Question

Dusty Rhodes Associates sells only one product, with a current selling price of $70 per unit. Variable costs are 30% of this selling price, and fixed costs are $12,000 per month. Dusty has decided to reduce the selling price to $65 per unit in an effort to increase sales. Assume that the cost of the product and fixed operating expenses are not changed by this reduction in selling price.

At the current selling price of $70 per unit, what dollar volume of sales per month is required for Accents to earn a monthly operating income of $30,000?
A. $42,000.
B. $45,000.
C. $60,000.
D. Some other amount.

Answer 1

To earn a monthly operating income of $30,000 with a selling price of $70 per unit, variable costs at 30% of the selling price, and fixed costs of $12,000, Dusty Rhodes Associates needs a dollar volume of sales per month equal to $60,000.

Step-by-step explanation:

To determine the dollar volume of sales per month required for Dusty Rhodes Associates to earn a monthly operating income of $30,000 with a selling price of $70 per unit, variable costs amounting to 30% of the selling price, and fixed costs of $12,000 per month, we will use the contribution margin approach.

The contribution margin per unit is the selling price minus the variable cost per unit. In this case, the variable cost per unit is 30% of $70, which equals $21. Therefore, the contribution margin per unit is $70 - $21 = $49.

To cover the fixed costs and earn the desired income, the total contribution margin needed is fixed costs plus target profit, which is $12,000 + $30,000 = $42,000. To find the required sales volume, we divide the total contribution margin needed by the contribution margin per unit. Required sales volume = $42,000 / $49 = approximately 857.14 units. To turn this into the dollar volume, we multiply the number of units by the selling price per unit: 857.14 units * $70 = $60,000.

Answer 2

Dusty Rhodes Associates needs a sales volume of $60,000 per month at a selling price of $70 per unit to earn a monthly operating income of $30,000.

Step-by-step explanation:

To calculate the sales volume required for Dusty Rhodes Associates to earn a monthly operating income of $30,000 at the current selling price of $70 per unit, we need to use the contribution margin approach. The variable costs are 30% of the selling price, which amounts to $21 per unit ($70 * 30%). The contribution margin per unit, therefore, is $70 - $21 = $49 per unit. The fixed costs remain at $12,000 per month. To find the number of units needed to achieve the target income, divide the sum of the target income and fixed costs by the contribution margin per unit: ($30,000 + $12,000) ∗ $49 = 857.14 units.

To find the required sales volume, multiply the number of units by the selling price: 857.14 units * $70 = $60,000. Hence, Dusty Rhodes Associates requires a sales volume of $60,000 per month to meet its target operating income of $30,000 at the current selling price of $70 per unit.