
To determine how many units must be sold to earn a post-tax income of $35,000 given a tax rate of 30%, we must first calculate the pre-tax income needed. To find the pre-tax income, we divide the desired post-tax income by (1 - tax rate), which is $35,000 / (1 - 0.30) = $50,000. Next, we calculate the total profit required by adding the fixed costs to the pre-tax income needed, which is $50,000 + $420,000 = $470,000.
We then calculate the contribution margin per unit by subtracting the variable costs per unit from the selling price per unit. The contribution margin per unit is $210 - $130 = $80. To find the number of units needed to be sold, we divide the total profit required by the contribution margin per unit which is $470,000 / $80 = 5875 units. Therefore, the firm must sell 5,875 units to achieve the desired post-tax income.